Direction Sense Test: Tracking Turns, Distance and Final Direction

Direction questions are easy to get wrong in your head and easy to get right on paper. Draw a small cross with north at the top, south at the bottom, east on the right and west on the left. Then treat the walk as moves on a grid: east is +x, west is −x, north is +y and south is −y.

Every question asks for one or both of two things: the shortest distance from the start, and the direction of the end point from the start. Both come from the net east–west and net north–south distances, so the first job is always to add those up.

"Turn left" and "turn right" are relative to the person's current direction, not to the page. A right turn is a quarter-turn clockwise and a left turn is a quarter-turn anticlockwise.

The trap cases are facing south or west. Someone walking south who turns right ends up walking west, which is the opposite of what the drawing seems to suggest if you forget to rotate.

After adding up the moves, the person is some distance east or west and some distance north or south of the start. These two distances are at right angles, so the straight-line distance is √(x² + y²). Learn the common Pythagorean triples (3-4-5, 5-12-13, 6-8-10, 8-15-17) and many answers become instant.

Because the end point is 8 m east and 8 m south, it lies exactly south-east of the start.

The final direction is read from the signs of the net distances. Positive x and positive y is north-east; positive x and negative y is south-east; and so on. If one of them is zero, the answer is a plain direction such as north. Exams use "north-east" for any point that is both north and east, but when the two distances are equal the point is exactly on the diagonal.

The end point is as far west as it is north, so it lies north-west of the start.

Questions with two people work the same way: place both on the grid and measure between them.

Shadow questions add one fact: the sun rises in the east and sets in the west. A morning shadow therefore points west and an evening shadow points east. Work out which way the shadow points, then use the left and right table to find the direction the person faces.

For example, if a man's evening shadow falls straight in front of him, the shadow points east, so he is facing east. If his morning shadow falls behind him, it points west and he is facing east as well.

• ✘ Turning relative to the page instead of the walker's direction.
• ✘ Adding the lengths of the legs instead of using net distances.
• ✘ Giving the direction of the start from the end when the question asks the reverse.
• ✘ Forgetting that morning shadows point west.

Related reasoning methods: coding-decoding by letter shift and calendar problems.

Which way is a right turn when facing south?

West. A right turn is always a quarter-turn clockwise on the compass: north to east, east to south, south to west and west to north. A left turn is anticlockwise: north to west, west to south, south to east and east to north.

Where does a shadow fall at noon in India?

Exam questions treat noon as the time with no usable shadow direction, and most questions use morning or evening instead. In the morning the sun is in the east and shadows fall west; in the evening the sun is in the west and shadows fall east.

All problems and solutions on this page are original. No outside facts are relied on; every numeric answer is recomputed by software before publishing.