Direction sense test

Direction problems track a person's position and facing direction. Use a mental compass with North at the top, East on the right, South at the bottom and West on the left; the eight directions also include North-East, South-East, South-West and North-West.

A right turn is clockwise and a left turn is anticlockwise. A 45 degree turn moves between neighbouring points of the eight-point compass, and 90 degrees moves two points.

For distance problems add up the east-west and north-south displacements separately: a walk of 8 km west and 6 km south ends sqrt(8^2 + 6^2) = 10 km from the start (Pythagoras). For the direction of the end point from the start use the signs of the two displacements, and the direction of the start from the end is the opposite.

Shadow rule: after sunrise the sun is in the east, so shadows point west; before sunset the sun is in the west, so shadows point east. If a morning shadow falls to your right, you face North.

Exam trap: the final distance is not the total length walked, and the start is in the opposite direction to the end point.