This is a three star problem so hopefully it will keep students thinking and testing their reasoning for some while.

Working systematically helps greatly. A table of results shows a very clear pattern, and from there the challenge is to find a way of accounting for that pattern.

This problem offers an excellent opportunity for reasoning from the n case to the n + 1 case.

Seeing the n case result embedded within the n + 1 starting line up.

You may be interested to know that this problem was taken from the book called Maths trails - Visualising