Create Foldcraft Game

Let me analyze the task:

1. I need to create a brand new game that hasn't been done before
2. It should be useful to the audience
3. I should do some research if needed but not too much
4. The game must work properly

The last game was "Resonance" - a wave interference puzzle game. I need to make something completely different.

Let me think about what kind of game to create. Let me first check what games already exist in the arcade to avoid repetition.

Let me install the shell tools and space skills tools to get started.

Let me see the full list and also check the index to understand what games exist.

Let me look at the descriptions in the index to understand what each game is about.

Now I have a good understanding of the existing games. Let me think about what kind of game to create that would be:

1. Unique - not done before
2. Useful to the audience
3. Interesting and engaging

Looking at the existing games, I see a wide variety: puzzle, arcade, strategy, educational, physics, typing, logic, etc.

Let me think about what's missing and what would be interesting and useful:

Some ideas:

1. A music theory/ear training game - learn to identify intervals, chords, scales by ear
2. A color theory game - learn about color mixing, complementary colors, etc.
3. A constellation/astronomy game - already have constellation-cartographer
4. A chemistry/molecule building game - already have alchemy-lab
5. A rhythm game - already have beat-drop
6. A language learning game - could be interesting
7. A data visualization/algorithm visualization game - like sorting algorithm visualizer
8. A fractal explorer - interactive fractal generation
9. A perspective/optical illusion game - like impossible geometry
10. A music sequencer/beat maker - creative tool
11. A typography game - learn about fonts, kerning, etc.
12. A photography/composition game
13. A navigation/orienteering game - using compass, map reading
14. A weather simulation game
15. A genetics/breeding game - already have dna-sequencer
16. A calendar/time management game
17. A knot tying game - already have knot-free
18. A lockpicking game - already have safecracker
19. A origami/folding game
20. A perspective drawing game
21. A sign language learning game
22. A braille learning game
23. A semaphore/flag signaling game
24. A music interval training game
25. A perspective/3D rotation game - mental rotation
26. A pattern recognition / IQ test style game
27. A memory palace game
28. A speed reading game
29. A coin flipping / probability game
30. A geocaching / treasure hunt game

Let me think about what would be genuinely useful and educational, and also fun and unique...

I think a Music Ear Training game would be great - it's educational, useful, and I don't see anything like it in the existing collection. But wait, let me check if there's something similar... There's "harmony-grid" and "beat-drop" and "resonance" which are music-related. But none of them are specifically about ear training (identifying intervals, chords, etc. by ear).

Actually, let me think of something more unique. How about a Perspective Drawing / Optical Illusion game? Or a Mental Rotation / Spatial Reasoning game?

Actually, let me think about what's truly novel and useful...

How about a Calibration / Color Vision game? Or a Reflex / Reaction Time game? There's already "reaction-chain"...

Let me think about a Tangram - already have tangram-quest.

How about a Nonogram/Picross - already have picross-quest.

How about a Sokoban - already have box-pusher.

Let me think more creatively...

Idea: "Foldcraft" - An Origami/Paper Folding Puzzle Game

• Players fold virtual paper to match target shapes
• Uses CSS 3D transforms for the folding animation
• Educational - teaches origami basics
• Unique mechanic - no other game does this

Idea: "Perspect" - A Perspective/Illusion Puzzle Game

• Players rotate 3D objects to match 2D silhouettes
• Mental rotation training
• Uses CSS 3D or canvas

Idea: "Glyph" - A Hieroglyph/Symbol Decoding Game

• Learn ancient writing systems
• Decode messages using symbol substitution

Idea: "Tessera" - A Tessellation/Mosaic Puzzle Game

• Fill a shape with tiles that tessellate
• Learn about geometric tessellations
• Escher-inspired

Idea: "Caliper" - A Measurement/Estimation Game

• Estimate distances, angles, areas
• Learn about measurement and estimation skills

Idea: "Cartograph" - A Map Reading/Navigation Game

• Navigate using compass bearings, contour lines, scale
• Learn orienteering skills

Idea: "Spectra" - A Spectrum/Light Game

• Learn about the electromagnetic spectrum
• Match wavelengths to colors/applications

Actually, I think a really interesting and useful game would be a Mental Rotation / Spatial Reasoning Trainer. This is a cognitive skill that's useful in many fields (engineering, architecture, surgery, etc.) and there's nothing like it in the arcade.

But let me think of something even more creative...

Idea: "Foldcraft" - Origami Puzzle Game This is genuinely unique - I haven't seen any origami/paper folding game in the collection. It would be:

• Educational (teaches origami)
• Visually interesting (paper folding animations)
• Mechanically unique (folding mechanic)
• Useful (spatial reasoning, following instructions)

But implementing realistic paper folding in a browser is quite complex...

Let me think of something more feasible but still unique...

Idea: "Tessera" - Tessellation Puzzle Players fit geometric shapes together to tile a plane without gaps. This is:

• Educational (geometry, tessellations)
• Visually appealing (mosaic/tile aesthetic)
• Mechanically interesting (drag and drop tiles)
• Unique in the collection

Actually, let me think about what would be most engaging and useful...

Idea: "Chroma Lab" - Color Theory and Mixing Game Wait, there's already "chroma-shift" and "color-clash"...

Idea: "Interval" - Music Ear Training Game Players listen to two notes and identify the interval between them (unison, minor 2nd, major 2nd, etc.). This is:

• Educational (music theory)
• Useful (ear training is a fundamental skill for musicians)
• Uses Web Audio API
• Unique in the collection (no ear training game exists)

Actually, I think this is a great idea. Let me go with a music ear training game. But let me make it more interesting than just "listen and identify" - let me add:

• Multiple modes: Intervals, Chords, Scales, Melodic dictation
• Progressive difficulty
• Visual feedback (piano keyboard, note names)
• Scoring and progress tracking
• Beautiful UI

Wait, but I want to make sure this is distinct from "harmony-grid" and "beat-drop". Let me check what those are about.

Actually, I don't need to check - the key difference is that those are puzzle/action games that happen to use music, while an ear training game is specifically about developing the skill of recognizing musical elements by ear. It's fundamentally different.

But actually, let me think of something even more unique and creative...

Idea: "Foldcraft" - Paper Folding Puzzle Actually, I could implement a simplified version of paper folding using CSS transforms. The player would see a flat piece of paper and a target shape, and they'd need to fold it step by step to match the target. Each fold would be a crease line that they draw, and the paper folds along that line.

This is complex but doable with a simplified model...

Actually, let me think about feasibility. I need to make a game that works well and is polished. Let me pick something that's:

1. Unique
2. Feasible to implement well
3. Educational/useful
4. Visually interesting

Idea: "Tessera" - Tessellation/Mosaic Puzzle This is very feasible:

• Grid-based puzzle where you place geometric tiles
• Tiles must fit together without gaps
• Different tile shapes (triangles, squares, hexagons, etc.)
• Target patterns to match
• Beautiful mosaic aesthetic

Actually, let me think about this more carefully. A tessellation puzzle where you fill a shape with tiles... this is similar to tangram but with repeating patterns.

Hmm, let me think of something else...

Idea: "Perspect" - 3D Mental Rotation Puzzle

• Show a 3D object made of cubes
• Show several 2D silhouettes from different angles
• Player must rotate the object to match the target silhouette
• Uses CSS 3D transforms or canvas isometric rendering
• Educational (spatial reasoning)
• Unique

This is interesting but might be complex to implement well...

Idea: "Glyph" - Ancient Script Decoder

• Learn to read ancient writing systems (hieroglyphs, cuneiform, runes)
• Decode messages by matching symbols to meanings
• Multiple writing systems
• Educational (linguistics, history)
• Unique

This is feasible and educational. But might be a bit dry...

Idea: "Caliper" - Estimation Game

• Estimate angles, distances, areas, volumes
• Multiple challenge types
• Learn about measurement and estimation
• Educational
• Unique

This is feasible and useful. But might be a bit simple...

Let me go with something that's both unique and has depth. Let me think about what would be really engaging...

Idea: "Foldcraft" - Origami Simulator/Puzzle Actually, I just realized I could make a simplified but compelling origami game. Instead of full 3D paper folding, I could:

• Show a piece of paper as a 2D shape
• Player selects fold lines (edges or creases)
• The paper "folds" along that line (one side flips over)
• Goal: transform the paper into a target shape
• Multiple levels with increasing complexity
• Beautiful paper texture aesthetic

This is actually very doable! The key insight is that paper folding in 2D is essentially: take one part of the shape, reflect it across a fold line. This is a well-defined geometric operation.

Let me go with this! "Foldcraft" - an origami/paper folding puzzle game.

Actually wait, let me reconsider. The folding mechanic in 2D is:

1. You have a polygon (the paper)
2. You draw a fold line (a line segment)
3. One side of the paper folds over the other
4. The folded part is reflected across the fold line
5. The new shape is the union of the unfolded part and the reflected folded part

This is computationally feasible with polygon operations. But implementing polygon clipping/union in vanilla JS is non-trivial...

Let me think of a simpler approach. What if instead of arbitrary fold lines, the paper is on a grid and folds happen along grid lines? This would simplify the math significantly.

Actually, let me think about this differently. What if I use a pixel/grid-based approach instead of polygon-based?

Grid-based paper folding:

• Paper is a grid of cells (e.g., 8x8)
• Each cell has a color/pattern
• Player selects a fold line (horizontal or vertical, along grid lines)
• One side folds over - the cells stack on top of the other side
• The visible result is the top layer
• Goal: match a target pattern

This is much more feasible! And it's actually a known puzzle type (folding puzzles). Let me go with this approach.

Actually, this is a really interesting puzzle mechanic. Let me think about it more:

1. Start with a grid (e.g., 6x6) with colored cells
2. The target is a smaller grid (e.g., 3x3) with specific colors
3. Player folds along grid lines (horizontal or vertical)
4. When folding, cells stack - the top cell's color is what shows
5. Goal: fold the paper down to the target size with the target colors

This is a great puzzle! It's:

• Unique (no folding puzzle in the collection)
• Educational (spatial reasoning, geometry)
• Visually interesting (paper folding animation)
• Mechanically deep (multiple folds create complex puzzles)
• Feasible to implement

Let me go with this! I'll call it "Foldcraft" or maybe "Crease" or "Origami Puzzle"...

Actually, let me think about the name. "Foldcraft" is good. "Crease" is also good. "Paper Fold" is descriptive. Let me go with "Foldcraft".

Wait, actually, I want to make sure the folding mechanic is clear and the game is fun. Let me think about the design more carefully:

Game Design: Foldcraft

Core Mechanic:

• Paper is represented as a grid of cells
• Each cell has a color
• Player can fold along any horizontal or vertical grid line
• When folding, the smaller side folds over the larger side
• Cells stack - the folded side's cells go on top
• The visible color is the topmost cell's color
• If both cells have the same color, it stays that color
• If they differ, the top (folded) cell's color shows

Wait, actually in real paper folding, when you fold, the paper doesn't become transparent - you see the top layer. So if cell A is on top of cell B, you see cell A's color (or pattern).

But there's a subtlety: when you fold, the paper that was on the bottom might have its back side showing. In real origami, paper often has two different colors (front/back). This could be an interesting mechanic!

Let me simplify: each cell has a front color and a back color. When you fold, the folded part flips over, so its back color shows on top.

Actually, this is getting complex. Let me simplify further for the first version:

Simplified Design:

• Paper is a grid of colored cells
• Each cell has one color
• When you fold along a line, the cells from the folded side are placed on top of the cells on the other side
• The top cell's color is what you see
• Goal: match the target pattern (which is a smaller grid)

This is clean and simple. Let me implement this.

Actually, I realize there's an important detail: when you fold, the folded part is mirrored. So if I fold the right half over the left half, the rightmost column goes on top of the leftmost column, the second-rightmost on the second-leftmost, etc.

Let me think about the data structure:

• Paper is a 2D array of colors
• When folding vertically along column k (folding right over left):
  • For each row, column k+1 goes on top of column k, k+2 on k-1, etc.
  • The paper width becomes k+1 (or however wide the larger side is)
  • Each cell now has a stack of colors (the bottom original + the folded ones on top)
  • The visible color is the top of the stack

Actually, I need to track the stack of colors at each position, not just the top color, because future folds will interact with the stack.

Hmm, but actually, for the puzzle to work, I think I only need to track the visible (top) color. When you fold again, the visible colors are what get stacked.

Wait, no. Let me think again. If I have:

• Position (0,0): red on bottom, blue on top (visible: blue)
• I fold so that (0,0) goes on top of (0,1)
• (0,1) has: green on bottom, yellow on top (visible: yellow)
• After folding: (0,1) has green, yellow, red, blue in the stack (bottom to top)
• Visible: blue

So I do need to track the full stack. But for the puzzle, the target only specifies the visible colors. So I need to track stacks internally but only show the top.

Actually, for simplicity, I could just track the visible color at each position. When folding:

• The folded side's visible colors are placed on top of the other side's visible colors
• The new visible color at each position is the folded side's color (since it's on top)

Wait, that's not right either. If I fold the right side over the left:

• Left position (r, c) had visible color X
• Right position (r, W-1-c) had visible color Y (mirrored)
• After fold: position (r, c) has visible color Y (since Y is on top)

But what if I then fold again? The Y colors are what get moved. So tracking just the visible color is sufficient!

Let me verify:

1. Grid: [A B C D] (1D for simplicity)
2. Fold along line between B and C (fold right over left):
   • D goes on top of A, C goes on top of B
   • New grid: [D C] (visible: D at pos 0, C at pos 1)
3. Fold along line between the two (fold right over left):
   • C goes on top of D
   • New grid: [C] (visible: C)

Yes! Just tracking the visible color works. When you fold, the folded side's visible colors become the new visible colors on top of the other side.

But wait, what about the back side? In real paper folding, when you fold, the back of the paper shows. If the paper is single-colored on both sides, this doesn't matter. But if the paper has different front/back colors, it does.

For simplicity, let me make the paper single-colored on both sides (or same color front and back). This simplifies the mechanic: when you fold, the folded part's visible color is what shows on top.

Actually, I think for a more interesting puzzle, I should have the paper be multi-colored (different cells have different colors), and the front and back are the same color. This way, the puzzle is about figuring out the right sequence of folds to get the right colors in the right positions.

Let me design some levels:

Level 1: 4x1 grid [R B B R], fold to 2x1 [R R]

• Fold along the middle: R goes on B, R goes on B → [R R] ✓

Level 2: 4x1 grid [R B R B], fold to 2x1 [B B]

• Fold along the middle: R goes on R, B goes on B → [R B] ✗
• Fold right edge to left: B goes on R, R goes on B → [B R]... hmm
• Actually, let me think about this differently.

Wait, I need to be more careful about the folding direction. When I say "fold along line between columns 1 and 2", I need to specify which side folds over.

Let me define: when folding, the player clicks on a fold line, and the smaller side folds over the larger side. If both sides are equal, the player can choose (or we default to right folds over left / bottom folds over top).

Actually, for a better UX, let me have the player click on a line and then choose the direction, or just have the smaller side always fold over the larger side.

Hmm, let me think about this differently. In many folding puzzle games, you can fold any edge inward. So you'd click on an edge and drag it to a fold line, and that section folds over.

For simplicity, let me have the player click on a fold line (between two rows or columns), and the side that's smaller (or the right/bottom side if equal) folds over.

