mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

Polygraph

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

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

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021

Advent calendar 2020


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2024