Start by drawing an r-by-r grid on paper.

(I suggest an r of 5 or so for beginners.)

Put a "1" in each square of the left-most column

and in each square of the top-most row of the grid.

On each move the player chooses any one of the grid's

empty squares. This square is (m,n), which is the

square in the mth column from the left side of the

grid and in the nth row from the top.

The player then sums up all the integers already

written in the mth column and nth row.

So, if the grid looks like this, where the * is

the square the player has chosen to fill in next

with an integer,

1 1 1 1

1 3

1 * 6

1 6

then the sum of the column 2's terms and row 3's

terms is 1+3+6 +1+6 = 17. Let this sum be s.

Next the player counts the number of integers in the

squares to the left of (m,n) and above (m,n)

(ie, the squares with coordinates (j,k), 1 <=j <=m,

1 <=k <=n) which are coprime to s.

If the count is c integers in the given rectangle

which are coprime to s, then the player writes c

in square (m,n).

Play continues until there is an integer in every

square of the grid.

The player's score is the number in the last square

he/she fills in.

## Sunday, September 21, 2008

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