Before starting college I read Paul Zeitz’s The Art and Craft of Problem Solving (a must read book along with the books by Arthur Engel and Terence Tao) and after the first example to illustrate *Psychological Strategies* he writes (pp. 15):

*Just because a problem seems impossible does not mean that it is impossible. Never admit defeat after a cursory glance. Begin optimistically; assume that the problem can be solved. Only after several failed attempts should try to prove impossibility. If you cannot do so, then do not admit defeat. Go back to the problem later.*

And today I will share a problem posed by August Ferdinand Möbius around 1840:

**Problem of the Five Princes**:

There was a king in India who had a large kingdom and five sons. In his last will, the king said that after his death the sons should divide the kingdom among themselves in such a way that the region belonging to each son should have a borderline (not just a point) in common with the remaining four regions. How should the kingdom be divided?

The hint is in the title of this blog post. The solution is easy, hence I won’t discuss it here. The reader is invited to write the solution as a comment to this post.

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*Related*

A simple example of the regions connected to a point will be a circle divided in 5 parts. But it was really hard to connect each shape with the borderlines of remaining shapes. Although I did it for 4.

And I just found out that its impossible to draw 5 shapes which are all connected in this manner.

So this time intuition is correct! 🙂

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Going to mull this one over today.

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