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PreprintCC BY-NC-ND 4.0HAL

On solutions to the Mondrian Puzzle

  • Noah Lebowitz-Lockard
  • Gérald Tenenbaum
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Abstract

We show that for a positive proportion of integers n, it is impossible to partition an n × n square into distinct rectangles with equal area and integer side lengths. We also obtain an analogue of this result in dimension 3.

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Cite

BibTeXRIS
BibTeX
@misc{lebowitzlockard2026solutions,
  title = {{On solutions to the Mondrian Puzzle}},
  author = {Noah Lebowitz-Lockard and Gérald Tenenbaum},
  howpublished = {HAL},
  year = {2026},
  month = aug,
  url = {https://hal.science/hal-05729522v2},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - On solutions to the Mondrian Puzzle
AU  - Noah Lebowitz-Lockard
AU  - Gérald Tenenbaum
PY  - 2026
DA  - 2026/08/27
PB  - HAL
UR  - https://hal.science/hal-05729522v2
AB  - We show that for a positive proportion of integers n, it is impossible to partition an n × n square into distinct rectangles with equal area and integer side lengths. We also obtain an analogue of this result in dimension 3.
ER  -