Today Puzzle #786
Puzzle No. 786鈥� Monday 20 July
What is the smallest number of colours needed to paint the faces of a regular dodecahedron so that adjacent faces have different colours?
Today’s #PuzzleForToday has been set by UK Mathematics Trust , a charity based at the University of Leeds whose aim is to advance the education of young people in mathematics, primarily through the organisation and running of national mathematics competitions.
Click here for the answer
4; each face is adjacent to a ring of five other faces, each touching two other faces of this ring. Three different colours are needed for the colours of the faces in this ring, as their colours cannot just alternate between two colours. A fourth colour is then needed for the face they surround. So at least four colours are needed. It is easy to see that four colours are sufficient.
-
![]()
Puzzle for Today 鈥� Index
Find all of the currently available Puzzles for Today, with answers.
More fiendish brain-teasers and quizzes on 大象传媒 Radio...
-
![]()
From autumn leaves to the magic roundabout: test yourself with our favourite quizzes.
-
![]()
We asked the intelligence agency to set our listeners a code-cracking challenge... Can you solve it?
-
![]()
Quiz: How many of these Mastermind music questions can you answer?
Here's a chance to find out whether your specialist subject on Mastermind could be the entire history of music.
-
![]()
Six conundrums to grapple with, including the Riddle of the Sphinx. Try not to forfeit your life...
