Henry Ernest Dudeney/Modern Puzzles/140 - The Four-Colour Map Theorem

by : $140$

 * The Four-Colour Map Theorem
 * In colouring any map under the condition that no contiguous countries shall be coloured alike,
 * not more than four colours can ever be necessary.
 * Countries only touching at a point ... are not contiguous.


 * I will give, in condensed form, a suggested proof of my own
 * which several good mathematicians to whom I have shown it accept it as quite valid.
 * Two others, for whose opinion I have great respect, think it fails for a reason that the former maintain will not "hold water".
 * The proof is in a form that anybody can understand.
 * It should be remembered that it is one thing to be convinced, as everybody is, that the thing is true,
 * but quite another to give a rigid proof of it.

Also see

 * Four Color Theorem