The Riddle of Scheherazade

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Oplossing week 49 A tacit assumption in the formulation of the problem is that the relationship of friendship is symmetric: two people are friends iff each is a friend of the other. However, friendship is not reflexive: no one is his own friend.


Reference R. Solution 1 A person at the party can have 0 up to N-1 friends at the party. However, if someone has 0 friends at the party, then no one at the party has N-1 friends at the party, and if someone has N-1 friends at the party, then no one has 0 friends at the party. Hence the number of possibilities for the number of friends the N people at the party have must be less than N.

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Hence two people at the party have the same number of friends at the party. Solution 2 Note, as in the first solution, that in general, in a group of N people, a fellow may have 0, 1, 2, Assume to the contrary that all N people have different number of friends.

Scheherazade, Op. 35: I. The Sea and Sinbad's Ship

Scheherazade, we find, has gotten back into hot water with the king, and is once more in danger of losing her But, thinking quickly, she tempts the king to stay her execution by posing him the most delightfully devious mathematical and logic puzzle ever invented. They keep "him "guessing for many more nights until the fatal hour has passed, and "she "keeps her head.

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