Sixteen unit squares are arranged to form a square array as shown in the diagram.

What is the maximum number of diagonals that can be drawn in these unit squares so that no two diagonals share a common point (including endpoints)?

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.