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Order Arrangement Puzzle

Introduction

Order arrangement puzzles ask you to place people or objects in a line or circle using relational clues (e.g., "A is left of B", "C sits between D and E"). These problems test logical sequencing and careful interpretation of directional language.

Mastering this pattern helps you convert textual clues into a visual order quickly - a must for many aptitude sections.

Pattern: Order Arrangement Puzzle

Pattern

Key concept: Translate each verbal relation into a positional constraint, build a partial order, then merge constraints step-by-step until a full order emerges.

Common clue types:

  • Direct adjacency (A is to the left of B; A sits next to B)
  • Relative order (A is immediately left of B; A is somewhere left of B)
  • Positional extremes (A is at the extreme left/right)
  • Between clues (A is between B and C)
  • Facing direction differences (facing north vs facing south reverses left/right)

Step-by-Step Example

Question

Five people A, B, C, D and E are sitting in a row facing north. D sits at the extreme left. A is to the left of B but to the right of C. E sits next to B. Who is sitting in the middle?

Solution

  1. Step 1: Note facing direction

    Facing north → left/right are the usual left/right as described.

  2. Step 2: Place the extreme

    D is at extreme left → row so far: D _ _ _ _

  3. Step 3: Use “A is left of B but right of C”

    That means order (from left → right): C - A - B (C left of A, A left of B). Insert into the remaining slots.

  4. Step 4: Place E next to B

    B must have E as a neighbour. Remaining arrangement slots after placing D at left are: D _ _ _ _. Fit C, A, B in sequence into these slots such that B has an adjacent spot for E.

  5. Step 5: Construct full order

    Try positions: D C A B E → satisfies D at extreme left; C left of A left of B; E next to B. This yields the row (left → right): D, C, A, B, E.

  6. Final Answer:

    A is sitting in the middle.

  7. Quick Check:

    Middle position (3rd) = A. Check clues: D extreme left ✅, C left of A and A left of B ✅, E next to B ✅

Quick Variations

1. People facing south - left/right reverse; always apply facing direction first.

2. Circular arrangements - there is no extreme left/right; use relative positions and modular counting.

3. Mixed adjacency and distance clues - convert "two to the left of" to fixed gap constraints.

4. Multiple valid orders - some clue sets permit more than one valid arrangement; check whether the question asks for all possible answers or a guaranteed element (e.g., who is definitely in middle).

Trick to Always Use

  • Step 1 → Draw a short line and mark definite extremes or fixed positions first (extreme left/right, between constraints).
  • Step 2 → Place blocks for sequences mentioned (e.g., C-A-B) rather than trying to place each person individually.
  • Step 3 → Use adjacency to attach remaining people and verify against all clues after each placement.

Summary

Summary

  • Convert verbal relations into positional constraints (use a sketch or slots).
  • Place fixed positions (extremes, explicit middle) first to reduce possibilities.
  • Treat sequences (A left of B left of C) as blocks and fit them into available slots.
  • Always re-check every clue after building a candidate order; reverse left/right if facing direction is south.

Example to remember:
Given D at extreme left and sequence C-A-B with E adjacent to B → D, C, A, B, E is a valid arrangement and A sits in the middle.

Practice

(1/5)
1. Five friends P, Q, R, S and T are sitting in a row facing north. Q is to the immediate right of P. R is at one end of the row. S is to the left of T but not next to R. Who is sitting in the middle?
easy
A. Q
B. S
C. T
D. P

Solution

  1. Step 1: Facing north

    Left/right directions remain normal.

  2. Step 2: Place R

    R is at one end → start with R _ _ _ _.

  3. Step 3: Q is immediate right of P

    Form a block (P-Q).

  4. Step 4: S is to the left of T but not next to R

    Place S after P-Q block and T at the end: R, P, Q, S, T satisfies all clues.

  5. Step 5: Check middle position

    Middle = 3rd → Q.

  6. Final Answer:

    Q → Option A

  7. Quick Check:

    Q right of P ✅, R at end ✅, S left of T and not beside R ✅
Hint: Always arrange fixed pairs first, then apply non-adjacency clues.
Common Mistakes: Placing S next to R violating the non-adjacency clue.
2. Six people A, B, C, D, E and F sit in a line facing north. B is third to the left of F. A is to the right of F but not adjacent. D is between B and C. Who sits at the extreme left?
easy
A. A
B. B
C. C
D. E

Solution

  1. Step 1: Interpret 'B is third to the left of F'

    So positions must satisfy B _ _ F (B is 3 positions left of F).

