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 2024

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2025