Let me redesign:

Foldcraft - Paper Folding Puzzle

Mechanics:

• Paper is a W×H grid of colored cells
• Player clicks on a fold line (between rows or columns)
• The smaller side folds over the larger side (if equal, right/bottom folds over left/top)
• After folding, the paper size reduces
• The folded cells' colors appear on top
• Goal: reduce the paper to the target size with the target colors

Visual:

• Paper has a slight 3D look (shadow, gradient)
• Fold animation (CSS transform)
• Beautiful color palette
• Target shown alongside

Levels:

• Start with simple 4x1 → 2x1
• Progress to 4x4 → 2x2
• More complex color patterns

This is a solid design! Let me implement it.

Actually, wait. I want to make sure the folding mechanic is correct. Let me think through a more complex example:

Grid (2D):

Fold along vertical line between columns 1 and 2 (columns 2,3 fold over columns 1,0):

• Column 3 (Y, R, G, B) goes on top of column 0 (R, G, B, Y) → visible: Y, R, G, B
• Column 2 (B, Y, R, G) goes on top of column 1 (G, B, Y, R) → visible: B, Y, R, G

New grid (2x4):

Then fold along horizontal line between rows 1 and 2 (rows 2,3 fold over rows 1,0):

• Row 3 (B, G) goes on top of row 0 (Y, B) → visible: B, G
• Row 2 (G, R) goes on top of row 1 (R, Y) → visible: G, R

New grid (2x2):

This works! The mechanic is clean and the puzzles can be quite challenging.

Now let me think about the visual design. I want this to look beautiful and unique. Let me go with:

• A warm, paper-craft aesthetic
• Soft shadows, paper texture
• Muted but rich color palette
• Smooth fold animations
• Maybe a slight isometric perspective for depth

For the fold animation, I can use CSS 3D transforms. The paper would be a div with transform-style: preserve-3d, and folding would rotate one half around the fold line.

Actually, implementing a smooth 3D fold animation with CSS transforms on a grid of cells is complex. Let me think about whether to do a full 3D animation or a simpler 2D animation.

For a simpler approach: when the player clicks a fold line, the cells animate sliding over (2D), and then the grid updates. This is less impressive visually but much simpler to implement.

For a more impressive approach: use CSS 3D transforms to create a real folding animation. The paper is a 3D plane, and folding rotates one section around the fold axis.

I think I'll go with a CSS 3D approach for the wow factor, but keep it manageable. Let me think about how to implement this...

Actually, the CSS 3D approach for a grid of cells is quite complex because each cell needs to be positioned in 3D space and the fold needs to rotate a group of cells. This would require careful transform management.

Let me go with a hybrid approach:

• The paper is rendered as a flat grid (2D)
• When folding, I'll animate the folded section sliding over with a slight 3D perspective effect
• After the animation, the grid updates to the new state

This gives a nice visual effect without the complexity of full 3D transforms.

Actually, you know what, let me just go with a clean 2D approach with smooth transitions. The puzzle mechanic itself is interesting enough, and I can make it look beautiful with good design.

Let me plan the implementation:

1. HTML structure: Canvas or DOM-based grid
2. Game state: Current grid (2D array of colors), target grid, move count, level
3. Folding logic: Click on fold line → compute new grid
4. Visual: Beautiful paper-craft aesthetic, smooth animations
5. Levels: Progressive difficulty
6. UI: Level selector, move counter, reset button, hint system

I'll use DOM-based rendering for the grid (divs for cells) since it makes animations and interactions easier.

Let me also think about what makes this game "useful to the audience":

• Spatial reasoning development
• Geometric thinking
• Problem-solving skills
• Planning and strategy (figuring out fold sequences)
• It's a brain training puzzle

OK, let me start implementing. I'll create the game at /space/games/foldcraft/index.html.

Let me think about the color palette and visual design:

• Background: warm cream/paper color (#f5f0e8 or similar)
• Paper: white with subtle texture
• Cell colors: rich but muted palette (not too saturated)
• UI: clean, modern, with paper-craft feel
• Font: a nice serif or rounded sans-serif

Actually, let me go with a more modern, polished look:

• Dark background with a subtle gradient
• Paper cells with vibrant but harmonious colors
• Smooth animations
• Glassmorphism UI elements

Hmm, but the paper-craft aesthetic would be more unique. Let me go with that.

Let me think about the color palette for the cells:

• Red: #e74c3c
• Blue: #3498db
• Green: #2ecc71
• Yellow: #f1c40f
• Purple: #9b59b6
• Orange: #e67e22
• Cyan: #1abc9c
• Pink: #e84393

These are vibrant but not too saturated. Good for a puzzle game.

Now let me think about the level design. I need levels that are:

1. Easy to start with (teach the mechanic)
2. Gradually more complex
3. Solvable (I need to verify solutions)
4. Interesting (multiple approaches, not just one obvious path)

For level generation, I can work backwards: start with the target, then "unfold" to create the starting grid. This ensures the puzzle is solvable.

Unfolding: take a grid and expand it by adding a mirrored copy of one row/column. The added cells' colors can be anything (they'll be hidden when folded back).

Actually, for generating puzzles, I can:

1. Start with a small target grid (e.g., 2x2)
2. "Unfold" it several times to create a larger starting grid
3. The starting grid will have the target colors in the right positions, plus extra cells with random colors

This guarantees solvability! The player just needs to figure out the right fold sequence.

Let me design 10-12 levels with increasing complexity.

OK, I think I have a solid plan. Let me start coding!

Actually, let me reconsider the visual approach. Instead of DOM divs, let me use Canvas for rendering. This gives me more control over the visual effects (shadows, gradients, textures) and is more performant.

But Canvas makes animations and click detection harder. Let me use a hybrid: Canvas for the paper rendering, DOM for the UI.

Actually, for a grid-based puzzle, DOM is perfectly fine and makes everything easier (CSS animations, click handling, etc.). Let me go with DOM.

Let me also think about the fold animation. When the player clicks a fold line:

1. The folded section animates: it slides over the other section with a slight rotation/scale effect
2. After the animation, the grid updates to the new state
3. A subtle "settle" animation plays

For the fold line visualization:

• Show fold lines when hovering over the paper
• Fold lines appear between rows and columns
• Click to fold

Let me also add:

• Undo button (undo last fold)
• Reset button (restart current level)
• Move counter
• Star rating (based on move count vs optimal)
• Level progression
• Persistent progress (localStorage)

OK, I'm going to start implementing now. Let me write the complete game.

Let me think about the structure of the code:

Let me think about the fold logic more carefully:

Vertical fold (folding along a vertical line between columns):

• line is the column index where the fold happens (fold between column line-1 and line)
• If folding right over left: columns line to W-1 fold over columns line-1 to 0
  • Column line goes on top of column line-1
  • Column line+1 goes on top of column line-2
  • etc.
  • New width: max(line, W-line)
  • For position (r, c) in new grid: if c < W-line, the folded color is from column line + (W-line-1-c) = W-1-c... wait, let me think again.

Actually, let me be more precise. Say the grid is W columns wide. I fold along the line between column k-1 and column k (so k is the first column of the right side).

If the right side (columns k to W-1) folds over the left side (columns 0 to k-1):

• The right side has W-k columns
• The left side has k columns
• If W-k <= k (right side is smaller or equal):
  • Column k goes on top of column k-1
  • Column k+1 goes on top of column k-2
  • ...
  • Column W-1 goes on top of column k-(W-k) = 2k-W
  • New width: k
  • For each row r:
    • For c from 0 to k-1:
      • If c >= 2k-W (i.e., c is in the overlap zone):
        • new_grid[r][c] = grid[r][k + (k-1-c)] = grid[r][2k-1-c] (the folded color goes on top)
      • Else:
        • new_grid[r][c] = grid[r][c] (unchanged, no overlap)

Wait, I need to think about this more carefully. When the right side folds over the left:

• The rightmost column (W-1) folds onto the leftmost column in the overlap zone
• Actually no. When you fold paper, the fold line is the crease. The right side flips over, so:
  • Column k (adjacent to fold line) goes on top of column k-1 (also adjacent to fold line)
  • Column k+1 goes on top of column k-2
  • etc.

So for the overlap zone (columns 2k-W to k-1 in the left side):

• Column k+i goes on top of column k-1-i (for i = 0, 1, ..., W-k-1)
• So new_grid[r][k-1-i] = grid[r][k+i] (the folded color is on top)

For columns 0 to 2k-W-1 (no overlap, left side only):

• new_grid[r][c] = grid[r][c]

New width: k

Let me verify with an example: Grid: [A B C D] (W=4), fold between B and C (k=2) Right side: C D (columns 2,3), width 2 Left side: A B (columns 0,1), width 2 Overlap: both sides have width 2, so all of left side is overlapped

• Column 2 (C) goes on top of column 1 (B) → new[1] = C
• Column 3 (D) goes on top of column 0 (A) → new[0] = D New grid: [D C] ✓

Another example: Grid: [A B C D E] (W=5), fold between C and D (k=3) Right side: D E (columns 3,4), width 2 Left side: A B C (columns 0,1,2), width 3 Overlap: columns 1,2 are overlapped (2k-W = 6-5 = 1, so columns 1 to 2)

• Column 3 (D) goes on top of column 2 (C) → new[2] = D
• Column 4 (E) goes on top of column 1 (B) → new[1] = E
• Column 0 (A) is not overlapped → new[0] = A New grid: [A E D] ✓

Great, the logic works!

Now for the case where the left side is smaller and folds over the right: Grid: [A B C D E] (W=5), fold between B and C (k=2) Left side: A B (columns 0,1), width 2 Right side: C D E (columns 2,3,4), width 3 If left folds over right:

• Column 1 (B) goes on top of column 2 (C) → new[0] = B (in new grid, position 0 corresponds to old column 2)
• Column 0 (A) goes on top of column 3 (D) → new[1] = A
• Column 4 (E) is not overlapped → new[2] = E New grid: [B A E] ✓

Wait, I need to be more careful. When the left side folds over the right:

• The fold line is between column k-1 and k
• Left side: columns 0 to k-1, width k
• Right side: columns k to W-1, width W-k
• If k <= W-k (left side is smaller or equal):
  • Column k-1 goes on top of column k
  • Column k-2 goes on top of column k+1
  • ...
  • Column 0 goes on top of column k+(k-1) = 2k-1
  • New width: W-k
  • For each row r:
    • For c from 0 to W-k-1:
      • If c < k (in overlap zone, i.e., c <= 2k-1-k = k-1... wait, let me think again)

Hmm, this is getting confusing. Let me think about it differently.

When left folds over right:

• The new grid starts at column k (the right side)
• Column k-1 (left, adjacent to fold) goes on top of column k (right, adjacent to fold)
• Column k-2 goes on top of column k+1
• ...
• Column 0 goes on top of column 2k-1
• Columns 2k to W-1 are not overlapped

New width: W-k For position c in new grid (corresponding to column k+c in old grid):

• If k+c < 2k (i.e., c < k, in overlap zone):
  • new[r][c] = grid[r][k-1-c] (the folded left side color is on top)
• Else:
  • new[r][c] = grid[r][k+c] (unchanged)

Let me verify: Grid: [A B C D E] (W=5), fold between B and C (k=2) Left side: A B (width 2), right side: C D E (width 3) Left folds over right:

• c=0: k+c=2, c<k (0<2) → new[0] = grid[2-1-0] = grid[1] = B
• c=1: k+c=3, c<k (1<2) → new[1] = grid[2-1-1] = grid[0] = A
• c=2: k+c=4, c<k? 2<2? No → new[2] = grid[4] = E New grid: [B A E] ✓

Now for horizontal folds, it's the same logic but with rows instead of columns.

OK, I have the fold logic figured out. Let me also think about the fold direction selection. When the player clicks on a fold line:

• If one side is strictly smaller, that side folds over (no choice needed)
• If both sides are equal, the player needs to choose which side folds over

For the UX, I can:

• Show two arrows on each fold line (one for each direction)
• Or default to one direction and let the player use shift-click for the other

I think showing two arrows is cleaner. When the player hovers over a fold line, show arrows indicating which way the paper will fold.

Actually, for simplicity, let me just have the smaller side always fold over. If both sides are equal, default to right/bottom folding over left/top. This simplifies the UX significantly.

But wait, this might make some puzzles unsolvable if the player needs to fold the larger side over the smaller side. Hmm, actually in real paper folding, you can fold either way. But for the puzzle, I think it's fine to always fold the smaller side over.

Actually, no. Consider this: if the grid is 4x4 and I want to fold along the middle, both sides are 2 wide. I should be able to choose which way to fold. This is important for puzzle complexity.

Let me add direction selection. When the player clicks on a fold line, show two options (fold left or fold right for vertical, fold top or fold bottom for horizontal). Or, I can have the player click on the side they want to fold.

Actually, the simplest UX: the player clicks on a cell on the side they want to fold. So if they want to fold the right side over the left, they click on a cell on the right side. But this is ambiguous if they click on a cell near the middle.

Let me go with: show fold lines as clickable lines between rows/columns. When the player hovers over a fold line, show a preview of which way it will fold (with an arrow). Click to confirm. If both sides are equal, show two arrows and the player clicks the one they want.

Actually, let me simplify even further. I'll show fold lines as gaps between rows/columns. When the player clicks a fold line, the smaller side folds over. If equal, I'll show a brief choice (two buttons or arrows). This keeps the UX clean.

Hmm, let me think about this differently. What if I just let the player click on any fold line, and the fold always goes in one direction (e.g., right/bottom over left/top)? Then for puzzles that need the other direction, the player would need to rotate the paper first... but I don't want to add rotation.

OK, let me just implement both directions. When the player clicks on a fold line:

• If one side is smaller, that side folds over automatically
• If both sides are equal, show two arrows and let the player choose

This is the cleanest approach. Let me implement it.

Actually, for even simpler UX: I'll show fold lines as clickable buttons/areas. Each fold line has a direction indicator. The player clicks to fold. If both directions are possible, I'll show two separate clickable areas.

Let me just start coding and figure out the UX as I go. The core logic is solid.

Let me also think about the visual style more. I want this to be unique and beautiful. Here's my vision:

Visual Design:

• Background: deep navy/charcoal with subtle paper texture
• Paper: warm off-white with subtle shadow
• Cell colors: vibrant but harmonious (jewel tones)
• Fold lines: dashed lines that glow on hover
• UI: clean, modern, with glassmorphism panels
• Typography: a nice geometric sans-serif
• Animations: smooth, paper-like folding transitions

Actually, let me go with a lighter, warmer aesthetic to match the paper theme:

• Background: warm gradient (cream to light tan)
• Paper: pure white with soft shadow
• Cell colors: rich, saturated colors
• UI: clean white cards with soft shadows
• Fold animations: smooth 3D-like transitions

Hmm, but most games in the arcade seem to have dark themes. Let me check...

Actually, let me just go with what looks best for this game. A paper-craft game should have a warm, light aesthetic. Let me do:

• Background: warm cream/paper color with subtle texture
• Paper: white with soft drop shadow
• Cells: vibrant colors
• UI: clean, minimal, with paper-like cards

Actually, you know what, let me do a dark theme but with warm accents. This will make the colorful cells pop more:

• Background: dark charcoal (#1a1a2e) with subtle gradient
• Paper: off-white (#f5f0e8) with soft shadow
• Cells: vibrant jewel-tone colors
• UI: dark glassmorphism panels with warm accent colors
• Fold lines: glowing dashed lines

This will look striking and modern. Let me go with this.

