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


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


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