## Tuesday, June 30, 2009

### Numerical Card Game

This is a game for any plural number of players. It is suggested that there be at least 3 players.

Each player has an identical deck of m notecards, each card in each deck labeled with a different integer from 1 to m, where m is a positive integer large enough to make the game interesting.

Players pair off during the game, where every possible one of n*(n-1)/2 (n= number of players) pairings occurs, and all the pairing occur in some predetermined order.

Each player has two piles of cards: Their "moldy" pile (which starts out with zero cards in it), and their "fresh" pile (which starts out with every one of their cards in it). The cards in their fresh pile are all turned face-down, but can be looked at by the player who owns the deck.

On a move, the two paired-off players each pick any card they choose from their fresh piles, not revealing the cards until both cards are picked.
After both cards are picked, they are turned face-up.

One of three possibilities takes place:

1) If the one player's card number divides the number on the other player's card, then the player with the dividing number (not with the divided number) gets 2 points added to his/her score. The players then both put their cards in their own moldy pile (face-down), unless their card is a 1. If 1, then go to possibility #3.

2) If the cards' numbers are not coprime, and neither number is a divisor nor a multiple of the other card's number, then both players get 1 point added to their scores. The cards are then placed in the players' own moldy piles face-down.

3) If the cards' numbers are coprime, then the players exchange these two cards with each other. The players then each put the newly-gotten card in their own fresh pile, face-down.

(So, if one player has a 1, then he first gets 2 points added to his score, then must exchange the card with his opponent. Both players then put their cards back in their own fresh piles.)
(If both players pick the same number, then both players get 2 points added to their score; then their cards are put in the moldy piles; unless both cards are 1, in which case the cards are exchanged {if you feel this is necessary} and put in the players' fresh piles.)

A player stays in the game until his/her fresh pile is exhausted, or until he/she agrees to drop out.
(A player may agree to drop out if, say, it is clear that his remaining cards in his fresh pile are each coprime to every card remaining in every other player's fresh pile, and he has no 1. Then there would be no point in continuing.)

The game continues until there is one player left.

Highest score wins.

Thanks,
Leroy Quet