By Barnette D.W.

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**Extra resources for A 2-manifold of genus 8 without the W v-property**

**Example text**

To play well, therefore, a player must try to get as much information as he can, at the same time revealing as little as possible, until he thinks he knows enough to call. The delightful feature of the game is that each player must resort to occasional bluffing, that is, asking about a card he himself holds. If he never bluffed, then whenever he asked about a card not in his opponent's hand, the opponent would immediately know that card must be the hidden o n e a n d would call and win. Bluffing is therefore an essential part of strategy, both for defense and for tricking the opponent into a false call.

1 is divisible by n if, and only if, n is a prime. For example, if n equals 13, then (n - 1) ! 1 becomes 12! 1 = 479,001,601. It is easy to see that 12! is not a multiple of 13, because 13 is prime and the factors of 12! do not include 13 or any of its multiples. But, astonishingly, the mere addition of 1 creates a number that is divisible by 13. Wilson's theorem is one of the most beautiful and important theorems in the history of number theory, even though it is not an efficient way to test primality.

The boldface numbers near the marks give the number of cards you hold. As before, pick the appropriate ring and spin the bobby pin. If it stops in the portion of the ring that extends from the proper mark clockwise to the horizontal line, call the card previously asked. If it does not stop in this portion of the ring, your next action depends on whether your opponent has just one card or more than one. If he has only one, call the other unknown card. If he has more than one (and you have at least one card), you must ask.

### A 2-manifold of genus 8 without the W v-property by Barnette D.W.

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