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

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

Archive

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