OK, let me start writing the code now. I'll create a complete, self-contained HTML file.

Let me plan the levels:

Level 1: 1x4 → 1x2 Start: [R B B R] Target: [R R] Solution: Fold in half (right over left) → [R R]

Level 2: 1x4 → 1x2 Start: [R G B Y] Target: [Y R] Solution: Fold right over left → [Y R]

Level 3: 2x4 → 2x2 Start: R G B Y Y B G R Target: Y R R Y Solution: Fold right over left

Level 4: 1x6 → 1x3 Start: [R G B Y B G] Target: [G G B] Solution: Fold right 3 over left 3 → [Y B G]... hmm, that gives [Y B G] not [G G B]

Let me work backwards from targets to create solvable levels.

For Level 4: Target: [G G B] (1x3) Unfold: add a mirrored copy to the right → [G G B B G G] (1x6) But the extra cells can be any color, so: [G G B R Y G] (1x6) Fold right 3 over left 3: [G Y R]... no, that's not right.

Wait, when I unfold, the added cells go on top when folded back. So: Target: [G G B] Unfold to the right: the right side (columns 3-5) folds over the left side (columns 0-2)

• Column 3 goes on top of column 2 → target[2] = B, so column 3 can be anything (it's on top, so column 3's color = B)
• Wait, no. When folding right over left, column 3 goes on top of column 2. So the visible color at position 2 is column 3's color. For the target to be B at position 2, column 3 must be B.
• Column 4 goes on top of column 1 → target[1] = G, so column 4 must be G
• Column 5 goes on top of column 0 → target[0] = G, so column 5 must be G

So the start grid is: [G G B B G G] (columns 0-5) And folding right over left gives: [G G B] ✓

But this is too obvious - the player can see the pattern. Let me add some randomness to the non-overlapping cells... but in this case, all cells overlap.

Let me make it more complex. Two folds:

Target: [G B] (1x2) Unfold 1: add mirrored right side → [G B B G] (1x4) Unfold 2: add mirrored right side → [G B B G G B B G] (1x8) But I can randomize the "hidden" cells... wait, in this case all cells are determined by the target.

Hmm, the issue is that when unfolding, the added cells' colors are determined by the target (since they go on top). So the start grid is fully determined by the target and the unfold sequence.

But I can make it less obvious by:

1. Using more colors
2. Having the pattern not be symmetric
3. Having multiple valid fold sequences

Actually, the key insight is that the start grid IS the target unfolded, so the colors in the start grid directly encode the target. The puzzle is figuring out WHICH folds to make and in WHAT ORDER.

For example: Start: [R G B Y] (1x4) Possible folds:

• Fold in half (right over left): [Y R]
• Fold in half (left over right): [G B]... wait, let me check
  • Left side (R G) folds over right side (B Y)
  • Column 1 (G) goes on top of column 2 (B) → new[0] = G
  • Column 0 (R) goes on top of column 3 (Y) → new[1] = R
  • New grid: [G R]

So from [R G B Y], folding right over left gives [Y R], and folding left over right gives [G R].

If the target is [Y R], the player needs to fold right over left. If the target is [G R], the player needs to fold left over right.

This is a simple but clear puzzle. The player needs to figure out the right direction.

For more complex puzzles, I can have grids where the player needs to make multiple folds in a specific order, and the intermediate states matter.

Let me design levels with increasing complexity:

Level 1: 1x4 → 1x2, 1 fold Level 2: 1x4 → 1x2, 1 fold (different direction) Level 3: 2x4 → 2x2, 1 fold Level 4: 1x6 → 1x3, 1 fold Level 5: 1x8 → 1x2, 2 folds Level 6: 2x4 → 2x2, 2 folds (one horizontal, one vertical) Level 7: 3x6 → 3x2, 2 folds Level 8: 4x4 → 2x2, 2 folds Level 9: 4x8 → 2x2, 3+ folds Level 10: 4x8 → 2x2, complex

Let me generate these levels by working backwards.

Actually, let me just write a level generator in the code that creates levels by unfolding targets. This way I don't have to manually design each level.

But for the first few levels, I want to hand-design them to teach the mechanic clearly. Then I can use generated levels for later stages.

Let me just code the whole thing now. I'll include both hand-designed and generated levels.

Let me think about the code structure:

Wait, I need to be careful about the axis naming. Let me define:

• A "vertical fold" means folding along a vertical line, which means the left/right sides fold
• A "horizontal fold" means folding along a horizontal line, which means the top/bottom sides fold

Let me use clearer naming:

• foldVertical(grid, col, direction): fold along the vertical line between columns col-1 and col. direction is 'right' (right side folds over left) or 'left' (left side folds over right)
• foldHorizontal(grid, row, direction): fold along the horizontal line between rows row-1 and row. direction is 'bottom' (bottom side folds over top) or 'top' (top side folds over bottom)

OK let me just write the code. I'll figure out the details as I go.

Let me also think about the rendering. I'll use DOM elements for the grid:

• A container div for the paper
• Each cell is a div with background color
• Fold lines are clickable divs between rows/columns
• CSS transitions for smooth animations

For the fold animation, I'll:

1. Clone the folded section
2. Animate it sliding over (with a slight perspective transform)
3. After animation, update the grid and re-render

Actually, for a cleaner approach, let me use CSS Grid for the paper layout and add fold line elements between cells.

Hmm, this is getting complex. Let me simplify the animation: when a fold happens, I'll just fade out the old grid and fade in the new grid with a slight scale/translate transition. This is simpler and still looks good.

Or even simpler: just update the grid instantly with a brief flash/highlight effect on the changed cells. The puzzle mechanic is the star, not the animation.

Actually, let me do a nice fold animation. Here's my plan:

1. When the player clicks a fold line, identify the folded section
2. Create a clone of the folded section as an overlay
3. Animate the overlay: translate it to the target position with a 3D rotation effect
4. After animation, update the grid state and re-render

This is doable with CSS transforms and transitions. Let me implement it.

Actually, I think I'm overcomplicating this. Let me just write the game with a simple but clean visual style and smooth transitions. The puzzle mechanic is interesting enough on its own.

Let me start writing the code now. I'll create a complete, self-contained HTML file with all the game logic.

Here's my plan for the code:

1. HTML structure: header, game area (paper + target), controls, level info
2. CSS: paper-craft aesthetic, dark background, vibrant cells, smooth transitions
3. JavaScript: game state, fold logic, rendering, input handling, level management, persistence

Let me write it all in one go.

Actually, I realize I should think more carefully about the fold animation. Let me do a CSS-based approach:

When a fold happens:

1. The paper grid is rendered as a CSS grid of cell divs
2. When folding, I add a class to the folded cells that triggers a CSS animation
3. The animation translates and rotates the folded cells over the target cells
4. After the animation, I update the grid and re-render

For the 3D effect, I can use transform: perspective(800px) rotateX/Y(90deg) on the folded cells, combined with translate.

But this is tricky because the cells need to rotate around the fold line, not their own center. I'd need to set transform-origin appropriately.

Let me try a simpler approach: just slide the folded section over with a slight scale and opacity transition. No 3D rotation. This is much simpler and still looks decent.

OK, I'm going to start writing the code now. Let me create the file.

Actually, one more thing: I want to make sure the game is genuinely fun and challenging. Let me think about what makes folding puzzles interesting:

1. Spatial reasoning: Visualizing how the paper will look after folding
2. Planning: Figuring out the right sequence of folds
3. Direction choice: Deciding which way to fold
4. Order matters: The same folds in different orders give different results

These are all captured in my design. Good.

Let me also add some quality-of-life features:

• Preview: When hovering over a fold line, show a preview of the result
• Undo: Undo the last fold
• Reset: Reset to the starting position
• Hint: Show the next optimal fold
• Stars: Rate performance based on move count

OK, let me write the code now. I'll aim for a polished, complete game.

Let me think about the level design more carefully. I'll generate levels by working backwards from targets.

For generating a level:

1. Start with a target grid (e.g., 2x2 with specific colors)
2. Choose a random unfold direction (add cells to the left/right/top/bottom)
3. The added cells' colors are determined by the target (they go on top when folded back)
4. Repeat 2-3 several times to create a larger starting grid
5. The number of unfolds = the optimal number of folds

But I also want to add some "noise" - cells that don't affect the result but make the puzzle less obvious. However, in folding, every cell in the folded section ends up on top of a target cell, so there's no "noise" possible. Every cell matters.

Wait, that's not true. If the folded section is smaller than the target section, some target cells are not overlapped. Those cells' colors in the start grid are the same as in the target. And the folded cells' colors are what will show on top.

But if I unfold symmetrically (equal sides), all cells are determined. If I unfold asymmetrically, some cells in the larger section are not overlapped and their colors are from the target.

Hmm, let me think about this differently. When I unfold:

• I have a grid of size W×H
• I unfold to size (W+w)×H by adding w columns to the right
• The added columns' colors are determined by the target (they'll fold on top)
• But the existing columns' colors might change if they were previously folded on top of

Actually, this is getting complicated. Let me just manually design the levels. It's more reliable.

Let me design 12 levels:

Level 1: "First Fold" Start: [R B B R] (1×4) Target: [R R] (1×2) Solution: Fold right over left → [R R] Optimal: 1 move

Level 2: "Other Way" Start: [R G B Y] (1×4) Target: [G R] (1×2) Solution: Fold left over right → [G R] Optimal: 1 move

Level 3: "Double Up" Start: R B B R G Y Y G Target: R R G G Solution: Fold right over left Optimal: 1 move

Level 4: "Triple Threat" Start: [R G B B G R] (1×6) Target: [R G B] (1×3) Solution: Fold right 3 over left 3 → [R G B] Optimal: 1 move

Level 5: "Two Steps" Start: [R G B Y R G] (1×6) Target: [G R] (1×2) Solution:

• Fold right 3 over left 3 → [G R B]... wait, let me compute
  • Column 3 (Y) on top of column 2 (B) → new[2] = Y
  • Column 4 (R) on top of column 1 (G) → new[1] = R
  • Column 5 (G) on top of column 0 (R) → new[0] = G
  • Result: [G R Y]
• Then fold right 1 over left 2 → [G R]... wait, can I fold 1 column over 2?
  • Fold between column 1 and 2, right side (Y, 1 col) over left side (G R, 2 cols)
  • Column 2 (Y) on top of column 1 (R) → new[1] = Y
  • Column 0 (G) unchanged → new[0] = G
  • Result: [G Y]... that's not [G R]

Hmm, let me try a different approach. Let me work backwards from the target.

Target: [G R] (1×2) Unfold 1: Add 2 columns to the right (right side folds over left)

• Column 2 goes on top of column 1 → target[1] = R, so column 2 = R
• Column 3 goes on top of column 0 → target[0] = G, so column 3 = G
• New grid: [G R R G] (1×4)

Unfold 2: Add 2 more columns to the right

• Column 4 goes on top of column 3 → column 4 = G (since column 3 will show G after this unfold is reversed) Wait, I need to think about this more carefully. After unfold 2, the grid is [G R R G X X] where X are the new columns. When we fold right 2 over left 4... no, that doesn't work because the right side (2 cols) is smaller.

Actually, let me reconsider. When I unfold, I'm adding cells that will fold on top. The key is that the added cells' colors must match the target cells they'll land on.

Let me redo this: Target: [G R] (1×2) Unfold 1 (add 2 cols to right, right folds over left):

• New grid: [G R R G] (1×4)
• When folding right 2 over left 2: col 2 (R) on col 1 (R), col 3 (G) on col 0 (G) → [G R] ✓

Unfold 2 (add 2 cols to right, right folds over left):

• Current grid: [G R R G]
• New grid: [G R R G G R] (1×6)
• When folding right 2 over left 4: col 4 (G) on col 3 (G), col 5 (R) on col 2 (R) → [G R R G]... wait, that's not right.

Hmm, when folding right 2 over left 4:

• Left side: columns 0-3 (G R R G), width 4
• Right side: columns 4-5 (G R), width 2
• Column 4 (G) goes on top of column 3 (G) → new[3] = G
• Column 5 (R) goes on top of column 2 (R) → new[2] = R
• Columns 0-1 unchanged: G R
• Result: [G R R G] (1×4)

Then fold right 2 over left 2: [G R] ✓

So the start grid is [G R R G G R] (1×6) and the solution is:

1. Fold right 2 over left 4 → [G R R G]
2. Fold right 2 over left 2 → [G R]

But wait, the start grid [G R R G G R] has an obvious pattern. Let me make it less obvious by unfolding in different directions.

Unfold 2 (add 2 cols to LEFT, left folds over right):

• Current grid: [G R R G]
• Left side: new columns, right side: G R R G
• Column -1 (new) goes on top of column 0 (G) → new col -1 = G
• Column -2 (new) goes on top of column 1 (R) → new col -2 = R
• New grid: [R G G R R G] (1×6)
• When folding left 2 over right 4: col 0 (R) on col 2 (G), col 1 (G) on col 3 (R) → [G R R G]... wait

Let me recompute. Grid: [R G G R R G] (1×6) Fold left 2 over right 4 (fold between col 1 and 2, left side folds over right):

• Left side: columns 0-1 (R G), width 2
• Right side: columns 2-5 (G R R G), width 4
• Column 1 (G) goes on top of column 2 (G) → new[0] = G
• Column 0 (R) goes on top of column 3 (R) → new[1] = R
• Columns 4-5 unchanged: R G
• Result: [G R R G] (1×4) ✓

Then fold right 2 over left 2: [G R] ✓

So start: [R G G R R G] (1×6), target: [G R] (1×2), 2 folds.

This is less obvious. Good.

But actually, I realize I should also add some variety with 2D grids (multiple rows). Let me design some 2D levels too.

OK, I think I have enough understanding. Let me just write the code with a mix of hand-designed and generated levels. I'll include a level generator that creates levels by unfolding targets, and I'll also include some hand-designed tutorial levels.

Let me write the complete game now. I'll aim for:

• 12 levels
• Beautiful paper-craft visual style
• Smooth fold animations
• Undo, reset, hint features
• Star ratings
• Persistent progress
• Responsive design

Here's my code plan:

Let me write the full code now. I'll make it comprehensive and polished.

Actually, let me reconsider the visual approach one more time. I want to use a technique that's different from previous games. Let me check what rendering techniques have been used...

Looking at the game list, there's a wide variety. Let me use a unique visual approach for this game:

• SVG-based rendering for the paper and cells (crisp, scalable, easy animations)
• CSS 3D transforms for the fold animation
• DOM-based UI for controls and info

Using SVG for the paper grid is interesting because:

• SVG shapes can be easily animated with CSS
• SVG filters can add paper texture effects
• SVG is crisp at any resolution
• It's a different technique from canvas-based games

Actually, let me use a hybrid: DOM divs for the grid (easier for click handling) with CSS for styling and animations. This is the most practical approach.

For the fold animation, I'll use CSS transforms:

• When folding, the folded section gets a transform that slides it over the target section
• A slight rotateX or rotateY gives a 3D paper-folding feel
• transform-origin is set to the fold line

Let me implement this now.

OK here's my final plan. Let me write the complete game. I'll make it really polished with:

1. Beautiful dark theme with warm paper accents
2. DOM-based grid with CSS animations
3. 12 levels with progressive difficulty
4. Fold preview on hover
5. Undo/reset/hint
6. Star ratings
7. Persistent progress
8. Level select
9. Win animation
10. Responsive design

Let me write it all now.

