Saturday, September 20, 2008

Prime Sum Game

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

1 comment:

Simone Severini said...

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