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 2020

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

List of all puzzles


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


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2021