A boy is facing north-east. He turns 135° clockwise, then turns 180° anticlockwise, and finally turns 90° clockwise. Which way is he facing at the end?

Measure every heading clockwise from north, so north-east is 45°. Turning 135° clockwise: 45 + 135 = 180°, which is south. Turning 180° anticlockwise: 180 − 180 = 0°, which is north. Turning 90° clockwise: 0 + 90 = 90°, which is east. The traps: west comes from taking the last turn the wrong way round, south is where he stood after only the first turn, and north-west comes from adding all three turns as if they were all clockwise.