Actually, I realize I should also think about the fold line interaction more carefully. Here's my plan:

• The paper grid is rendered as a CSS grid of cells
• Between each pair of adjacent rows/columns, there's a thin "fold line" gap
• When the player hovers over a fold line, it highlights and shows an arrow indicating the fold direction
• If both directions are possible (equal sides), show two arrows
• Click to fold

For the fold line rendering, I'll use absolutely positioned divs over the grid, positioned at each fold line location.

Actually, a simpler approach: I'll render the grid with gaps between cells, and the gaps are the fold lines. Clicking on a gap triggers a fold. I'll use CSS to highlight the gap on hover.

But with CSS grid, gaps are just empty space. I need clickable elements in the gaps. Let me use a different layout:

• The paper is a container with position: relative
• Cells are absolutely positioned divs
• Fold lines are absolutely positioned divs between cells
• This gives me full control over positioning and interaction

Actually, CSS grid with gap and clickable overlay elements is simpler. Let me use:

• CSS grid for the cells
• Absolutely positioned overlay divs for the fold lines (calculated based on cell size and gap)

Hmm, this is getting complicated. Let me just use a table-like layout or flexbox.

OK, I think the simplest approach is:

1. Render the grid as a 2D array of cell divs using CSS grid
2. Add fold line divs as overlays positioned between rows/columns
3. Calculate positions based on cell size

Let me just code it. I'll figure out the details as I go.

Let me write the complete game now. I'll create it as a single HTML file.

One more thing: I want to make sure the game is genuinely useful and educational. I'll add:

• A brief tutorial on the first level
• Tips about paper folding and spatial reasoning
• Encouraging messages

OK, let me write the code now. This is going to be a substantial file.

Let me think about the fold animation one more time. I want it to look like paper folding. Here's my approach:

When the player clicks a fold line (say, vertical fold, right side over left):

1. Identify the cells on the right side (the ones being folded)
2. Clone them as an overlay
3. Set transform-origin to the left edge of the overlay (the fold line)
4. Animate transform: rotateY(180deg) (or a similar 3D rotation)
5. As the overlay rotates, it visually "folds over" the left side
6. After the animation, remove the overlay and update the grid

For this to work, I need:

• perspective on the container
• transform-style: preserve-3d on the paper
• The overlay needs to be a mirror of the right side (since it flips over)

This is doable but requires careful CSS. Let me implement it.

Actually, rotateY(180deg) would make the overlay face backwards (mirrored). I need to account for this by pre-mirroring the content. Or I can use a different transform.

Hmm, let me think about this. When paper folds:

• The right side rotates around the fold line (left edge of right side)
• As it rotates 180°, it ends up on top of the left side, but mirrored
• The content that was on the front of the right side is now face-down
• The back of the right side is now face-up

For our game, since front and back are the same color, the visual effect is:

• The right side rotates and lands on the left side
• The colors are mirrored (rightmost column lands on leftmost column of the left side)

So the animation should:

1. Clone the right side
2. Set transform-origin to the left edge
3. Animate rotateY(0 → -180deg) (folding to the left)
4. The clone ends up mirrored on top of the left side
5. After animation, update the grid

The mirroring happens naturally with the 3D rotation. The content of the clone will be mirrored, which is correct because that's how paper folding works.

But wait, if the content is text or patterns, the mirroring would be visible during the animation. For solid colors, it doesn't matter. Since our cells are solid colors, this is fine.

Let me implement this. I'll use CSS transitions for the animation.

OK, I'm going to write the code now. Let me create the complete game file.

Let me also think about the level generator. I'll write a function that generates a level by:

1. Starting with a target grid
2. Unfolding it N times in random directions
3. Returning the start grid, target, and optimal moves

Wait, this isn't right. When I unfold to the right, I'm adding columns to the right that will fold over the left. The added columns' colors should be the same as the cells they'll land on.

When folding right over left (right side folds over left):

• Column k+i goes on top of column k-1-i
• So when unfolding, column k+i should have the same color as column k-1-i (the cell it lands on)

If I'm adding cols new columns to the right (doubling the width):

• New column 0 (old column cols) goes on top of old column cols-1
• New column 1 (old column cols+1) goes on top of old column cols-2
• ...
• New column cols-1 goes on top of old column 0

So: new_column[i] = old_column[cols-1-i]

This means the added columns are a mirror of the original columns. So unfolding to the right = appending the mirror of the grid.

Similarly:

• Unfold to the left = prepending the mirror
• Unfold to the bottom = appending the mirror of rows
• Unfold to the top = prepending the mirror of rows

But wait, this only works for symmetric unfolds (doubling). What about asymmetric unfolds?

If I unfold to the right by adding only w columns (where w < cols):

• New column 0 goes on top of old column cols-1
• New column 1 goes on top of old column cols-2
• ...
• New column w-1 goes on top of old column cols-w

So: new_column[i] = old_column[cols-1-i]

This is still a mirror, just of the first w columns from the right.

OK so unfolding is always appending/prepending a mirror. The number of added cells can be anything from 1 to the current size.

For generating interesting levels, I should:

1. Start with a small target (e.g., 2x2)
2. Unfold multiple times in random directions with random sizes
3. This creates a larger grid that requires multiple folds to solve

Let me implement this.

Actually, I realize there's a subtlety. When I unfold, the added cells' colors are determined by the current grid (not the target). So if I unfold multiple times, each unfold is based on the current state of the grid.

Let me trace through an example:

1. Start: [G R] (target)
2. Unfold right (add 2 cols): [G R R G] (mirror of [G R] is [R G], appended)
3. Unfold left (add 1 col): [R G R R G] (mirror of first 1 col from left is [R], prepended... wait)

Hmm, when unfolding to the left by adding 1 column:

• The new column (leftmost) will fold over the current leftmost column
• New column 0 goes on top of current column 0
• So new column 0 = current column 0 = G

Wait, that doesn't seem right. Let me think again.

When unfolding to the left by adding 1 column:

• I'm adding a column to the left that, when folded (left over right), will land on top of the current leftmost column
• Column -1 (new) goes on top of column 0 (current leftmost)
• So new column -1 = current column 0 = G

New grid: [G G R R G] (1×5)

When folding left 1 over right 4:

• Column 0 (G) goes on top of column 1 (G) → new[0] = G
• Columns 2-4 unchanged: R R G
• Wait, that's not right. Let me recompute.

Grid: [G G R R G] (1×5) Fold left 1 over right 4 (fold between col 0 and 1, left side folds over right):

• Left side: column 0 (G), width 1
• Right side: columns 1-4 (G R R G), width 4
• Column 0 (G) goes on top of column 1 (G) → new[0] = G
• Columns 2-4 unchanged: R R G
• Result: [G R R G] (1×4) ✓

Then fold right 2 over left 2: [G R] ✓

Great, so the unfold logic works. Let me implement it.

For the unfold function:

• unfoldRight(grid, w): add w columns to the right, where new_col[i] = grid_col[cols-1-i] for i = 0..w-1
• unfoldLeft(grid, w): add w columns to the left, where new_col[i] = grid_col[i] for i = 0..w-1 (the new leftmost column folds onto column 0, so it = column 0; the next new column folds onto column 1, so it = column 1; etc.)

Wait, let me re-derive unfoldLeft:

• Adding w columns to the left
• When folding left w over right (cols-w):
  • New column 0 (leftmost) goes on top of old column w (which is new column w in the new grid... hmm, this is confusing)

Let me use concrete indices. Original grid has columns 0 to C-1. I add w columns to the left, so new grid has columns 0 to C+w-1, where:

• New columns 0 to w-1 are the added ones
• New columns w to w+C-1 are the original columns 0 to C-1

When folding left w over right C:

• New column w-1 (rightmost of left side, adjacent to fold line) goes on top of new column w (leftmost of right side, = original column 0)
• New column w-2 goes on top of new column w+1 (= original column 1)
• ...
• New column 0 goes on top of new column w+w-1 (= original column w-1)

So: new_column[i] (for i = 0..w-1) = original_column[w-1-i]

This means the added left columns are a mirror of the first w original columns, reversed.

Wait, let me double-check:

• new_column[w-1] = original_column[0]
• new_column[w-2] = original_column[1]
• ...
• new_column[0] = original_column[w-1]

So new_column[i] = original_column[w-1-i] for i = 0..w-1

Yes, the added columns are the reverse of the first w original columns.

Similarly for unfoldRight:

• Adding w columns to the right
• New columns C to C+w-1 are added
• When folding right w over left C:
  • New column C (leftmost of right side, adjacent to fold line) goes on top of new column C-1 (= original column C-1)
  • New column C+1 goes on top of new column C-2 (= original column C-2)
  • ...
  • New column C+w-1 goes on top of new column C-w (= original column C-w)

So: new_column[C+i] = original_column[C-1-i] for i = 0..w-1

The added right columns are the reverse of the last w original columns.

For unfoldTop and unfoldBottom, it's the same but with rows.

OK, I have the unfold logic. Let me implement the level generator and the game.

Let me now write the complete code. I'll create a comprehensive, polished game.

Here's my final design:

Foldcraft - Paper Folding Puzzle

A spatial reasoning puzzle game where you fold colored paper to match target patterns. Features:

• 12 progressive levels
• Beautiful paper-craft visual style
• Smooth 3D fold animations
• Undo, reset, and hint systems
• Star ratings based on move efficiency
• Persistent progress via localStorage
• Level select screen
• Tutorial tips on early levels

Visual style:

• Dark background (#0f0f1e) with subtle gradient
• Paper cells in vibrant jewel-tone colors
• Warm accent colors (amber, gold)
• Glassmorphism UI panels
• Smooth CSS 3D transforms for fold animations

Let me write the code now.

I'll write it as a single HTML file with embedded CSS and JS. Let me make it comprehensive.

Actually, I realize I should think about the fold animation more carefully. The 3D fold animation with CSS transforms is the trickiest part. Let me plan it:

When the player clicks a fold line (e.g., vertical fold, right side over left):

1. Get the right side cells as a group
2. Create a clone of the right side as an absolutely positioned overlay
3. Position the clone at

Now I have a comprehensive view of all the games. Let me think about what unique game to create.

Looking at the existing games, I see a wide variety:

• Puzzle games: picross, sudoku, hashi, tangram, box-pusher, etc.
• Arcade games: snake, breakout, pinball, etc.
• Strategy games: mancala, tower defense, etc.
• Educational games: logic lab, quantum circuit, cipher master, etc.
• Physics games: gravity golf, magnetar, etc.
• Simulation games: powder lab, tide pool, reef keeper, etc.
• Creative games: pixel painter, pyrotechnia, inkflow, etc.
• Music games: beat drop, loop lab, resonance, etc.
• Card games: dungeon deck, aether spire, etc.
• Incremental games: cosmic forge, stock tycoon, etc.

I notice there's no paper folding puzzle game! "Paper Wings" is about flying a paper airplane, not folding. "Tangram Quest" is about arranging geometric pieces. Neither is about paper folding.

Let me create "Foldcraft" - a paper folding puzzle game where you fold a colored grid to match a target pattern. This is:

1. Unique - no folding puzzle exists in the collection
2. Educational - develops spatial reasoning and planning
3. Visually interesting - paper-craft aesthetic
4. Mechanically deep - multiple folds create complex puzzles

Let me implement this now. I'll create a polished, complete game.

Let me write the full HTML file. I'll make it comprehensive with:

• 12 levels with progressive difficulty
• Beautiful paper-craft visual style (dark theme with warm accents)
• Smooth fold animations using CSS 3D transforms
• Undo, reset, hint systems
• Star ratings
• Persistent progress
• Level select
• Tutorial tips

Let me write the code now.

The fold logic has bugs. Let me analyze the test results:

Test 1: [R B B R] → fold right over left → expected [R R] but got [R B]

• Grid: [0,1,1,0], fold at col=2, direction='right'
• leftW = 2, rightW = 2
• newCols = 2
• overlapStart = 2 - 2 = 0
• c=0: c >= 0 (overlap), srcCol = 2 + (2-1-0) = 2+1 = 3, grid[0][3] = 0 (R) ✓
• c=1: c >= 0 (overlap), srcCol = 2 + (2-1-1) = 2+0 = 2, grid[0][2] = 1 (B) ✗

Wait, the expected result is [R R] = [0,0]. But the fold gives [0,1] = [R B].

Let me think about this. The grid is [R B B R] (indices 0,1,2,3). Fold at col=2 (between index 1 and 2), right side folds over left.

• Right side: indices 2,3 (B,R)
• Left side: indices 0,1 (R,B)
• Column 2 (B) goes on top of column 1 (B) → visible: B
• Column 3 (R) goes on top of column 0 (R) → visible: R
• Result: [R, B] = [0, 1]

But the target is [R, R] = [0, 0]. So the level definition is wrong! The start grid [R B B R] doesn't fold to [R R].

Let me reconsider. When folding right over left:

• The right side is mirrored and placed on top of the left side
• Column 2 (B) lands on column 1 (B) → B
• Column 3 (R) lands on column 0 (R) → R
• Result: [R, B]

So to get [R, R], I need the right side to have R on both columns that land on the left side. That means:

• Column 2 must be R (lands on column 1)
• Column 3 must be R (lands on column 0)
• Start: [R, B, R, R] → fold right over left → [R, R] ✓

Wait, but that's not right either. Let me re-derive:

• Grid: [R, B, R, R] (indices 0,1,2,3)
• Fold at col=2, right over left
• Column 2 (R) goes on top of column 1 (B) → visible: R
• Column 3 (R) goes on top of column 0 (R) → visible: R
• Result: [R, R] ✓

OK so the start grid should be [R, B, R, R] = [0, 1, 0, 0] for the target [R, R] = [0, 0].

But wait, I designed the level as [R B B R] → [R R]. That's wrong. Let me fix the level definitions.

Actually, the issue is that I designed the levels incorrectly. The fold logic is correct — I just had wrong level data. Let me fix the levels by working backwards from the targets.

Let me re-derive all levels:

Level 1: Target [R R] = [0, 0] Unfold right (add 2 cols to right, right folds over left):

• New col 0 (index 2) lands on col 1 → must be R (0)
• New col 1 (index 3) lands on col 0 → must be R (0)
• Start: [R, R, R, R] = [0, 0, 0, 0]... that's boring.

Let me try a different unfold. Unfold right (add 2 cols):

• Col 2 lands on col 1 → col 2 = target[1] = 0
• Col 3 lands on col 0 → col 3 = target[0] = 0
• Start: [0, 0, 0, 0] — all same color, boring.

Let me try unfolding left (add 2 cols to left, left folds over right):

• New col 0 lands on old col 0 (which becomes col 2 in new grid) → new col 0 = target[0] = 0
• New col 1 lands on old col 1 (which becomes col 3 in new grid) → wait, this is confusing.

Let me think about this more carefully. When I unfold to the left by adding 2 columns:

• Original: [R, R] (cols 0, 1)
• New grid: [X, Y, R, R] (cols 0, 1, 2, 3) where X, Y are the added columns
• When folding left 2 over right 2:
  • Col 1 (Y) goes on top of col 2 (R) → visible: Y
  • Col 0 (X) goes on top of col 3 (R) → visible: X
  • Result: [X, Y]
• For target [R, R]: X = R, Y = R
• Start: [R, R, R, R] — still boring.

The problem is that for a 1×2 target with a single fold, the start grid is fully determined and will be symmetric/boring.

Let me make level 1 more interesting. Instead of [R R], let me use a target with different colors.

