To solve a four-by-four fold-to-shape puzzle, undo the last fold first, reflect each punch across that crease, and keep both the original and mirrored positions.
The Paper Folding Puzzle applies that method across five fixed rounds. Each round presents a four-by-four sheet, one or two half-sheet folds, a punch coordinate on the folded paper, and four diagrams to choose from.
This guide covers the game’s specific fold-and-punch format. It is not a general origami guide, a cube-net test, or a method for predicting holes in arbitrarily folded shapes.
Read the grid and fold directions
The prompt gives you a fold order and a coordinate on the folded sheet. The visible grid is oriented from the top-left, while the underlying logic uses zero-based x and y cell coordinates. Treat x as the column position and y as the row position, with x increasing from left to right and y increasing from top to bottom.
Only two fold directions appear in the supported rounds. Folding the right half to the left creates a vertical mirror, so each cell at (x, y) gains a partner at (3 − x, y). Folding the bottom half to the top creates a horizontal mirror, so each cell at (x, y) gains a partner at (x, 3 − y).
| Round structure | Reflection to perform | Normal result |
|---|---|---|
| Right half folded to the left | Keep (x, y) and add (3 − x, y) | Two hole positions |
| Bottom half folded to the top | Keep (x, y) and add (x, 3 − y) | Two hole positions |
| Right-to-left and bottom-to-top folds | Undo the last fold first, then reflect every current position across the earlier crease | Four hole positions |
The important rule is to preserve the original position whenever you create a mirror. A fold does not move one hole somewhere else; unfolding adds a reflected copy while retaining the hole already found.
Solve a four-by-four fold-to-shape round
Use the same ordered workflow for every sheet, including rounds with only one fold.
- Read the complete fold sequence. Identify which fold was made last. The punch coordinate refers to the fully folded packet, so the last fold must be undone first.
- Locate the punch. Translate the shown row and column into the game’s zero-based x and y coordinates. Write down the starting position before adding any reflections.
- Undo the final fold. For every current position, keep the original coordinate and add its mirror. A right-to-left fold uses x → 3 − x; a bottom-to-top fold uses y → 3 − y.
- Apply the earlier fold if there is one. Mirror every position already in the set, not just the original punch. With two folds, the first reflection normally creates two positions and the second expands those two into four.
- Remove duplicates and sanity-check the count. Duplicate coordinates are collapsed. One fold normally gives two positions, while two perpendicular folds normally give four, so a diagram with an impossible count can be rejected immediately.
- Compare exact cells with the four diagrams. Holes are marked in the game’s accent color, while unpunched cells remain on the normal surface. Check every row and column rather than relying only on the overall shape.
- Submit with a number or button. Press 1, 2, 3, or 4 for the matching diagram, or use one of the four visible on-screen buttons.
Working backward matters because each fold creates another layer of mirrored positions. Once all reflections are added, compare the complete coordinate set with the answer rather than trying to predict how a diagram “looks” from the folded view.
Work through one two-fold example
The disclosed combined case uses a punch at (0, 1) after right-to-left and bottom-to-top folds. Taking bottom-to-top as the final fold, the reverse walk is as follows:
- Begin with the punch: (0, 1).
- Undo the bottom-to-top fold. Keep (0, 1), then apply y → 3 − y. Substituting the row gives 3 − 1 = 2, so the current set becomes (0, 1) and (0, 2).
- Undo the right-to-left fold. Keep both current points and apply x → 3 − x to each. Substituting the column gives 3 − 0 = 3, adding (3, 1) and (3, 2).
- Read the final set: (0, 1), (0, 2), (3, 1), and (3, 2). These are the four cells that must be marked in the correct diagram.
If the round has only one fold, stop after its single reflection. Applying a second transformation when the prompt does not contain a second fold would create holes that the sheet never had.
Use symmetry to eliminate weak choices
Symmetry is a fast filter, not a replacement for checking coordinates. A pattern produced by one vertical fold must contain matching positions across the vertical center. A pattern produced by two perpendicular folds must also mirror across the horizontal center.
- Count first: Reject a diagram that does not have the expected number of holes.
- Check the original punch: The punch coordinate should still appear in the final set because every reflection preserves the current position.
- Look for opposite partners: A vertical fold pairs columns from the outside toward the center; a horizontal fold does the same for rows.
- Compare every accent cell: Two patterns can share the same count and broad symmetry while placing one hole in the wrong cell.
This is why one punch can make four holes. Two perpendicular half-sheet folds stack four layers, and unfolding reflects the punch across both center lines. The final diagram must match all four resulting positions, including edge and corner cells.
Controls, scoring, and mistake recovery
The game provides complete keyboard play and large on-screen answer buttons, while the pattern diagrams include accessible coordinate labels. There is no timer, so the score depends on completing the five disclosed rounds rather than answering quickly.
- Correct answer: Award 200 points and advance to the next sheet immediately.
- Completion: Five correct patterns complete the game with exactly 1,000 points.
- First mistake: The same sheet remains visible and the mistake counter increases, so you can work through the reflection again.
- Second mistake: The game enters a terminal deadlock and ignores later answers until Restart is used.
- Restart: Return to sheet one with zero points and no mistakes.
On a keyboard, double-press Escape to open the spreadsheet-style Boss Key screen, then repeat the shortcut to resume the current round without losing progress. The best score is stored only in that browser. The game also requires no account, upload, download, audio, hardware permission, or network request.
Know the limits of the fold-to-shape method
The supported workflow is deliberately narrow: a four-by-four sheet, one or two half-sheet folds, one punch coordinate, and four answer diagrams. It does not ask you to infer the shape of an origami model, judge a cube net, rotate a folded piece in three dimensions, or account for arbitrary crease angles.
The fixed rounds include positions near edges and corners, so a punch should never be dismissed because it looks close to the boundary. The same reflection formula still applies. A dependable practice routine is to write the fold order, identify the final fold, draw one mirror at a time, and only then inspect the diagrams. That prevents the most common error: applying both creases to the original punch while forgetting to reflect the position created by the first unfold.
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