Click here to win prizes by solving the puzzle Advent calendar.
Click here to win prizes by solving the puzzle Advent calendar.



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


Show me a random puzzle
 Most recent collections 

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

Sunday Afternoon Maths LXV

Cryptic crossnumber #1
Breaking Chocolate
Square and cube endings

List of all puzzles


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


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2019