Here is a game for 2 or more players.

Start with a deck of cards with n cards labeled 1 to n.

On each move the player whose move it is draws one card.

Do not replace card.

Write down first number drawn.

On each move (after the first) a player draws a card to get

the value k.

He/she may either add k to the written down number,

subtract k from the written down number (as long as the

difference is not negative), multiply k with the written down

number, or divide the written down number by k

(as long as k divides evenly into the written down number).

A new written down number, in this way, is obtained.

A player gets a point every time the written down number

they generate is a prime number.

Play continues for a total of n moves (when the deck

of cards runs out).

Here is an example game (for 2 players). (n=10)

First move: Player 1 draws 7. (Gets a point)

2nd move: Player 2 draws a 4. 7 + 4 = 11. (Gets a point)

3rd move:Player 1 draws a 1. 11/1 = 11. (Gets a point)

4th move: Player 2 draws a 9. 11-9 = 2. (Gets a point)

5th move: Player 1 draws a 2. 2/2=1. (No point)

6th move: Player 2 draws a 3. 1*3 = 3. (Gets a point)

7th move: Player 1 draws a 10. 3+10=13. (Gets a point)

8th move: Player 2 draws a 5. 13*5= 65. (No point)

9th move: Player 1 draws a 8. 65+8=73. (Gets a point)

10th move: Player 2 draws a 6. 73-6=67. (Gets a point)

So player 1 gets 4 points, player 2 gets 4 points too, a tie.

(What do you expect when I play myself?)

In practice, it would probably be better to have a higher n.

Also, if you prefer a pure-strategy game without luck, you can,

instead of using cards, have the integers "drawn" be from a

predetermined sequence (such as 1,2,3,4,....,n or such as

the primes taken in order.)

thanks,

Leroy Quet

## Saturday, September 20, 2008

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