Turning squares

Each square on a chessboard contains an arrow point up, down, left or right. You start in the bottom left square. Every second you move one square in the direction shown by the arrow in your square. Just after you move, the arrow on the square you moved from rotates 90° clockwise. If an arrow would take you off the edge of the board, you stay in that square (the arrow will still rotate).
You win the game if you reach the top right square of the chessboard. Can I design a starting arrangement of arrows that will prevent you from winning?

Show answer

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

Chessboard squares

It was once claimed that there are 204 squares on a chessboard. Can you justify this claim?

Show answer & extension


Show me a random puzzle
 Most recent collections 

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles


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


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2020