"A man walks 5 km north, turns right, walks 3 km, then turns right again and walks 5 km. How far is he from where he started?" Puzzles like this feel dizzying — until you pick up a pen. Sketch each move as you read it, and the man's path draws itself into a shape whose answer you can simply see. Direction-sense questions reward a simple compass sketch far more than mental gymnastics. This chapter gives you the drawing method, the turn rules, and the displacement math that make these questions quick and error-proof.
Direction-sense questions describe someone moving through a series of directions and turns, then ask for their final position or direction relative to the start — or the straight-line distance home. The reliable method is to draw a compass sketch as you read, tracking each leg.
On the Civil Service Exam, direction items appear in Analytical Reasoning, usually 1 to 3 questions. They test spatial reasoning and careful step-tracking, and a good sketch prevents nearly every mistake.
The difficulty is beginner to intermediate. The keys are to fix the compass (North up, East right), understand that left/right turns depend on facing, know that "turn back" means 180°, track net displacement separately in the North-South and East-West directions, and distinguish distance traveled from displacement. This lesson builds each.
After completing this lesson you will be able to:
You should be comfortable with:
A quick refresher on the fixed compass: North is up, South is down, East is right, West is left — keep this constant throughout every problem. And the turn rule you'll use most: a right turn is a 90° clockwise turn from your current facing; a left turn is 90° counter-clockwise. Facing North and turning right → East; facing East and turning right → South, and so on around the clock. Hold these fixed conventions in mind; the whole method depends on them.
Spatial and directional reasoning is a practical everyday skill:
The exam tests direction sense because spatial reasoning and careful step-tracking are core analytical skills used in real navigation.
Let's build the sketch method and the rules.
Mark your starting point, then draw each move roughly to scale in the stated direction, turning as instructed. Keep North up, South down, East right, West left fixed. Adding each leg to the sketch turns a confusing word problem into a picture you can read.
Analogy: A direction puzzle is a story you're illustrating. Each sentence is one pen-stroke on your map. By the end, the picture shows exactly where the traveler stands relative to home — no memory required.
A "right turn" does not always mean "turn toward East." It means a 90° turn to your current right, which depends on where you're already facing:
Left turns go the opposite way (North → West → South → East → North). Picture a clock: right turns step clockwise through the directions, left turns counter-clockwise.
If a problem says someone "turns back" or "turns around," that's a full 180° reversal, not a 90° turn. Facing North and turning back → now facing South. Don't confuse this with a quarter-turn.
For "how far from the start" questions, you often don't need the exact path — just the net displacement. Track two running totals:
Opposite-direction legs cancel. In the opening example (5 km N, then 3 km E, then 5 km S), the North 5 and South 5 cancel, leaving 3 km East — the final position.
A diagonal move (NE, SW, etc.) contributes to both a North-South and an East-West total at once. For a pure 45° diagonal of distance d, it moves about d ÷ √2 (≈ 0.71 × d) in each of the two relevant directions. Add those contributions to your running totals separately.
When the final answer needs the straight-line ("as the crow flies") distance, combine the net North-South and East-West displacements with the Pythagorean theorem:
distance = √((net N-S)² + (net E-W)²).
Net 3 km East and 4 km North → distance = √(3² + 4²) = √25 = 5 km (a 3-4-5 triangle).
These are two different questions, and it's easy to answer the wrong one:
Read carefully which one is asked. For "5 km N, 3 km E, 5 km S": total distance walked = 13 km; displacement from start = 3 km.
With the toolkit built, let's picture, tabulate, and drill.
Direction sense uses rules plus one formula:
| Rule | What to do |
|---|---|
| Fixed compass | N up, S down, E right, W left |
| Right turn | 90° clockwise from current facing |
| Left turn | 90° counter-clockwise |
| Turn back | 180° reversal |
| Net displacement | track N-S and E-W separately; opposites cancel |
| Diagonal leg | ≈ 0.71 × d in each of two directions |
| Straight-line distance | √((net N-S)² + (net E-W)²) |
| Distance vs. displacement | total path vs. straight-line home |
| When the problem… | Do this… |
|---|---|
| lists moves and turns | sketch each leg on a compass |
| says "turn right/left" | rotate 90° from the current facing |
| says "turn back/around" | reverse 180° |
| asks "how far from start" | net displacement (cancel opposites) |
| needs a straight-line distance | Pythagorean theorem on the net legs |
| asks "how far did he walk" | sum all leg distances |
| includes NE/SW moves | split into two directional contributions |
Step 1 — Draw a compass (N up) and mark the start. ↓ Step 2 — Plot each leg in turn, updating the facing direction after every turn (right = 90° clockwise, back = 180°). ↓ Step 3 — Track net North-South and East-West totals, letting opposite legs cancel. ↓ Step 4 — Answer what's asked: final direction (read the sketch), straight-line distance (Pythagorean theorem), or total distance (sum the legs). ↓ Step 5 — Double-check the facing after each turn and whether the question wants distance or displacement.
Why Step 2 matters most: the top error is misreading a turn (assuming "right" always means East). Updating the facing after every turn — ideally on the sketch — keeps the whole path correct.
