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 2023

Advent calendar 2022

Advent calendar 2021

Advent calendar 2020


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2024