Sunday Afternoon Maths LIX

 Posted on 2017-04-23 

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

Elastic numbers

Throughout this puzzle, expressions like \(AB\) will represent the digits of a number, not \(A\) multiplied by \(B\).
A two-digit number \(AB\) is called elastic if:
  1. \(A\) and \(B\) are both non-zero.
  2. The numbers \(A0B\), \(A00B\), \(A000B\), ... are all divisible by \(AB\).
There are three elastic numbers. Can you find them?

Show answer & extension

Square pairs

Source: Maths Jam
Can you order the integers 1 to 16 so that every pair of adjacent numbers adds to a square number?
For which other numbers \(n\) is it possible to order the integers 1 to \(n\) in such a way?

Show answer

If you enjoyed these puzzles, check out Sunday Afternoon Maths LXVII,
puzzles about regular shapes, or a random puzzle.


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


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


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