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Geometry dissection — rules and where to play

GEOMETRY DISSECTION · Dissection puzzle / Geometric cut

Cut a figure into pieces and reassemble another, or find a length. It tests area conservation and transform vision.

Origin
—
Difficulty
★★★★★ 3–5 / 5
Time
10–40 min
Grid
—
Sites
1

Rules

  1. A figure and a cut/reassemble goal (e.g. two squares into one).
  2. Pieces may rotate and flip; area is conserved.
  3. Classics: equal-area transforms, missing-area, the haberdasher triangle.
  4. Many contest problems hide the cut lines; the diagram is a hint, not the full answer.

How to start

Use area conservation

Total area is invariant; list each piece's area relation first.

Find symmetry and midpoints

Many cuts run along an axis or midpoint — draw helpers.

Go to extremes

For parametric ones, plug special values (0, equal, square) to feel the law.

Name the theorem

Pythagoras, similar triangles, or van Aubel often close the gap faster than guessing cuts.

Where players get stuck

  • Assuming shape change means area change, missing conservation.
  • No auxiliary lines, guessing cuts instead of seeing them.
  • Forgetting flips are allowed when the puzzle permits reflection.

Play Geometry dissection

1 site
Erich's Puzzle PalaceFree

Erich Friedman's long collection — 130-plus types, all over the map.

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About this page
  • Last updated 2026-09-22
  • Source Curated compilation of established puzzle rules and listed third-party play sites
  • Audience Players learning Geometry dissection rules or looking for online sites to play
  • Covers Rules summary, how to start, common pitfalls, and the dedicated play sites listed on this page
  • Does not cover Hosted puzzles, worked solutions, official contest rankings, third-party uptime or pricing guarantees
  • Not advice This page is puzzle reference content only. It does not constitute financial, legal, medical or other professional advice.
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