Direction Sense and Ranking: Draw the Constraints

Use a fixed reference

Draw north upward, east right, south downward and west left. Track the person's position separately from the direction they face. Turning right depends on the current facing direction, not on the page's right side.

Worked route

A person walks 6 km east, 8 km north and 6 km west. East and west cancel; the final displacement is 8 km north. Total distance walked is 20 km. Distance travelled and shortest distance from the start are different quantities.

If the route is 6 km east then 8 km north, the straight-line distance is √(6²+8²) = 10 km. The person is northeast of the start, but not necessarily at a 45-degree angle because the components differ.

Turning example

Facing north, turn right, then left, then left. Directions become east, north, west. A 180-degree turn reverses the current direction; two consecutive 90-degree right turns have the same effect.

Ranking in one line

If a person is 7th from the left and 12th from the right, total people = 7+12−1 = 18. Subtract one because the person is counted from both ends. This assumes a single line with distinct positions.

People between two ranks

If A is 5th and B is 14th from the same end, there are 14−5−1 = 8 people between them. If the ranks are given from different ends, first convert to a common reference using the total.

Worked conversion

There are 30 people. P is 8th from the left; Q is 10th from the right, hence 21st from the left. People between them = 21−8−1 = 12.

Practice with explanations

1. Facing west, turn right: north.
2. Walk 5 m south then 12 m east: shortest distance 13 m, direction southeast.
3. A person is 9th from each end: total 17.
4. In a line of 25, 6th from the right is 20th from the left.
5. Positions 4 and 11 from the same end: 6 people between.

Avoid hidden assumptions

Do not infer someone's gender, age or relationship from a name alone. Do not assume a circular arrangement has a leftmost seat. In directions, distinguish facing direction from displacement. In ranking, check whether ties are possible and whether the question supplies enough information for a unique answer.