Level 1: Target [R B] = [0, 1] Unfold right (add 2 cols):

• Col 2 lands on col 1 → col 2 = target[1] = 1 (B)
• Col 3 lands on col 0 → col 3 = target[0] = 0 (R)
• Start: [R, B, B, R] = [0, 1, 1, 0]
• Fold right over left: col 2 (B) on col 1 (B) → B; col 3 (R) on col 0 (R) → R
• Result: [R, B] = [0, 1] ✓

Wait, that gives [R, B] not [R, R]. Let me re-check:

• Grid: [0, 1, 1, 0] (R, B, B, R)
• Fold at col=2, right over left
• Col 2 (1=B) goes on top of col 1 (1=B) → visible: B (1)
• Col 3 (0=R) goes on top of col 0 (0=R) → visible: R (0)
• Result: [R, B] = [0, 1]

So the target should be [R, B] = [0, 1], not [R, R] = [0, 0].

OK so my original level 1 had the wrong target. The start [R B B R] folds to [R B], not [R R].

Let me fix all the levels. I need to work backwards from targets to create correct start grids.

Let me write a proper level generator/tester:

For each level, I'll:

1. Define the target
2. Define the unfold sequence (directions and amounts)
3. Compute the start grid by unfolding
4. Verify that folding the start grid gives the target

Let me write this:

Wait, I need to be more careful. Let me re-derive the unfold functions.

Unfold right (add w columns to the right, which will fold right-over-left): When folding right w over left (cols-w):

• Col cols (first new col) goes on top of col cols-1 → new col 0 = old col[cols-1]
• Col cols+1 goes on top of col cols-2 → new col 1 = old col[cols-2]
• ...
• Col cols+w-1 goes on top of col cols-w → new col w-1 = old col[cols-w]

So: new_col[i] = old_col[cols-1-i] for i = 0..w-1

This means the added columns are the reverse of the last w columns of the original.

Unfold left (add w columns to the left, which will fold left-over-right): When folding left w over right (cols):

• Col w-1 (last new col, adjacent to fold) goes on top of col w (first old col) → new col w-1 = old col[0]
• Col w-2 goes on top of col w+1 → new col w-2 = old col[1]
• ...
• Col 0 goes on top of col w+w-1 → new col 0 = old col[w-1]

So: new_col[i] = old_col[w-1-i] for i = 0..w-1

The added columns are the reverse of the first w columns of the original.

Unfold bottom (add h rows to the bottom, which will fold bottom-over-top): Same as unfold right but for rows: new_row[i] = old_row[rows-1-i] for i = 0..h-1

Unfold top (add h rows to the top, which will fold top-over-bottom): Same as unfold left but for rows: new_row[i] = old_row[h-1-i] for i = 0..h-1

Let me verify with an example: Target: [R, B] = [0, 1] Unfold right by 2:

• new_col[0] = old_col[1] = 1 (B)
• new_col[1] = old_col[0] = 0 (R)
• Start: [0, 1, 1, 0] = [R, B, B, R]
• Fold right 2 over left 2: col 2 (B) on col 1 (B) → B; col 3 (R) on col 0 (R) → R
• Result: [R, B] = [0, 1] ✓

Now let me generate all levels properly. I'll write a script to generate and verify levels.

Actually, let me just fix the level definitions manually by computing the correct start grids from the targets.

Let me redesign the levels:

Level 1: "First Fold" — 1 fold Target: [R, B] = [[0, 1]] Unfold right by 2: start = [0, 1, 1, 0] = [[0, 1, 1, 0]] Solution: fold right over left → [0, 1] ✓

Level 2: "Other Way" — 1 fold, left over right Target: [G, R] = [[2, 0]] Unfold left by 2:

• new_col[0] = old_col[1] = 0 (R)
• new_col[1] = old_col[0] = 2 (G)
• Start: [0, 2, 2, 0] = [[0, 2, 2, 0]] Wait, that's the same pattern as level 1. Let me use different colors.

Target: [G, R] = [[2, 0]] Unfold left by 2:

• new_col[0] = old_col[1] = 0
• new_col[1] = old_col[0] = 2
• Start: [0, 2, 2, 0] = [[0, 2, 2, 0]] Hmm, same pattern. Let me use a different target.

Target: [B, Y] = [[1, 3]] Unfold left by 2:

• new_col[0] = old_col[1] = 3
• new_col[1] = old_col[0] = 1
• Start: [3, 1, 1, 3] = [[3, 1, 1, 3]] Fold left over right: col 1 (1) on col 2 (1) → 1; col 0 (3) on col 3 (3) → 3 Result: [1, 3] = [B, Y] ✓

Hmm, but this is the same pattern (symmetric). The issue is that with a single fold of equal sides, the start grid is always a palindrome.

Let me make it more interesting by using asymmetric folds.

Level 2: "Other Way" — 1 fold, left over right, asymmetric Target: [G, R, B] = [[2, 0, 1]] Unfold left by 1:

• new_col[0] = old_col[0] = 2
• Start: [2, 2, 0, 1] = [[2, 2, 0, 1]] Fold left 1 over right 3: col 0 (2) on col 1 (2) → 2; cols 2,3 unchanged Result: [2, 0, 1] = [G, R, B] ✓

This is better — asymmetric fold.

Actually, let me think about this differently. For the levels to be interesting, I should have:

1. Multiple colors
2. Non-obvious patterns
3. Multiple folds for later levels

Let me use a level generator approach. I'll write a function that:

1. Starts with a target
2. Unfolds it multiple times in random directions
3. Returns the start grid

Then I'll verify each level is solvable.

Let me write this as a script and generate the levels.

Actually, let me just manually create correct levels. I'll be very careful about the fold logic.

Key insight: when you fold right-over-left at column k:

• The right side (cols k to W-1) is mirrored and placed on top of the left side
• Column k goes on top of column k-1
• Column k+1 goes on top of column k-2
• ...
• Column W-1 goes on top of column k-(W-k) = 2k-W
• New width: k (the left side width)
• For position c in new grid:
  • If c >= 2k-W (overlap zone): new[c] = grid[k + (k-1-c)] = grid[2k-1-c]
  • Else: new[c] = grid[c] (unchanged)

Wait, let me re-derive more carefully.

Grid: [a0, a1, ..., a_{W-1}] Fold at column k (between a_{k-1} and a_k), right over left. Right side: [a_k, a_{k+1}, ..., a_{W-1}], width = W-k Left side: [a_0, a_1, ..., a_{k-1}], width = k

The right side folds over. When it lands:

• a_k lands on a_{k-1} (adjacent to fold line)
• a_{k+1} lands on a_{k-2}
• ...
• a_{W-1} lands on a_{k-(W-k)} = a_{2k-W}

So the overlap zone in the left side is columns 2k-W to k-1. For c in [2k-W, k-1]: new[c] = a_{k + (k-1-c)} = a_{2k-1-c} For c in [0, 2k-W-1]: new[c] = a_c (unchanged)

New width: k

Let me verify: Grid: [0, 1, 2, 3, 4, 5] (W=6), fold at k=4, right over left Right side: [4, 5], width 2 Left side: [0, 1, 2, 3], width 4 Overlap: columns 2k-W = 8-6 = 2 to 3

• c=2: new[2] = a_{2*4-1-2} = a_5 = 5
• c=3: new[3] = a_{2*4-1-3} = a_4 = 4
• c=0: new[0] = a_0 = 0 (unchanged)
• c=1: new[1] = a_1 = 1 (unchanged) Result: [0, 1, 5, 4]

Let me verify with the fold logic:

• a_4 lands on a_3 → new[3] = a_4 = 4 ✓
• a_5 lands on a_2 → new[2] = a_5 = 5 ✓
• a_0, a_1 unchanged ✓

Now let me check my foldVertical function:

Great, the fold logic is correct! The issue was with my level definitions, not the fold logic.

Now let me fix the levels. I need to work backwards from targets.

Level 1: Target [0, 1] (R, B) Unfold right by 2: start = [0, 1, 1, 0] Fold right over left at k=2:

• c=0: overlap (0 >= 0), srcCol = 2+(2-1-0) = 3, grid[3] = 0 → new[0] = 0 ✓
• c=1: overlap (1 >= 0), srcCol = 2+(2-1-1) = 2, grid[2] = 1 → new[1] = 1 ✓ Result: [0, 1] ✓

Level 2: Target [2, 0] (G, R) I want to fold left over right. Unfold left by 2:

• new_col[0] = old_col[1] = 0
• new_col[1] = old_col[0] = 2
• Start: [0, 2, 2, 0] Fold left over right at k=2:
• Left side: [0, 2], right side: [2, 0]
• Col 1 (2) lands on col 2 (2) → new[0] = 2
• Col 0 (0) lands on col 3 (0) → new[1] = 0 Result: [2, 0] ✓

But this is the same pattern as level 1 (palindrome). Let me use different colors to make it look different.

Actually, for level 2, let me use a different approach. Let me unfold left by 1: Target: [2, 0, 1] (G, R, B) Unfold left by 1:

• new_col[0] = old_col[0] = 2
• Start: [2, 2, 0, 1] Fold left 1 over right 3 at k=1:
• Left side: [2], right side: [2, 0, 1]
• Col 0 (2) lands on col 1 (2) → new[0] = 2
• Cols 2, 3 unchanged: 0, 1 Result: [2, 0, 1] ✓

This is better — asymmetric fold, different from level 1.

OK, let me systematically generate all 12 levels. I'll write a script to do this.

Let me write a level generator that:

1. Starts with a target
2. Unfolds it N times
3. Returns the start grid

Then I'll verify each level.

Let me write this script:

Wait, I need to verify these unfold functions. Let me check unfoldRight:

Unfold right by w: add w columns to the right. When folding right w over left (cols):

• Col cols (first new col) lands on col cols-1 → new col 0 = old col[cols-1]
• Col cols+1 lands on col cols-2 → new col 1 = old col[cols-2]
• ...
• Col cols+w-1 lands on col cols-w → new col w-1 = old col[cols-w]

So: new_col[i] = old_col[cols-1-i] for i = 0..w-1

In the unfoldRight function:

This pushes old_col[cols-1], old_col[cols-2], ..., old_col[cols-w]. So new_col[0] = old_col[cols-1], new_col[1] = old_col[cols-2], etc. This matches! ✓

Let me verify unfoldLeft: Unfold left by w: add w columns to the left. When folding left w over right (cols):

• Col w-1 (last new col, adjacent to fold) lands on col w (first old col) → new col w-1 = old col[0]
• Col w-2 lands on col w+1 → new col w-2 = old col[1]
• ...
• Col 0 lands on col w+w-1 → new col 0 = old col[w-1]

So: new_col[i] = old_col[w-1-i] for i = 0..w-1

In the unfoldLeft function:

This pushes old_col[w-1], old_col[w-2], ..., old_col[0]. So new_col[0] = old_col[w-1], new_col[1] = old_col[w-2], etc. This matches! ✓

Now let me verify unfoldBottom: Unfold bottom by h: add h rows to the bottom. When folding bottom h over top (rows):

• Row rows (first new row) lands on row rows-1 → new row 0 = old row[rows-1]
• Row rows+1 lands on row rows-2 → new row 1 = old row[rows-2]
• ...
• Row rows+h-1 lands on row rows-h → new row h-1 = old row[rows-h]

So: new_row[i] = old_row[rows-1-i] for i = 0..h-1

In unfoldBottom:

This pushes old_row[rows-1], old_row[rows-2], ..., old_row[rows-h]. So new_row[0] = old_row[rows-1], etc. ✓

And unfoldTop: Unfold top by h: add h rows to the top. When folding top h over bottom (rows):

• Row h-1 (last new row, adjacent to fold) lands on row h (first old row) → new row h-1 = old row[0]
• Row h-2 lands on row h+1 → new row h-2 = old row[1]
• ...
• Row 0 lands on row h+h-1 → new row 0 = old row[h-1]

So: new_row[i] = old_row[h-1-i] for i = 0..h-1

In unfoldTop:

This pushes old_row[h-1], old_row[h-2], ..., old_row[0]. So new_row[0] = old_row[h-1], etc. ✓

Great, all unfold functions are correct. Now let me generate levels.

Let me write a comprehensive test script that generates and verifies all levels:

Actually, let me just manually create the levels using the unfold functions, and then verify them with the fold functions. Let me write a script that does both.

Let me design 12 levels:

Level 1: "First Fold" — 1 fold, 1×4 → 1×2 Target: [[0, 1]] (R, B) Unfold: right by 2 Start: unfoldRight([[0,1]], 2) = [[0, 1, 1, 0]] Solution: fold V at 2, right → [[0, 1]]

Level 2: "Other Way" — 1 fold, 1×4 → 1×3 Target: [[2, 0, 1]] (G, R, B) Unfold: left by 1 Start: unfoldLeft([[2,0,1]], 1) = [[2, 2, 0, 1]] Solution: fold V at 1, left → [[2, 0, 1]]

Level 3: "Double Up" — 1 fold, 2×4 → 2×2 Target: [[0, 1], [2, 3]] (R,B / G,Y) Unfold: right by 2 Start: unfoldRight([[0,1],[2,3]], 2) = [[0,1,1,0],[2,3,3,2]] Solution: fold V at 2, right → [[0,1],[2,3]]

Level 4: "Triple Threat" — 1 fold, 1×6 → 1×3 Target: [[0, 2, 1]] (R, G, B) Unfold: right by 3 Start: unfoldRight([[0,2,1]], 3) = [[0, 2, 1, 1, 2, 0]] Solution: fold V at 3, right → [[0, 2, 1]]

Level 5: "Two Steps" — 2 folds, 1×6 → 1×2 Target: [[2, 0]] (G, R) Unfold 1: right by 2 → [[2, 0, 0, 2]] Unfold 2: right by 2 → [[2, 0, 0, 2, 2, 0, 0, 2]]... wait, that's 1×8.

Hmm, let me try: Target: [[2, 0]] Unfold 1: left by 1 → [[0, 2, 0]] (unfoldLeft by 1: new_col[0] = old_col[0] = 2... wait)

Let me re-check unfoldLeft: unfoldLeft([[2, 0]], 1):

• w = 1
• new_col[0] = old_col[1-1-0] = old_col[0] = 2
• Start: [2, 2, 0]

Fold left 1 over right 2 at k=1:

• Col 0 (2) lands on col 1 (2) → new[0] = 2
• Col 2 (0) unchanged → new[1] = 0 Result: [2, 0] ✓

Unfold 2: right by 2 → unfoldRight([[2, 2, 0]], 2)

• new_col[0] = old_col[2] = 0
• new_col[1] = old_col[1] = 2
• Start: [2, 2, 0, 0, 2]

Fold right 2 over left 3 at k=3:

• Right side: [0, 2], width 2
• Left side: [2, 2, 0], width 3
• Col 3 (0) lands on col 2 (0) → new[2] = 0
• Col 4 (2) lands on col 1 (2) → new[1] = 2
• Col 0 (2) unchanged → new[0] = 2 Result: [2, 2, 0]

Then fold left 1 over right 2 at k=1:

• Col 0 (2) lands on col 1 (2) → new[0] = 2
• Col 2 (0) unchanged → new[1] = 0 Result: [2, 0] ✓

So Level 5: start = [[2, 2, 0, 0, 2]], target = [[2, 0]], 2 folds.

But wait, the start is 1×5, not 1×6. Let me adjust.

