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


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


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