Direction Sense

Navigation using compass directions

110 practice questionsPage updated 5 Apr 2026Review metadata pendingPractice questions

Direction Sense tests your ability to navigate using cardinal directions (North, South, East, West) and their intercardinal directions (NE, NW, SE, SW). These problems involve tracking movement, calculating final positions, determining distances from starting points, and understanding left/right turns based on facing direction. Mastery of direction sense is essential for solving complex logical puzzles involving spatial reasoning.

Key formulas and rules

Distance from starting point = sqrt(horizontal displacement^2 + vertical displacement^2) using Pythagorean theorem

When facing North: Left = West, Right = East, Back = South

When facing South: Left = East, Right = West, Back = North

When facing East: Left = North, Right = South, Back = West

When facing West: Left = South, Right = North, Back = East

After 90 deg right turn from any direction: North->East->South->West->North (clockwise)

After 90 deg left turn from any direction: North->West->South->East->North (anticlockwise)

Shadow direction at sunrise: Towards West; at sunset: Towards East; at noon: Towards North (in Northern hemisphere)

Shadow is opposite to the sun's position: Morning sun in East -> shadow in West

Key concepts

Cardinal and Intercardinal Directions

The four cardinal directions are North (N), South (S), East (E), and West (W). The intercardinal directions are Northeast (NE), Northwest (NW), Southeast (SE), and Southwest (SW). North and South are opposite; East and West are opposite. In direction sense problems, movements are typically described using these eight directions. Remember that directions are relative to your current facing direction, not absolute.

Worked examples

Example 1

A person walks 10m North, then 10m East, then 10m South, then 10m West. How far is he from the starting point and in which direction?

Solution

Step 1: Set starting point as (0, 0). North = +y, East = +x, South = -y, West = -x.
Step 2: After 10m North: position = (0, 10).
Step 3: After 10m East: position = (10, 10).
Step 4: After 10m South: position = (10, 0).
Step 5: After 10m West: position = (0, 0).
Step 6: Final position (0, 0) equals starting position.
Answer: The person is 0m from the starting point (back at start). This forms a square path.

Example 2

Ravi walks 5m towards East, turns left and walks 4m, then turns left again and walks 5m. How far is he from his starting point and in which direction?

Solution

Step 1: Start at (0, 0) facing East.
Step 2: Walk 5m East: position = (5, 0), still facing East.
Step 3: Turn left (from East, left = North): now facing North.
Step 4: Walk 4m North: position = (5, 4), facing North.
Step 5: Turn left (from North, left = West): now facing West.
Step 6: Walk 5m West: position = (0, 4), facing West.
Step 7: Final position is (0, 4), starting was (0, 0).
Step 8: Distance = sqrt(0^2 + 4^2) = sqrt16 = 4m.
Step 9: Direction from (0,0) to (0,4) is North (positive y only).
Answer: Ravi is 4m from starting point towards North.

Example 3

A man faces North. He turns 135 deg clockwise and then 180 deg anticlockwise. Which direction is he facing now?

Solution

Step 1: Initial facing direction: North.
Step 2: 135 deg clockwise from North: 90 deg takes him to East, remaining 45 deg takes him to between East and South (southeast direction, 45 deg south of East).
Step 3: Now facing Southeast (135 deg from North, measured clockwise).
Step 4: 180 deg anticlockwise from Southeast: this is equivalent to facing opposite direction.
Step 5: 180 deg turn from any direction faces the exact opposite.
Step 6: Opposite of Southeast is Northwest.
Answer: The man is facing Northwest.

Example 4

At sunrise, two friends A and B are standing in a park. A's shadow falls exactly on B. If B is to the right of A, which direction is A facing?

Solution

Step 1: At sunrise, sun rises in the East.
Step 2: Shadows fall opposite to the sun, so at sunrise, shadows fall towards West.
Step 3: A's shadow falls on B, so B is in the direction of A's shadow.
Step 4: Therefore, B is to the West of A (since shadow is towards West).
Step 5: Given that B is to the RIGHT of A.
Step 6: If B (West) is to A's right, then A must be facing South.
Step 7: Verification: When facing South, right hand points West. B is West of A, so B is to A's right.
Answer: A is facing South.

Direction Sense

Key formulas and rules

Key concepts

Cardinal and Intercardinal Directions

Left and Right Turns

Calculating Final Position

Distance from Starting Point

Shadow and Sun Position Problems

Complex Movement Patterns

Worked examples

Example 1

Example 2

Example 3

Example 4

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

Key formulas and rules

Key concepts

Cardinal and Intercardinal Directions

Left and Right Turns

Calculating Final Position

Distance from Starting Point

Shadow and Sun Position Problems

Complex Movement Patterns

Worked examples

Example 1

Example 2

Example 3

Example 4

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

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