  2. Step 2: Place D between B and C

    We need B-D-C as contiguous triple (B left, D middle, C right).

  3. Step 3: Place A to the right of F but not adjacent

    A must be somewhere right of F with at least one person between them.

  4. Step 4: Build a valid order

    One arrangement that satisfies all clues is: B, D, C, F, E, A (positions 1→6). Check: B (pos1) is third left of F (pos4); D is between B and C (pos2 between pos1 & pos3); A (pos6) is to the right of F (pos4) and not adjacent (E at pos5 in between).

  5. Final Answer:

    B → Option B

  6. Quick Check:

    B at extreme left (pos1) ✅; B is 3 left of F (1 → 4) ✅; D between B & C ✅; A right of F and not adjacent ✅
Hint: Place fixed-distance patterns (like 'third left') first, then insert adjacency blocks and non-adjacent constraints.
Common Mistakes: Putting A adjacent to F or not ensuring D sits between B and C.
3. Five persons A, B, C, D, and E are sitting in a row. C is to the immediate right of A. D is to the right of C but not at the end. B is at one end. Who is sitting at the other end?
easy
A. A
B. D
C. E
D. C

Solution

  1. Step 1: Form block A-C

    C sits immediately right of A → (A-C).

  2. Step 2: D is to the right of C but not at the end

    So D must be somewhere to the right but not final position.

  3. Step 3: B sits at one end

    Place B at left end → sequence B, A, C, D, E fits all clues.

  4. Final Answer:

    E → Option C

  5. Quick Check:

    C right of A ✅, D right of C (not at end) ✅, B at left end ✅
Hint: Build pair relationships (A-C) before checking ends.
Common Mistakes: Placing D at the end.
4. Six people L, M, N, O, P, and Q sit in a row facing north. L is third to the left of P. O is not at any end. M sits second to the right of Q. Who are sitting in the two middle positions?
medium
A. L and O
B. Q and P
C. M and O
D. Q and M

Solution

  1. Step 1: Interpret clues

    ‘L is third to the left of P’ → pattern L _ _ P (difference of 3).
    ‘M sits second to the right of Q’ → pattern Q _ M (M is two seats to right of Q).
    ‘O is not at any end’ → O must be placed in positions 2-5.

  2. Step 2: Construct a valid placement

    Place Q at pos1 so M becomes pos3 (Q pos1, M pos3). To satisfy L _ _ P, place L at pos2 and P at pos5 (L pos2, P pos5). Put O at pos4 (not an end). The remaining person N goes to pos6. Full order: Q, L, M, O, P, N.

  3. Step 3: Verify all clues

    L (pos2) is third left of P (pos5) ✅; M (pos3) is second right of Q (pos1) ✅; O (pos4) is not at an end ✅.

  4. Final Answer:

    M and O → Option C

  5. Quick Check:

    Middle positions for six people are 3rd & 4th → pos3=M and pos4=O ✅
Hint: Place the fixed-distance clues first (third/second), then slot the 'not end' person into a middle spot.
Common Mistakes: Miscounting the gap for 'third to the left' (should be two people between).
5. Seven friends A, B, C, D, E, F, and G sit in a row facing north. E is between A and D. C is to the left of A but not adjacent. B sits at one end. F is to the right of D. Who are sitting next to G?
medium
A. C and A
B. A and F
C. D and F
D. B and C

Solution

  1. Step 1: E is between A and D

    → A-E-D forms a contiguous block.

  2. Step 2: C is to the left of A but not adjacent

    → there must be exactly one person between C and A.

  3. Step 3: F is to the right of D

    → D must have F somewhere to its right.

  4. Step 4: B sits at one end

    → placing B at the left end yields a valid arrangement that fits all clues: B, C, G, A, E, D, F.

  5. Step 5: Identify neighbours of G

    G has C on the left and A on the right.

  6. Final Answer:

    C and A → Option A

  7. Quick Check:

    E is between A and D ✅; C is left of A with one gap (not adjacent) ✅; B at an end ✅; F is to the right of D ✅
Hint: Use 'between' blocks as anchors, place non-adjacent constraints with a single gap, then fit end constraints.
Common Mistakes: Misplacing C adjacent to A or selecting the wrong neighbour due to ambiguous arrangements.

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