mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

Cross diagonal cover problem

Draw with an \(m\times n\) rectangle, split into unit squares. Starting in the top left corner, move at 45° across the rectangle. When you reach the side, bounce off. Continue until you reach another corner of the rectangle:
How many squares will be coloured in when the process ends?

Show answer

If you enjoyed this puzzle, check out Sunday Afternoon Maths LIV,
puzzles about geometry, 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

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

Archive

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