mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

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

Archive

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

Tags

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

Archive

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