mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

The mutilated chessboard

You are given a chessboard where two diagonally opposite corners have been removed and a large bag of dominoes of such size that they exactly cover two adjacent squares on the chessboard.
Is it possible to place 31 dominoes on the chessboard so that all the squares are covered? If yes, how? If no, why not?

Show answer & extension

Tags: chess
If you enjoyed this puzzle, check out Sunday Afternoon Maths XV,
puzzles about chess, or a random puzzle.

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2025

Advent calendar 2024

Advent calendar 2023

Advent calendar 2022


List of all puzzles

Tags

advent multiplication sum to infinity partitions range spheres the only crossnumber floors square grids even numbers cube numbers circles coordinates integration surds rugby lists tiling powers square roots combinatorics logic integers binary regular shapes decahedra parabolas menace geometry dominos routes calculus money xor mean products determinants odd numbers digits grids consecutive numbers chalkdust crossnumber expansions pascal's triangle functions indices crosswords star numbers games coins square numbers geometric mean christmas cryptic clues trigonometry geometric means symmetry angles multiples planes shape people maths cryptic crossnumbers quadrilaterals dodecagons numbers medians books balancing speed gerrymandering perimeter percentages averages quadratics elections cubics palindromes polynomials cards axes sequences perfect numbers wordplay irreducible numbers crossnumbers 2d shapes ave folding tube maps shapes proportion means dates colouring area fractions probabilty tangents sport polygons hexagons differentiation factorials median triangle numbers digital products sets number prime factors squares albgebra chocolate remainders complex numbers digital clocks taxicab geometry time ellipses sums matrices addition pentagons multiplaction squares algebra neighbours bases graphs prime numbers unit fractions 3d shapes scales dice tournaments arrows factors rectangles lines clocks triangles chess volume doubling probability consecutive integers division

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2026