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Problem 633
Classify those triangles which can only be cut into a square number of congruent triangles.
Source: erdosproblems.com/633
- Geometry
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Solved, AnsweredAn accepted solution exists. Settled in another form, for example when its parts resolve differently or the question is open-ended.
Solved by the classification of Beeson, Laczkovich, and Zhang, Theorem 1, arXiv:2604.03609v3. The site page accessed records the solution, and the authors' primary paper supplies the argument. The eight families in that theorem are exactly the triangles admitting a nonsquare tiling; all other triangles answer this question. The accepted claim is Beeson–Laczkovich–Zhang 2026.