Saturday, October 30, 2010

Prime Target Game

A game for any plural number of players: (Number of players = m.)

Draw m*k+1 incrementally larger concentric circles on a piece of paper, where k is some positive integer >= 2.

Subdivide the circles by drawing n equally spaced rays from their center, where n is at least 6, say.

(So now you should have a target.)

The players start the game by taking turns, and each player on a turn places an integer -- 1 to n and which has not been written down earlier in the game -- in an empty pie-shaped wedge in the central circle. After n moves, there should be a permutation of (1,2,3,...,n) in the central circle, one integer per wedge.

In the second part of the game, the players take turns, each player "completing a ring" on a move. By completing a ring, the player fills in the n sections of the innermost *empty* ring. The player fills in each section of the ring either with the sum of (the integer immediately adjacent to the section, but in the next ring inward) and (the integer one position clockwise to the section, but in the next ring inward), or with the absolute value of the difference between these particular two integers (in the next ring inward).

8 = 2+6.
(The 8 could have been a 4.)

After the ring is completed, the player gets the number of primes in his latest ring added to his score, OR, if there is exactly one prime in his ring (no more, no fewer), he gets the value of that prime added to his score.

After all rings are completed, the game is over. Largest score wins.

Leroy Quet

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