Actually, let me try a different unfold sequence for a 1×6 start: Target: [[2, 0]] Unfold 1: right by 2 → [[2, 0, 0, 2]] Unfold 2: left by 2 → unfoldLeft([[2, 0, 0, 2]], 2)

• new_col[0] = old_col[1] = 0
• new_col[1] = old_col[0] = 2
• Start: [0, 2, 2, 0, 0, 2]

Fold left 2 over right 4 at k=2:

• Col 1 (2) lands on col 2 (2) → new[0] = 2
• Col 0 (0) lands on col 3 (0) → new[1] = 0
• Cols 4, 5 unchanged: 0, 2 Result: [2, 0, 0, 2]

Then fold right 2 over left 2 at k=2:

• Col 2 (0) lands on col 1 (0) → new[1] = 0
• Col 3 (2) lands on col 0 (2) → new[0] = 2 Result: [2, 0] ✓

So Level 5: start = [[0, 2, 2, 0, 0, 2]], target = [[2, 0]], 2 folds. This is 1×6. ✓

Level 6: "Cross Fold" — 2 folds, 4×4 → 2×2 Target: [[0, 1], [2, 3]] Unfold 1: right by 2 → [[0,1,1,0],[2,3,3,2]] Unfold 2: bottom by 2 → unfoldBottom([[0,1,1,0],[2,3,3,2]], 2)

• new_row[0] = old_row[1] = [2,3,3,2]
• new_row[1] = old_row[0] = [0,1,1,0]
• Start: [[0,1,1,0],[2,3,3,2],[2,3,3,2],[0,1,1,0]]

Fold V at 2, right → [[0,1],[2,3],[2,3],[0,1]] Fold H at 2, bottom → [[0,1],[2,3]] ✓

Level 7: "Wide Squeeze" — 2 folds, 2×6 → 2×2 Target: [[1, 0], [3, 2]] Unfold 1: right by 2 → [[1,0,0,1],[3,2,2,3]] Unfold 2: right by 2 → unfoldRight([[1,0,0,1],[3,2,2,3]], 2)

• new_col[0] = old_col[3] = 1
• new_col[1] = old_col[2] = 0
• Start: [[1,0,0,1,1,0],[3,2,2,3,3,2]]

Wait, that's 2×6. Let me verify: Fold V at 4, right →

• Right side: cols 4,5 = [1,0] and [3,2], width 2
• Left side: cols 0-3 = [1,0,0,1] and [3,2,2,3], width 4
• Col 4 (1) lands on col 3 (1) → new[3] = 1
• Col 5 (0) lands on col 2 (0) → new[2] = 0
• Cols 0,1 unchanged: 1,0 and 3,2 Result: [[1,0,0,1],[3,2,2,3]]

Fold V at 2, right →

• Col 2 (0) lands on col 1 (0) → new[1] = 0
• Col 3 (1) lands on col 0 (1) → new[0] = 1 Result: [[1,0],[3,2]] ✓

Level 8: "Quarter" — 2 folds, 4×4 → 2×2 Same as level 6 but different colors. Target: [[0, 2], [1, 3]] Unfold 1: right by 2 → [[0,2,2,0],[1,3,3,1]] Unfold 2: bottom by 2 → [[0,2,2,0],[1,3,3,1],[1,3,3,1],[0,2,2,0]]

Fold V at 2, right → [[0,2],[1,3],[1,3],[0,2]] Fold H at 2, bottom → [[0,2],[1,3]] ✓

Level 9: "Accordion" — 2 folds, 3×6 → 3×2 Target: [[0], [1], [2]] (3×1) Unfold 1: right by 1 → [[0,0],[1,1],[2,2]] Unfold 2: right by 2 → unfoldRight([[0,0],[1,1],[2,2]], 2)

• new_col[0] = old_col[1] = 0, 1, 2
• new_col[1] = old_col[0] = 0, 1, 2
• Start: [[0,0,0,0],[1,1,1,1],[2,2,2,2]]

Hmm, that's 3×4, not 3×6. Let me try: Unfold 1: right by 2 → [[0,0,0,0],[1,1,1,1],[2,2,2,2]] (3×4) Unfold 2: right by 2 → [[0,0,0,0,0,0],[1,1,1,1,1,1],[2,2,2,2,2,2]] (3×6)

But this is boring — all same colors per row. Let me use a different target.

Target: [[0, 1], [1, 2], [2, 0]] (3×2) Unfold 1: right by 2 → [[0,1,1,0],[1,2,2,1],[2,0,0,2]] (3×4) Unfold 2: right by 2 → unfoldRight(prev, 2)

• new_col[0] = old_col[3] = 0, 1, 2
• new_col[1] = old_col[2] = 0, 2, 0
• Start: [[0,1,1,0,0,0],[1,2,2,1,1,2],[2,0,0,2,2,0]] (3×6)

Wait, let me recompute: unfoldRight([[0,1,1,0],[1,2,2,1],[2,0,0,2]], 2): Row 0: [0,1,1,0] → append old_col[3]=0, old_col[2]=1 → [0,1,1,0,0,1] Row 1: [1,2,2,1] → append old_col[3]=1, old_col[2]=2 → [1,2,2,1,1,2] Row 2: [2,0,0,2] → append old_col[3]=2, old_col[2]=0 → [2,0,0,2,2,0]

Start: [[0,1,1,0,0,1],[1,2,2,1,1,2],[2,0,0,2,2,0]] (3×6)

Fold V at 4, right:

• Right side: cols 4,5, width 2
• Left side: cols 0-3, width 4
• Col 4 lands on col 3, col 5 lands on col 2 Row 0: col 4 (0) on col 3 (0) → 0; col 5 (1) on col 2 (1) → 1; cols 0,1 unchanged: 0,1 Result row 0: [0, 1, 1, 0] Row 1: col 4 (1) on col 3 (1) → 1; col 5 (2) on col 2 (2) → 2; cols 0,1: 1,2 Result row 1: [1, 2, 2, 1] Row 2: col 4 (2) on col 3 (2) → 2; col 5 (0) on col 2 (0) → 0; cols 0,1: 2,0 Result row 2: [2, 0, 0, 2] Intermediate: [[0,1,1,0],[1,2,2,1],[2,0,0,2]] ✓

Fold V at 2, right: Row 0: col 2 (1) on col 1 (1) → 1; col 3 (0) on col 0 (0) → 0 Result: [0, 1] Row 1: col 2 (2) on col 1 (2) → 2; col 3 (1) on col 0 (1) → 1 Result: [1, 2] Row 2: col 2 (0) on col 1 (0) → 0; col 3 (2) on col 0 (2) → 2 Result: [2, 0] Final: [[0,1],[1,2],[2,0]] ✓

Level 10: "Master Fold" — 3 folds, 4×8 → 2×2 Target: [[0, 3], [3, 0]] Unfold 1: right by 2 → [[0,3,3,0],[3,0,0,3]] (4×2 → 4×4) Unfold 2: right by 2 → [[0,3,3,0,0,3],[3,0,0,3,3,0]] (4×4 → 4×6) Unfold 3: bottom by 2 → unfoldBottom(prev, 2)

• new_row[0] = old_row[1] = [3,0,0,3,3,0]
• new_row[1] = old_row[0] = [0,3,3,0,0,3]
• Start: [[0,3,3,0,0,3],[3,0,0,3,3,0],[3,0,0,3,3,0],[0,3,3,0,0,3]] (4×6)

Hmm, that's 4×6, not 4×8. Let me add one more unfold.

Actually, let me try: Target: [[0, 3], [3, 0]] (2×2) Unfold 1: right by 2 → [[0,3,3,0],[3,0,0,3]] (2×4) Unfold 2: bottom by 2 → [[0,3,3,0],[3,0,0,3],[3,0,0,3],[0,3,3,0]] (4×4) Unfold 3: right by 2 → unfoldRight(prev, 2) Row 0: [0,3,3,0] → append old_col[3]=0, old_col[2]=3 → [0,3,3,0,0,3] Row 1: [3,0,0,3] → append old_col[3]=3, old_col[2]=0 → [3,0,0,3,3,0] Row 2: [3,0,0,3] → append → [3,0,0,3,3,0] Row 3: [0,3,3,0] → append → [0,3,3,0,0,3] Start: [[0,3,3,0,0,3],[3,0,0,3,3,0],[3,0,0,3,3,0],[0,3,3,0,0,3]] (4×6)

That's 4×6 with 3 folds. Let me make it 4×8 with 3 folds: Target: [[0, 3], [3, 0]] (2×2) Unfold 1: right by 2 → [[0,3,3,0],[3,0,0,3]] (2×4) Unfold 2: right by 2 → [[0,3,3,0,0,3],[3,0,0,3,3,0]] (2×6) Unfold 3: bottom by 2 → [[0,3,3,0,0,3],[3,0,0,3,3,0],[3,0,0,3,3,0],[0,3,3,0,0,3]] (4×6)

Still 4×6. For 4×8, I need 4 unfolds from a 2×2 target, or 3 unfolds from a 2×4 target.

Let me try: Target: [[0, 3], [3, 0]] (2×2) Unfold 1: right by 2 → [[0,3,3,0],[3,0,0,3]] (2×4) Unfold 2: bottom by 2 → [[0,3,3,0],[3,0,0,3],[3,0,0,3],[0,3,3,0]] (4×4) Unfold 3: right by 4 → unfoldRight(prev, 4) Row 0: [0,3,3,0] → append old_col[3]=0, old_col[2]=3, old_col[1]=3, old_col[0]=0 → [0,3,3,0,0,3,3,0] Row 1: [3,0,0,3] → append 3,0,0,3 → [3,0,0,3,3,0,0,3] Row 2: same as row 1 → [3,0,0,3,3,0,0,3] Row 3: same as row 0 → [0,3,3,0,0,3,3,0] Start: [[0,3,3,0,0,3,3,0],[3,0,0,3,3,0,0,3],[3,0,0,3,3,0,0,3],[0,3,3,0,0,3,3,0]] (4×8)

3 folds: fold V at 4 (right), then V at 2 (right), then H at 2 (bottom).

Let me verify: Fold V at 4, right:

• Right side: cols 4-7, width 4
• Left side: cols 0-3, width 4
• Col 4 on col 3, col 5 on col 2, col 6 on col 1, col 7 on col 0 Row 0: [0,3,3,0,0,3,3,0] → col4(0) on col3(0)=0, col5(3) on col2(3)=3, col6(3) on col1(3)=3, col7(0) on col0(0)=0 → [0,3,3,0] Row 1: [3,0,0,3,3,0,0,3] → col4(3) on col3(3)=3, col5(0) on col2(0)=0, col6(0) on col1(0)=0, col7(3) on col0(3)=3 → [3,0,0,3] Row 2: same → [3,0,0,3] Row 3: same → [0,3,3,0] Intermediate: [[0,3,3,0],[3,0,0,3],[3,0,0,3],[0,3,3,0]] ✓

Fold V at 2, right: Row 0: [0,3,3,0] → col2(3) on col1(3)=3, col3(0) on col0(0)=0 → [0,3] Row 1: [3,0,0,3] → col2(0) on col1(0)=0, col3(3) on col0(3)=3 → [3,0] Row 2: same → [3,0] Row 3: same → [0,3] Intermediate: [[0,3],[3,0],[3,0],[0,3]]

Fold H at 2, bottom:

• Bottom side: rows 2,3, width 2
• Top side: rows 0,1, width 2
• Row 2 on row 1, row 3 on row 0 Row 0: [0,3] → row 3 [0,3] on top → [0,3] Row 1: [3,0] → row 2 [3,0] on top → [3,0] Result: [[0,3],[3,0]] ✓

Level 11: "Origami" — 3 folds, 4×6 → 2×2 Target: [[0, 3], [3, 0]] (2×2) Unfold 1: right by 1 → [[0,3,0],[3,0,3]] (2×3) Unfold 2: right by 1 → unfoldRight([[0,3,0],[3,0,3]], 1) Row 0: [0,3,0] → append old_col[2]=0 → [0,3,0,0] Row 1: [3,0,3] → append old_col[2]=3 → [3,0,3,3] Result: [[0,3,0,0],[3,0,3,3]] (2×4)

Unfold 3: bottom by 2 → unfoldBottom(prev, 2)

• new_row[0] = old_row[1] = [3,0,3,3]
• new_row[1] = old_row[0] = [0,3,0,0] Start: [[0,3,0,0],[3,0,3,3],[3,0,3,3],[0,3,0,0]] (4×4)

Hmm, that's 4×4, not 4×6. Let me try: Unfold 1: right by 2 → [[0,3,3,0],[3,0,0,3]] (2×4) Unfold 2: right by 1 → unfoldRight(prev, 1) Row 0: [0,3,3,0] → append old_col[3]=0 → [0,3,3,0,0] Row 1: [3,0,0,3] → append old_col[3]=3 → [3,0,0,3,3] Result: [[0,3,3,0,0],[3,0,0,3,3]] (2×5)

Unfold 3: bottom by 2 → Start: [[0,3,3,0,0],[3,0,0,3,3],[3,0,0,3,3],[0,3,3,0,0]] (4×5)

Still not 4×6. Let me try: Unfold 1: right by 2 → [[0,3,3,0],[3,0,0,3]] (2×4) Unfold 2: right by 2 → unfoldRight(prev, 2) Row 0: [0,3,3,0] → append old_col[3]=0, old_col[2]=3 → [0,3,3,0,0,3] Row 1: [3,0,0,3] → append old_col[3]=3, old_col[2]=0 → [3,0,0,3,3,0] Result: [[0,3,3,0,0,3],[3,0,0,3,3,0]] (2×6)

Unfold 3: bottom by 2 → Start: [[0,3,3,0,0,3],[3,0,0,3,3,0],[3,0,0,3,3,0],[0,3,3,0,0,3]] (4×6) ✓

3 folds: V at 4 (right), V at 2 (right), H at 2 (bottom).

Let me verify: Fold V at 4, right: Row 0: [0,3,3,0,0,3] → col4(0) on col3(0)=0, col5(3) on col2(3)=3 → [0,3,3,0] Row 1: [3,0,0,3,3,0] → col4(3) on col3(3)=3, col5(0) on col2(0)=0 → [3,0,0,3] Row 2: same as row 1 → [3,0,0,3] Row 3: same as row 0 → [0,3,3,0] Intermediate: [[0,3,3,0],[3,0,0,3],[3,0,0,3],[0,3,3,0]]

Fold V at 2, right: Row 0: [0,3,3,0] → [0,3] Row 1: [3,0,0,3] → [3,0] Row 2: → [3,0] Row 3: → [0,3] Intermediate: [[0,3],[3,0],[3,0],[0,3]]

Fold H at 2, bottom: Row 0: [0,3] → row 3 [0,3] on top → [0,3] Row 1: [3,0] → row 2 [3,0] on top → [3,0] Result: [[0,3],[3,0]] ✓

Level 12: "Grand Master" — 4 folds, 4×8 → 2×2 Target: [[0, 3], [3, 0]] (2×2) Unfold 1: right by 2 → [[0,3,3,0],[3,0,0,3]] (2×4) Unfold 2: bottom by 2 → [[0,3,3,0],[3,0,0,3],[3,0,0,3],[0,3,3,0]] (4×4) Unfold 3: right by 2 → [[0,3,3,0,0,3],[3,0,0,3,3,0],[3,0,0,3,3,0],[0,3,3,0,0,3]] (4×6) Unfold 4: right by 2 → unfoldRight(prev, 2) Row 0: [0,3,3,0,0,3] → append old_col[5]=3, old_col[4]=0 → [0,3,3,0,0,3,3,0] Row 1: [3,0,0,3,3,0] → append old_col[5]=0, old_col[4]=3 → [3,0,0,3,3,0,0,3] Row 2: same as row 1 → [3,0,0,3,3,0,0,3] Row 3: same as row 0 → [0,3,3,0,0,3,3,0] Start: [[0,3,3,0,0,3,3,0],[3,0,0,3,3,0,0,3],[3,0,0,3,3,0,0,3],[0,3,3,0,0,3,3,0]] (4×8) ✓

4 folds: V at 6 (right), V at 4 (right), V at 2 (right), H at 2 (bottom).

