Here is a simple mathematical game.

(For any number of players.)

You start with an n-by-n grid drawn on paper.

(I suggest an n of about 5 for a 2-player game.)

Players take turns writing, in order, the integers 1, 2, 3,...,n^2

into any of the empty squares of the grid.

(So, for a 2-player game, one player writes the odd integers, the

other player writes the even integers.)

Play continues until every square of the grid has an integer in it.

A player gets a point every time {the integer he/she is writing in a

square} plus {a lower integer in an immediately adjacent

(in the directions of left, right, above, or below) square} is a prime.

For example, if we have the grid, in-part, below:

3 5 2

1 . 6

4

and a player places an 12 into the grid like this:

3 5 2

1 12 6

4

the player gets 2 points for this move, since 12+1 and 12+5 are primes.

And, obviously, the player with the highest score at the end of the

game

is the winner.

What is a good strategy for this game, especially for a 2-person game?

thanks,

Leroy Quet

## Saturday, September 20, 2008

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## 1 comment:

I really like the game. I did spend some time to think about arrays of prime numbers and related objects.

In this context, I did formulate the following conjecture:

http://www.primepuzzles.net/conjectures/conj_042.htm

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