Henry Ernest Dudeney/Puzzles and Curious Problems/214 - Colouring the Map/Solution

by : $214$

 * Colouring the Map

Solution
The solver will be excused for giving the perfectly reasonable answer of $3$.

However, the tricksy answer given by is:
 * Two!

Proof
It is immediately apparent by inspection of the general central area that at least $4$ colours are needed.

By the Four Color Theorem it is known that no more than $4$ are needed.

Hence, being one short of $4$, there are only $3$ colours in the box.

's reasoning is that if he has two colours in his box, he can create a third colour by mixing the two, but cannot make a fourth.

Hence and so.