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

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

Archive

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