1) Mobius raised this classical problem in about 1840. As amended it reads: a king with five argumentative arrogant sons and five bright reasonable daughters died. His Will gave the kingdom to his five sons provided they, within thirty days, divided it into five parts such that each part had a common boundary with the other four. If they couldn’t do this, the kingdom as a single unit would go to his daughters to rule together. Of course, the sons quarreled and one after the other died mysteriously until just one remained. But even the best mathematicians in the realm couldn’t find a way to divide the kingdom as required, and after the expiry of the thirty days the kingdom passed to the princesses who governed it peacefully and happily. Question: was there a mathematical way for the princes to do what the Will asked?

2) If the answer to question 1 above is yes, what is the answer to the question: are four colours enough to make any map on a plane surface unambiguous?

The answers to October’s puzzles were supplied in the October issue.

Here are the answers to this month’s puzzles:

1) Try it. The answer is no.

2) If the answer to question one is yes, then more colours are needed. But the answer to question one is no and only four are required.

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