Challenge Level

A robot, which is initially facing North, is programmed to travel 5m then turn through $10^{\circ}$, travel 5m then turn through $20^{\circ}$ clockwise, travel 5m then turn through $30^{\circ}$ clockwise, and so on. Each move consists of moving 5m in a straight line and then turning clockwise through an angle which increases by $10^{\circ}$ clockwise at each move.

How far has it travelled by the time it is first facing due East at the end of a move?

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.