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Weekly Problem 51 - 2008

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2
$3$, $4$ and $5$ are on diagonals, so can't go in the centre square (since each number must appear just once on each diagonal).

So the number in the centre sqaure must be a $1$ or a $2$. Suppose it was a $1$. Then we must put $1$s as shown in red:

solution 1
and $2$s as shown in blue:
solution 2
So there must be a $1$ in place of one of the crosses:
solution 3
But the top and bottom cross couldn't be $1$, since they are on the diagonal, and the middle cross can't be $1$ since it's on the $3$rd row (where there's already a $1$). So $1$ can't go in the centre square after all!

$2$ goes in the centre square.

This problem is taken from the UKMT Mathematical Challenges.

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