Introduction
Direction-based puzzles require you to track movements and turns (north, south, east, west; left/right turns) or determine relative positions after a series of moves. These are excellent for testing spatial imagination, step-tracking, and conversion between facing-direction and absolute-map directions.
You will often be asked to find final location, relative direction between two people, distance moved, or orientation after a sequence of turns.
Pattern: Direction-Based Puzzle
Pattern
The key idea is to convert each instruction into a vector or turn, track the current facing direction, and update the position step-by-step (or draw a quick map).
Typical clue types include: 1) “X walks 5 m North, turns right, walks 3 m.” 2) “A starts facing East, makes two left turns - which way is A facing now?” 3) “Who is to the south-east of whom after the moves?”
Step-by-Step Example
Question
Ravi starts at point P and walks 8 m North. He then turns right and walks 6 m. He then turns right again and walks 8 m. Finally he turns left and walks 4 m. What is Ravi’s final direction from the starting point P?
Options:
- A) East of P
- B) West of P
- C) North of P
- D) South of P
Solution
Step 1: Convert moves to vectors
Start at P (0,0). Walk 8 m North → new position (0, +8).Step 2: First right turn (facing East) and move
From facing North, right → East. Walk 6 m → position (+6, +8).Step 3: Second right turn (now facing South) and move
Facing East, right → South. Walk 8 m → position (+6, 0) because +8 - 8 = 0.Step 4: Final left turn (now facing East) and move
Facing South, left → East. Walk 4 m → final position (+10, 0).Final Answer:
East of P → Option AQuick Check:
Net displacement along X = +10 (east), along Y = 0 → directly east of start ✅
Quick Variations
1. Movement with turns while maintaining a facing-direction anchor (use relative turns).
2. Multiple people start from different points and move - find who ends up north-west of whom.
3. Mixed distance + grid steps (unit steps) - convert to vectors and sum.
4. Orientation-only questions - after sequence of left/right turns, what direction is the person facing?
Trick to Always Use
- Step 1 → Anchor the start point on a small sketch or use coordinates (x,y).
- Step 2 → Convert every straight move to a vector (North = +y, South = -y, East = +x, West = -x).
- Step 3 → When turns are given, update facing direction before converting the next move to a vector.
- Step 4 → After processing all moves, compare final (x,y) to origin: sign of x gives East/West, sign of y gives North/South; zero means aligned on that axis.
Summary
Summary
- Convert each instruction into a vector or a turn - track (x,y) changes step-by-step.
- Maintain current facing direction; apply left/right as rotations before next move.
- Final direction from origin determined by sign of net X and Y (e.g., +x & +y → North-East).
- Use a tiny sketch for quick verification and perform a one-line Quick Check: compare each original clue with final coordinates.
Example to remember:
Use coordinates: North = (0,+), East = (+,0). After summing vectors, interpret (x,y). If x>0 and y=0 → East of origin.
Hint: Two right turns with equal up-down moves bring you horizontally aligned on the right side.
Common Mistakes: Assuming the last direction same as the start without checking displacement.