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Magical Products

Age 11 to 14 Short
Challenge Level

Put the nine numbers below onto a 3 by 3 grid so that each number occupies one space, and the product of every row, column and diagonal is equal to 1.

$$1         2         3         6         \frac{1}{6}         \frac{1}{3}         \frac{1}{2}         \frac{2}{3}         \frac{3}{2}$$ 
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.