One two three

Each point on a straight line is either red or blue. Show that it's always possible to find three points of the same color in which one is the midpoint of the other two.

Show answer & extension

Tags: colouring

Coloured pins

A bowling alley has a mixture of red and blue pins. Ten of these pins are randomly chosen and arranged in a triangle.
Will there always be three pins of the same colour which lie on the vertices of an equilateral triangle?

Show answer & extension

Tags: colouring


Draw a regular polygon. Connect all its vertices to every other vertex. For example, if you picked a pentagon or a hexagon, the result would look as follows:
Colour the regions of your shape so that no two regions which share an edge are the same colour. (Regions which only meet at one point can be the same colour.)
What is the least number of colours which this can be done with?

Show answer & extension


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


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


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