Example 1. A person walks 4 km East, then 3 km North. How far is he from the start (straight line)? Solution: Net 4 East, 3 North → √(4² + 3²) = √25 = 5 km. Difficulty: ★☆☆☆☆
Example 2. Facing North, a person turns right. Which direction now? Solution: East (right turn from North). Difficulty: ★☆☆☆☆
Example 3 (the classic). A man walks 5 km North, turns right and walks 3 km, turns right again and walks 5 km. How far and in what direction is he from the start? Thinking: N 5 → right (now East) 3 → right (now South) 5. North 5 and South 5 cancel; 3 East remains. Solution: 3 km East of the start. Difficulty: ★★☆☆☆
Example 4 (turn back). Facing East, a person turns back and walks 2 km. Which direction did she walk? Solution: Turn back = 180° → now facing West; she walked 2 km West. Difficulty: ★★☆☆☆
Example 5 (net displacement). A person walks 6 km South, 4 km West, 6 km North. How far from the start? Thinking: South 6 and North 6 cancel; 4 West remains. Solution: 4 km West. Difficulty: ★★★☆☆
Example 6 (Pythagorean finish). A person walks 8 km North, then 6 km East. Find the straight-line distance from the start. Solution: √(8² + 6²) = √100 = 10 km. Difficulty: ★★★☆☆
Example 7 (several turns). Starting facing North: walk 10 km, turn left, walk 10 km, turn left, walk 5 km. Where is the endpoint relative to start? Thinking: N 10 → left (now West) 10 → left (now South) 5. Net: N 10 − S 5 = 5 North; W 10. So 5 km North and 10 km West of start. Solution: Endpoint is 10 km West and 5 km North of the start; straight-line = √(10² + 5²) = √125 ≈ 11.2 km. Difficulty: ★★★★☆
Example 8 (distance vs. displacement). A person walks 7 km East, 7 km West, then 5 km North. How far did he walk, and how far is he from the start? Thinking: Distance walked = 7 + 7 + 5 = 19 km. Displacement: East 7 and West 7 cancel; 5 North remains. Solution: Walked 19 km; 5 km from the start (North). Difficulty: ★★★★☆
Example 9 (facing after multiple turns). A person faces South, turns right, then right again, then left. Which direction is he facing? Thinking: South → right (West) → right (North) → left (West). Solution: West. Difficulty: ★★★★☆
Example 10 (final direction from start). From home, a boy cycles 3 km North, 4 km East. In which direction is he from home (as a compass direction)? Thinking: He is North and East of home → northeast-ish; the exact compass direction is North-East (he's to the NE of home). Solution: North-East of home. Difficulty: ★★★☆☆
Example 11 (shadow/orientation aside). A man walks 12 km North, turns right, walks 5 km. Find his straight-line distance from the start. Solution: Net 12 North, 5 East → √(12² + 5²) = √169 = 13 km (5-12-13 triple). Difficulty: ★★★★☆
Example 12 (full multi-leg). Start facing East: walk 3 km, turn left, walk 4 km, turn left, walk 3 km, turn right, walk 2 km. Find the net displacement. Thinking: E 3 → left (North) 4 → left (West) 3 → right (North) 2. East-West: 3 E − 3 W = 0. North-South: 4 N + 2 N = 6 N. Net = 6 km North. Solution: 6 km North of the start. Difficulty: ★★★★★
Direction-sense puzzles are best solved by sketching a compass (North up, East right) and plotting each leg as you read. Update the facing after every turn — a right turn is 90° clockwise, a left turn 90° counter-clockwise, and "turn back" is a 180° reversal. For "how far from start," track net North-South and East-West displacement, letting opposite legs cancel, and use the Pythagorean theorem (recognizing triples like 3-4-5, 5-12-13) for the straight-line distance. Always distinguish total distance walked (sum of legs) from displacement (straight-line home). Draw it, track the facing, cancel opposites, and answer the right question — and these become quick, reliable points, plus sharper real-world navigation.
| Item | Key point |
|---|---|
| Compass | N up, S down, E right, W left |
| Right turn | 90° clockwise |
| Left turn | 90° counter-clockwise |
| Turn back | 180° reversal |
| Displacement | track N-S and E-W; opposites cancel |
| Straight-line | √((N-S)² + (E-W)²) |
| Triples | 3-4-5, 5-12-13, 8-15-17 |
| Distance vs. displacement | sum of legs vs. straight line |
Does "turn right" always mean go East? No. A right turn is 90° clockwise from your current facing. Facing North, right → East; facing South, right → West. Always track which way you're facing.
What does "turn back" mean? A 180° reversal — the opposite direction. Facing East and turning back means now facing West. It's a U-turn, not a 90° turn.
How do I find the distance from the start? Track net North-South and East-West displacement (opposite legs cancel), then use the Pythagorean theorem: distance = √((net N-S)² + (net E-W)²).
What's the difference between distance and displacement? Distance is the total length you walked (sum of all legs). Displacement is the straight-line distance from start to finish, usually shorter because opposite legs cancel.
How do I handle diagonal moves like Northeast? A diagonal contributes to both a North-South and an East-West total. For a 45° diagonal of length d, add about 0.71 × d to each of the two relevant directions.
Tick them all and direction-sense questions become quick, dependable points — and your real-world sense of direction sharpens too.
Put it to the test with 988 practice questions on this topic.