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 

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

Sunday Afternoon Maths LXV

Cryptic crossnumber #1
Breaking Chocolate
Square and cube endings

List of all puzzles


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


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2019