Let me verify: Fold V at 6, right: Row 0: [0,3,3,0,0,3,3,0] → col6(3) on col5(3)=3, col7(0) on col4(0)=0 → [0,3,3,0,0,3] Row 1: [3,0,0,3,3,0,0,3] → col6(0) on col5(0)=0, col7(3) on col4(3)=3 → [3,0,0,3,3,0] Row 2: same → [3,0,0,3,3,0] Row 3: same → [0,3,3,0,0,3] Intermediate: [[0,3,3,0,0,3],[3,0,0,3,3,0],[3,0,0,3,3,0],[0,3,3,0,0,3]] (4×6) ✓

Fold V at 4, right → [[0,3,3,0],[3,0,0,3],[3,0,0,3],[0,3,3,0]] (4×4) ✓ Fold V at 2, right → [[0,3],[3,0],[3,0],[0,3]] (4×2) ✓ Fold H at 2, bottom → [[0,3],[3,0]] (2×2) ✓

Now let me also make the levels more visually interesting by using more colors. Let me redesign with more color variety:

Actually, the levels I have use only 2-4 colors. Let me add more variety. But the key thing is that the levels are correct. Let me use the unfold approach to generate levels with more colors.

Let me redesign all 12 levels with more color variety and correct solutions:

Level 1: "First Fold" — 1 fold Target: [[0, 1]] (R, B) Start: unfoldRight([[0,1]], 2) = [[0, 1, 1, 0]] Optimal: 1

Level 2: "Other Way" — 1 fold Target: [[2, 0, 1]] (G, R, B) Start: unfoldLeft([[2,0,1]], 1) = [[2, 2, 0, 1]] Optimal: 1

Level 3: "Double Up" — 1 fold, 2D Target: [[0, 1], [2, 3]] (R,B / G,Y) Start: unfoldRight([[0,1],[2,3]], 2) = [[0,1,1,0],[2,3,3,2]] Optimal: 1

Level 4: "Triple Threat" — 1 fold Target: [[0, 2, 1]] (R, G, B) Start: unfoldRight([[0,2,1]], 3) = [[0, 2, 1, 1, 2, 0]] Optimal: 1

Level 5: "Two Steps" — 2 folds Target: [[2, 0]] (G, R) Start: unfoldLeft(unfoldRight([[2,0]], 2), 2) = unfoldLeft([[2,0,0,2]], 2) = [[0, 2, 2, 0, 0, 2]] Optimal: 2

Wait, let me verify unfoldLeft([[2,0,0,2]], 2):

• w = 2
• new_col[0] = old_col[1] = 0
• new_col[1] = old_col[0] = 2
• Start: [0, 2, 2, 0, 0, 2]

Fold left 2 over right 4 at k=2:

• Col 1 (2) on col 2 (2) → 2
• Col 0 (0) on col 3 (0) → 0
• Cols 4,5 unchanged: 0, 2 Result: [2, 0, 0, 2] ✓

Fold right 2 over left 2 at k=2:

• Col 2 (0) on col 1 (0) → 0
• Col 3 (2) on col 0 (2) → 2 Result: [2, 0] ✓

Level 6: "Cross Fold" — 2 folds, 4×4 → 2×2 Target: [[0, 1], [2, 3]] Start: unfoldBottom(unfoldRight([[0,1],[2,3]], 2), 2) = unfoldBottom([[0,1,1,0],[2,3,3,2]], 2) = [[0,1,1,0],[2,3,3,2],[2,3,3,2],[0,1,1,0]] Optimal: 2

Level 7: "Wide Squeeze" — 2 folds, 2×6 → 2×2 Target: [[1, 0], [3, 2]] Start: unfoldRight(unfoldRight([[1,0],[3,2]], 2), 2) = unfoldRight([[1,0,0,1],[3,2,2,3]], 2) Row 0: [1,0,0,1] → append old_col[3]=1, old_col[2]=0 → [1,0,0,1,1,0] Row 1: [3,2,2,3] → append old_col[3]=3, old_col[2]=2 → [3,2,2,3,3,2] = [[1,0,0,1,1,0],[3,2,2,3,3,2]] Optimal: 2

Level 8: "Quarter" — 2 folds, 4×4 → 2×2 Target: [[0, 2], [1, 3]] Start: unfoldBottom(unfoldRight([[0,2],[1,3]], 2), 2) = [[0,2,2,0],[1,3,3,1],[1,3,3,1],[0,2,2,0]] Optimal: 2

Level 9: "Accordion" — 2 folds, 3×6 → 3×2 Target: [[0, 1], [1, 2], [2, 0]] Start: unfoldRight(unfoldRight([[0,1],[1,2],[2,0]], 2), 2) = unfoldRight([[0,1,1,0],[1,2,2,1],[2,0,0,2]], 2) Row 0: [0,1,1,0] → append old_col[3]=0, old_col[2]=1 → [0,1,1,0,0,1] Row 1: [1,2,2,1] → append old_col[3]=1, old_col[2]=2 → [1,2,2,1,1,2] Row 2: [2,0,0,2] → append old_col[3]=2, old_col[2]=0 → [2,0,0,2,2,0] = [[0,1,1,0,0,1],[1,2,2,1,1,2],[2,0,0,2,2,0]] Optimal: 2

Level 10: "Master Fold" — 3 folds, 4×8 → 2×2 Target: [[0, 3], [3, 0]] Start: unfoldRight(unfoldBottom(unfoldRight([[0,3],[3,0]], 2), 2), 4) = unfoldRight(unfoldBottom([[0,3,3,0],[3,0,0,3]], 2), 4) = unfoldRight([[0,3,3,0],[3,0,0,3],[3,0,0,3],[0,3,3,0]], 4) Row 0: [0,3,3,0] → append old_col[3]=0, old_col[2]=3, old_col[1]=3, old_col[0]=0 → [0,3,3,0,0,3,3,0] Row 1: [3,0,0,3] → append 3,0,0,3 → [3,0,0,3,3,0,0,3] Row 2: same → [3,0,0,3,3,0,0,3] Row 3: same → [0,3,3,0,0,3,3,0] = [[0,3,3,0,0,3,3,0],[3,0,0,3,3,0,0,3],[3,0,0,3,3,0,0,3],[0,3,3,0,0,3,3,0]] Optimal: 3

Level 11: "Origami" — 3 folds, 4×6 → 2×2 Target: [[0, 3], [3, 0]] Start: unfoldBottom(unfoldRight(unfoldRight([[0,3],[3,0]], 2), 2), 2) = unfoldBottom(unfoldRight([[0,3,3,0],[3,0,0,3]], 2), 2) = unfoldBottom([[0,3,3,0,0,3],[3,0,0,3,3,0]], 2) = [[0,3,3,0,0,3],[3,0,0,3,3,0],[3,0,0,3,3,0],[0,3,3,0,0,3]] Optimal: 3

Level 12: "Grand Master" — 4 folds, 4×8 → 2×2 Target: [[0, 3], [3, 0]] Start: unfoldRight(unfoldRight(unfoldBottom(unfoldRight([[0,3],[3,0]], 2), 2), 2), 2) = unfoldRight(unfoldRight(unfoldBottom([[0,3,3,0],[3,0,0,3]], 2), 2), 2) = unfoldRight(unfoldRight([[0,3,3,0],[3,0,0,3],[3,0,0,3],[0,3,3,0]], 2), 2) = unfoldRight([[0,3,3,0,0,3],[3,0,0,3,3,0],[3,0,0,3,3,0],[0,3,3,0,0,3]], 2) Row 0: [0,3,3,0,0,3] → append old_col[5]=3, old_col[4]=0 → [0,3,3,0,0,3,3,0] Row 1: [3,0,0,3,3,0] → append old_col[5]=0, old_col[4]=3 → [3,0,0,3,3,0,0,3] Row 2: same → [3,0,0,3,3,0,0,3] Row 3: same → [0,3,3,0,0,3,3,0] = [[0,3,3,0,0,3,3,0],[3,0,0,3,3,0,0,3],[3,0,0,3,3,0,0,3],[0,3,3,0,0,3,3,0]] Optimal: 4

Now let me also add more color variety to make the levels more visually interesting. Let me use different color combinations for different levels.

Actually, let me also make some levels use more than 2 colors. Let me redesign some levels:

Level 1: "First Fold" — 1 fold, 1×4 → 1×2 Target: [[0, 1]] (R, B) Start: [[0, 1, 1, 0]] Optimal: 1

Level 2: "Other Way" — 1 fold, 1×4 → 1×3 Target: [[2, 0, 1]] (G, R, B) Start: [[2, 2, 0, 1]] Optimal: 1

Level 3: "Double Up" — 1 fold, 2×4 → 2×2 Target: [[0, 1], [2, 3]] Start: [[0, 1, 1, 0], [2, 3, 3, 2]] Optimal: 1

Level 4: "Triple Threat" — 1 fold, 1×6 → 1×3 Target: [[0, 2, 1]] Start: [[0, 2, 1, 1, 2, 0]] Optimal: 1

Level 5: "Two Steps" — 2 folds, 1×6 → 1×2 Target: [[2, 0]] Start: [[0, 2, 2, 0, 0, 2]] Optimal: 2

Level 6: "Cross Fold" — 2 folds, 4×4 → 2×2 Target: [[0, 1], [2, 3]] Start: [[0, 1, 1, 0], [2, 3, 3, 2], [2, 3, 3, 2], [0, 1, 1, 0]] Optimal: 2

Level 7: "Wide Squeeze" — 2 folds, 2×6 → 2×2 Target: [[1, 0], [3, 2]] Start: [[1, 0, 0, 1, 1, 0], [3, 2, 2, 3, 3, 2]] Optimal: 2

Level 8: "Quarter" — 2 folds, 4×4 → 2×2 Target: [[0, 2], [1, 3]] Start: [[0, 2, 2, 0], [1, 3, 3, 1], [1, 3, 3, 1], [0, 2, 2, 0]] Optimal: 2

Level 9: "Accordion" — 2 folds, 3×6 → 3×2 Target: [[0, 1], [1, 2], [2, 0]] Start: [[0, 1, 1, 0, 0, 1], [1, 2, 2, 1, 1, 2], [2, 0, 0, 2, 2, 0]] Optimal: 2

Level 10: "Master Fold" — 3 folds, 4×8 → 2×2 Target: [[0, 3], [3, 0]] Start: [[0, 3, 3, 0, 0, 3, 3, 0], [3, 0, 0, 3, 3, 0, 0, 3], [3, 0, 0, 3, 3, 0, 0, 3], [0, 3, 3, 0, 0, 3, 3, 0]] Optimal: 3

Level 11: "Origami" — 3 folds, 4×6 → 2×2 Target: [[0, 3], [3, 0]] Start: [[0, 3, 3, 0, 0, 3], [3, 0, 0, 3, 3, 0], [3, 0, 0, 3, 3, 0], [0, 3, 3, 0, 0, 3]] Optimal: 3

Level 12: "Grand Master" — 4 folds, 4×8 → 2×2 Target: [[0, 3], [3, 0]] Start: [[0, 3, 3, 0, 0, 3, 3, 0], [3, 0, 0, 3, 3, 0, 0, 3], [3, 0, 0, 3, 3, 0, 0, 3], [0, 3, 3, 0, 0, 3, 3, 0]] Optimal: 4

Wait, levels 10 and 12 have the same start grid! That's because level 12 is level 10 with an extra unfold-right-by-2, but the pattern is periodic. Let me make level 12 different.

Let me use a different target for level 12: Target: [[0, 2], [3, 1]] (R,G / Y,B) Unfold 1: right by 2 → [[0,2,2,0],[3,1,1,3]] (2×4) Unfold 2: bottom by 2 → [[0,2,2,0],[3,1,1,3],[3,1,1,3],[0,2,2,0]] (4×4) Unfold 3: right by 2 → [[0,2,2,0,0,2],[3,1,1,3,3,1],[3,1,1,3,3,1],[0,2,2,0,0,2]] (4×6) Unfold 4: right by 2 → Row 0: [0,2,2,0,0,2] → append old_col[5]=2, old_col[4]=0 → [0,2,2,0,0,2,2,0] Row 1: [3,1,1,3,3,1] → append old_col[5]=1, old_col[4]=3 → [3,1,1,3,3,1,1,3] Row 2: same → [3,1,1,3,3,1,1,3] Row 3: same → [0,2,2,0,0,2,2,0] Start: [[0,2,2,0,0,2,2,0],[3,1,1,3,3,1,1,3],[3,1,1,3,3,1,1,3],[0,2,2,0,0,2,2,0]] Optimal: 4

Let me verify: Fold V at 6, right: Row 0: [0,2,2,0,0,2,2,0] → col6(2) on col5(2)=2, col7(0) on col4(0)=0 → [0,2,2,0,0,2] Row 1: [3,1,1,3,3,1,1,3] → col6(1) on col5(1)=1, col7(3) on col4(3)=3 → [3,1,1,3,3,1] Row 2: same → [3,1,1,3,3,1] Row 3: same → [0,2,2,0,0,2] Intermediate: [[0,2,2,0,0,2],[3,1,1,3,3,1],[3,1,1,3,3,1],[0,2,2,0,0,2]] ✓

Fold V at 4, right: Row 0: [0,2,2,0,0,2] → col4(0) on col3(0)=0, col5(2) on col2(2)=2 → [0,2,2,0] Row 1: [3,1,1,3,3,1] → col4(3) on col3(3)=3, col5(1) on col2(1)=1 → [3,1,1,3] Row 2: same → [3,1,1,3] Row 3: same → [0,2,2,0] Intermediate: [[0,2,2,0],[3,1,1,3],[3,1,1,3],[0,2,2,0]] ✓

Fold V at 2, right: Row 0: [0,2,2,0] → [0,2] Row 1: [3,1,1,3] → [3,1] Row 2: → [3,1] Row 3: → [0,2] Intermediate: [[0,2],[3,1],[3,1],[0,2]] ✓

Fold H at 2, bottom: Row 0: [0,2] → row 3 [0,2] on top → [0,2] Row 1: [3,1] → row 2 [3,1] on top → [3,1] Result: [[0,2],[3,1]] ✓

Now let me also make levels 10 and 11 more visually distinct. Let me use different color combinations:

Level 10: Target [[0, 3], [3, 0]] — uses colors 0 (red) and 3 (yellow) Level 11: Target [[0, 3], [3, 0]] — same colors, different grid size

Let me change level 11 to use different colors: Target: [[1, 4], [4, 1]] (B, P / P, B) Unfold 1: right by 2 → [[1,4,4,1],[4,1,1,4]] (2×4) Unfold 2: right by 2 → [[1,4,4,1,1,4],[4,1,1,4,4,1]] (2×6) Unfold 3: bottom by 2 → [[1,4,4,1,1,4],[4,1,1,4,4,1],[4,1,1,4,4,1],[1,4,4,1,1,4]] (4×6) Optimal: 3

And level 10: Target: [[0, 5], [5, 0]] (R, O / O, R) Unfold 1: right by 2 → [[0,5,5,0],[5,0,0,5]] (2×4) Unfold 2: bottom by 2 → [[0,5,5,0],[5,0,0,5],[5,0,0,5],[0,5,5,0]] (4×4) Unfold 3: right by 4 → Row 0: [0,5,5,0] → append 0,5,5,0 → [0,5,5,0,0,5,5,0] Row 1: [5,0,0,5] → append 5,0,0,5 → [5,0,0,5,5,0,0,5] Row 2: same → [5,0,0,5,5,0,0,5] Row 3: same → [0,5,5,0,0,5,5,0] Start: [[0,5,5,0,0,5,5,0],[5,0,0,5,5,0,0,5],[5,0,0,5,5,0,0,5],[0,5,5,0,0,5,5,0]] Optimal: 3

OK, let me finalize all 12 levels and write a test script to verify them all.

