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Paper Folding Puzzle

Predict where punched holes appear after unfolding five transparent four-by-four paper fixtures.

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How to use

  1. 1.Read the fold order and punch coordinate, then mentally reverse the final fold first.
  2. 2.Reflect every current hole across each crease while keeping both the original and mirrored positions.
  3. 3.Press 1, 2, 3, or 4 for the matching diagram and solve all five sheets before making two mistakes.

About Paper Folding Puzzle

Paper Folding Puzzle is a five-round spatial reasoning game about folds, punches, and reflection. Each round starts with a four-by-four sheet, describes one or two half-sheet folds, gives the punch coordinate on the folded paper, and asks which of four diagrams shows the holes after the sheet is fully opened.

The coordinate model is deliberately small and disclosed. Columns and rows are numbered from the top-left for the prompt, while the logic stores zero-based x and y cell coordinates. Folding the right half to the left mirrors a punched cell across the vertical center line. Folding the bottom half to the top mirrors it across the horizontal center line. When two folds occur, unfolding reverses their order and doubles the affected points at each crease.

For example, after a right-to-left fold, a punch in folded cell x 0, y 0 opens at original cells 0,0 and 3,0. After both right-to-left and bottom-to-top folds, a punch at folded cell 0,1 opens at 0,1; 0,2; 3,1; and 3,2. The diagrams mark holes with the site's accent color and leave unpunched cells on the normal surface.

Press keys 1 through 4 to choose an answer, or use the four visible buttons. Each correct round awards 200 points and advances immediately. Five correct patterns complete the game at exactly 1,000 points. A wrong choice leaves the same sheet visible and increments the mistake counter. One error is recoverable; a second error creates a terminal deadlock until Restart.

The algorithm begins with the punch on the fully folded sheet. It walks the fold list backward. For a vertical fold it preserves each current point and adds its x-reflection at 3 minus x. For a horizontal fold it preserves each point and adds its y-reflection at 3 minus y. Duplicate coordinates are removed and the final coordinate keys are sorted for deterministic comparison and display.

Eight explicit transformation fixtures test the algorithm. They cover no fold, one vertical fold at two positions, one horizontal fold at two positions, and combined folds at three positions. The test also answers all five game rounds using their disclosed correct choices, checks the 1,000-point completion, triggers the two-error deadlock, and proves later answers cannot mutate a terminal state.

The game uses semantic HTML buttons and CSS grid rather than canvas. All colors come from the site's surface, line, foreground, accent, muted, and danger tokens. Keyboard play is complete, mobile buttons remain large enough to tap, and the pattern diagrams include accessible coordinate labels. No image, animation dependency, random generator, timer, audio, upload, download, account, hardware permission, or network request is required.

To solve a round, reverse the last fold first. Reflect the punch across that crease, keep both positions, then repeat for the earlier crease. Count the expected holes: one fold normally creates two positions and two perpendicular folds normally create four. Use symmetry to reject options before comparing exact cells.

Restart returns to sheet one with zero points and no mistakes. Double-press Escape to show the spreadsheet-style Boss Key screen, then repeat the shortcut to resume without losing the current round. Best score is stored only in this browser. Try Mosaic Puzzle, Shingoki Puzzle, Thermometers Puzzle, or Stitches Puzzle for another visual logic break.

Methodology & sources

A folded punch begins as one 4 by 4 coordinate. Folds are reversed: right-to-left adds x reflection 3-x, bottom-to-top adds y reflection 3-y, duplicates are removed, and keys are sorted. Five fixed multiple-choice fixtures award 200 each; two wrong choices deadlock; terminal states ignore later input.

Frequently asked questions

Why can one punch make four holes?
Two perpendicular half-sheet folds stack four layers, so unfolding reflects the punch across both center lines.
Which fold should I undo first?
Reverse the most recent fold first, then continue backward through the displayed fold sequence.
Are edge and corner coordinates included?
Yes. The fixed rounds include several positions so the reflection logic is not limited to the center.
Is this a timed test?
No. There is no timer; the score depends only on completing the five disclosed rounds.

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