Ivan Shishkin, Rye (1878)

Problems/CombinatoricsUnreviewed

The truncated chessboard

by Évariste d'aubergine·
20
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
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Consider a chessboard from which two squares at two diagonally opposite corners have been removed.

Knowing that a domino covers two adjacent squares, is it possible to cover the chessboard with dominoes? In other words, is it possible to cover the entire chessboard with dominoes without any of them overlapping?

Capture d’écran 2026 09 02 à 11.48.50

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If we remove two diagonally opposite corners from the chessboard, it has 30 white squares and 32 black squares, or 32 white squares and 30 black squares. In either case, it is impossible to cover the chessboard, because each domino covers one white square and one black square.

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