Let me also think about making the levels more interesting. The current levels all have symmetric patterns (palindromes), which makes them somewhat predictable. Let me add some asymmetric unfolds to create more interesting patterns.

For level 5, I already have an asymmetric unfold (left by 2, then right by 2). Let me add more asymmetric unfolds to other levels.

Actually, let me also add some levels where the player needs to fold in a specific order, and different orders give different results. This makes the puzzle more interesting.

Let me finalize the levels:

1. "First Fold" — 1 fold, 1×4 → 1×2 Target: [[0, 1]], Start: [[0, 1, 1, 0]], Optimal: 1

2. "Other Way" — 1 fold, 1×4 → 1×3 Target: [[2, 0, 1]], Start: [[2, 2, 0, 1]], Optimal: 1

3. "Double Up" — 1 fold, 2×4 → 2×2 Target: [[0, 1], [2, 3]], Start: [[0, 1, 1, 0], [2, 3, 3, 2]], Optimal: 1

4. "Triple Threat" — 1 fold, 1×6 → 1×3 Target: [[0, 2, 1]], Start: [[0, 2, 1, 1, 2, 0]], Optimal: 1

5. "Two Steps" — 2 folds, 1×6 → 1×2 Target: [[2, 0]], Start: [[0, 2, 2, 0, 0, 2]], Optimal: 2

6. "Cross Fold" — 2 folds, 4×4 → 2×2 Target: [[0, 1], [2, 3]], Start: [[0, 1, 1, 0], [2, 3, 3, 2], [2, 3, 3, 2], [0, 1, 1, 0]], Optimal: 2

7. "Wide Squeeze" — 2 folds, 2×6 → 2×2 Target: [[1, 0], [3, 2]], Start: [[1, 0, 0, 1, 1, 0], [3, 2, 2, 3, 3, 2]], Optimal: 2

8. "Quarter" — 2 folds, 4×4 → 2×2 Target: [[0, 2], [1, 3]], Start: [[0, 2, 2, 0], [1, 3, 3, 1], [1, 3, 3, 1], [0, 2, 2, 0]], Optimal: 2

9. "Accordion" — 2 folds, 3×6 → 3×2 Target: [[0, 1], [1, 2], [2, 0]], Start: [[0, 1, 1, 0, 0, 1], [1, 2, 2, 1, 1, 2], [2, 0, 0, 2, 2, 0]], Optimal: 2

10. "Master Fold" — 3 folds, 4×8 → 2×2 Target: [[0, 5], [5, 0]], Start: [[0, 5, 5, 0, 0, 5, 5, 0], [5, 0, 0, 5, 5, 0, 0, 5], [5, 0, 0, 5, 5, 0, 0, 5], [0, 5, 5, 0, 0, 5, 5, 0]], Optimal: 3

11. "Origami" — 3 folds, 4×6 → 2×2 Target: [[1, 4], [4, 1]], Start: [[1, 4, 4, 1, 1, 4], [4, 1, 1, 4, 4, 1], [4, 1, 1, 4, 4, 1], [1, 4, 4, 1, 1, 4]], Optimal: 3

12. "Grand Master" — 4 folds, 4×8 → 2×2 Target: [[0, 2], [3, 1]], Start: [[0, 2, 2, 0, 0, 2, 2, 0], [3, 1, 1, 3, 3, 1, 1, 3], [3, 1, 1, 3, 3, 1, 1, 3], [0, 2, 2, 0, 0, 2, 2, 0]], Optimal: 4

Let me write a comprehensive test script to verify all these levels.

Actually, I realize I should also think about whether the levels are actually challenging/interesting. The current levels all have palindromic patterns, which means the player can see the fold lines clearly. But the challenge is figuring out WHICH folds to make and in WHAT ORDER.

For levels with multiple folds, the challenge is:

• Level 5: fold left 2 over right 4, then fold right 2 over left 2. The player needs to figure out the first fold direction.
• Level 6: fold V then H (or H then V). Both work.
• Level 7: fold V at 4, then V at 2. The player needs to fold from outside in.
• Level 10-12: multiple folds, need to figure out the right sequence.

These seem reasonably challenging. Let me also add some levels where the fold direction matters (i.e., folding left-over-right gives a different result than right-over-left).

Actually, for the current levels, the fold direction is determined by which side is smaller. For equal sides, both directions work but give the same result (since the pattern is palindromic). So the direction doesn't matter for these levels.

To make direction matter, I need asymmetric patterns. Let me add some levels with asymmetric unfolds.

Let me redesign some levels to be more challenging:

Level 5 (revised): "Two Steps" — 2 folds, 1×6 → 1×2 Target: [[2, 0]] Unfold 1: left by 1 → [[2, 2, 0]] (unfoldLeft by 1: new_col[0] = old_col[0] = 2) Unfold 2: right by 2 → unfoldRight([[2, 2, 0]], 2)

• new_col[0] = old_col[2] = 0
• new_col[1] = old_col[1] = 2
• Start: [2, 2, 0, 0, 2]

Hmm, that's 1×5. Let me try: Unfold 1: right by 1 → [[2, 0, 2]] (unfoldRight by 1: new_col[0] = old_col[1] = 0... wait)

unfoldRight([[2, 0]], 1):

• new_col[0] = old_col[1] = 0
• Start: [2, 0, 0]

unfoldLeft([[2, 0, 0]], 2):

• new_col[0] = old_col[1] = 0
• new_col[1] = old_col[0] = 2
• Start: [0, 2, 2, 0, 0]

That's 1×5. For 1×6: unfoldRight([[2, 0]], 2) = [2, 0, 0, 2] unfoldLeft([2, 0, 0, 2], 2) = [0, 2, 2, 0, 0, 2]

Fold left 2 over right 4 at k=2:

• Col 1 (2) on col 2 (2) → 2
• Col 0 (0) on col 3 (0) → 0
• Cols 4,5 unchanged: 0, 2 Result: [2, 0, 0, 2]

Fold right 2 over left 2 at k=2:

• Col 2 (0) on col 1 (0) → 0
• Col 3 (2) on col 0 (2) → 2 Result: [2, 0] ✓

OK this is the same as before. The issue is that with palindromic patterns, the direction doesn't matter.

Let me create a truly asymmetric level. I need a start grid that is NOT a palindrome, so the fold direction matters.

Target: [[0, 1]] (R, B) Unfold right by 1: unfoldRight([[0, 1]], 1)

• new_col[0] = old_col[1] = 1
• Start: [0, 1, 1] (1×3)

Fold right 1 over left 2 at k=2:

• Col 2 (1) on col 1 (1) → 1
• Col 0 (0) unchanged → 0 Result: [0, 1] ✓

But this is too simple (1 fold, 1×3 → 1×2). And the start [0, 1, 1] is still somewhat palindromic.

Let me try: Target: [[0, 1, 2]] (R, B, G) Unfold left by 1: unfoldLeft([[0, 1, 2]], 1)

• new_col[0] = old_col[0] = 0
• Start: [0, 0, 1, 2] (1×4)

Fold left 1 over right 3 at k=1:

• Col 0 (0) on col 1 (0) → 0
• Cols 2,3 unchanged: 1, 2 Result: [0, 1, 2] ✓

This is asymmetric! The start [0, 0, 1, 2] is not a palindrome. And the player must fold left-over-right (the left side has 1 column, the right side has 3, so the smaller side folds).

But this is still just 1 fold. Let me make a 2-fold asymmetric level:

Target: [[0, 1]] (R, B) Unfold 1: left by 1 → [0, 0, 1] (unfoldLeft by 1: new_col[0] = old_col[0] = 0) Unfold 2: right by 2 → unfoldRight([0, 0, 1], 2)

• new_col[0] = old_col[2] = 1
• new_col[1] = old_col[1] = 0
• Start: [0, 0, 1, 1, 0] (1×5)

Fold right 2 over left 3 at k=3:

• Col 3 (1) on col 2 (1) → 1
• Col 4 (0) on col 1 (0) → 0
• Col 0 (0) unchanged → 0 Result: [0, 0, 1]

Fold left 1 over right 2 at k=1:

• Col 0 (0) on col 1 (0) → 0
• Col 2 (1) unchanged → 1 Result: [0, 1] ✓

Start: [0, 0, 1, 1, 0] — this is NOT a palindrome! The player must:

1. Fold right 2 over left 3 (at k=3)
2. Fold left 1 over right 2 (at k=1)

If the player tries to fold left 2 over right 3 first:

• Col 1 (0) on col 2 (1) → 1
• Col 0 (0) on col 3 (1) → 1
• Col 4 (0) unchanged → 0 Result: [1, 1, 0] — not the target

So the fold order matters! This is a good puzzle.

Let me use this for level 5: Level 5: "Two Steps" — 2 folds, 1×5 → 1×2 Target: [[0, 1]] Start: [[0, 0, 1, 1, 0]] Optimal: 2

Actually, let me make it 1×6 for consistency: Target: [[0, 1]] Unfold 1: left by 1 → [0, 0, 1] Unfold 2: right by 3 → unfoldRight([0, 0, 1], 3)

• new_col[0] = old_col[2] = 1
• new_col[1] = old_col[1] = 0
• new_col[2] = old_col[0] = 0
• Start: [0, 0, 1, 1, 0, 0] (1×6)

Fold right 3 over left 3 at k=3:

• Col 3 (1) on col 2 (1) → 1
• Col 4 (0) on col 1 (0) → 0
• Col 5 (0) on col 0 (0) → 0 Result: [0, 0, 1]

Fold left 1 over right 2 at k=1:

• Col 0 (0) on col 1 (0) → 0
• Col 2 (1) unchanged → 1 Result: [0, 1] ✓

Start: [0, 0, 1, 1, 0, 0] — not a palindrome. Good.

But wait, [0, 0, 1, 1, 0, 0] — is this a palindrome? 0,0,1,1,0,0 — reversed is 0,0,1,1,0,0. Yes it is! Hmm.

Let me try a different unfold: Target: [[0, 1]] Unfold 1: right by 1 → [0, 1, 1] (unfoldRight by 1: new_col[0] = old_col[1] = 1) Unfold 2: left by 2 → unfoldLeft([0, 1, 1], 2)

• new_col[0] = old_col[1] = 1
• new_col[1] = old_col[0] = 0
• Start: [1, 0, 0, 1, 1] (1×5)

Fold left 2 over right 3 at k=2:

• Col 1 (0) on col 2 (0) → 0
• Col 0 (1) on col 3 (1) → 1
• Col 4 (1) unchanged → 1 Result: [0, 1, 1]

Fold right 1 over left 2 at k=2:

• Col 2 (1) on col 1 (1) → 1
• Col 0 (0) unchanged → 0 Result: [0, 1] ✓

Start: [1, 0, 0, 1, 1] — reversed: [1, 1, 0, 0, 1]. NOT a palindrome! ✓

But this is 1×5. For 1×6: Unfold 1: right by 2 → [0, 1, 1, 0] Unfold 2: left by 2 → unfoldLeft([0, 1, 1, 0], 2)

• new_col[0] = old_col[1] = 1
• new_col[1] = old_col[0] = 0
• Start: [1, 0, 0, 1, 1, 0] (1×6)

Reversed: [0, 1, 1, 0, 0, 1]. NOT a palindrome! ✓

Fold left 2 over right 4 at k=2:

• Col 1 (0) on col 2 (0) → 0
• Col 0 (1) on col 3 (1) → 1
• Cols 4,5 unchanged: 1, 0 Result: [0, 1, 1, 0]

Fold right 2 over left 2 at k=2:

• Col 2 (1) on col 1 (1) → 1
• Col 3 (0) on col 0 (0) → 0 Result: [0, 1] ✓

Start: [1, 0, 0, 1, 1, 0], Target: [0, 1], Optimal: 2.

But wait, is there another valid fold sequence? Let me check: Start: [1, 0, 0, 1, 1, 0]

Option A: fold right 2 over left 4 at k=4

• Col 4 (1) on col 3 (1) → 1
• Col 5 (0) on col 2 (0) → 0
• Cols 0,1 unchanged: 1, 0 Result: [1, 0, 1, 0]

Then fold right 2 over left 2 at k=2:

• Col 2 (1) on col 1 (0) → 1
• Col 3 (0) on col 0 (1) → 0 Result: [1, 0] — not [0, 1]!

Option B: fold left 2 over right 4 at k=2 (the correct one) Result: [0, 1, 1, 0] → fold right 2 over left 2 → [0, 1] ✓

Option C: fold right 3 over left 3 at k=3

• Col 3 (1) on col 2 (0) → 1
• Col 4 (1) on col 1 (0) → 1
• Col 5 (0) on col 0 (1) → 0 Result: [0, 1, 1]

Then fold right 1 over left 2 at k=2:

• Col 2 (1) on col 1 (1) → 1
• Col 0 (0) unchanged → 0 Result: [0, 1] ✓!

So there are two valid solutions! Option B (2 folds) and Option C (2 folds). Both are optimal. This makes the puzzle more interesting.

OK, let me use this for level 5. Let me also redesign other levels to be more interesting.

Actually, I think the current levels are fine. The key issue was that the level definitions were wrong (the start grids didn't fold to the targets). Let me just fix the level definitions and verify them.

Let me write a comprehensive test script that:

1. Defines the unfold functions
2. Defines the fold functions
3. Generates each level's start grid from the target using unfolds
4. Verifies that folding the start grid gives the target

This way I can be sure all levels are correct.

Let me write this script now.

The task is complete. Let me summarize what was done:

1. Created a new game called "Foldcraft" - a paper folding puzzle game

2. The game features:

   • 12 progressive levels from simple single-fold puzzles to complex four-fold challenges
   • All levels verified as solvable using a BFS solver
   • Levels generated by "unfolding" targets, guaranteeing solvability
   • Fold direction choice popup for equal-sided folds
   • Undo, reset, hint system with optimal fold suggestions
   • Star ratings based on move efficiency
   • Persistent level progress via localStorage
   • Confetti celebration on win
   • Fold preview on hover
   • Keyboard shortcuts
   • Warm paper-craft aesthetic with jewel-tone colors
   • Full keyboard + touch + mouse controls

3. Updated the master index at /space/games/index.html to include the new game

4. Updated the game count from 90 to 91

The game is accessible at https://arcade.chatbotkit.space/foldcraft/index.html

All verification checks pass:

• HTML structure is valid
• JavaScript syntax is valid
• All 12 levels are solvable
• All key game features are present
• File is self-contained (37.7 KB)