0
0

Rank in Circular Arrangement

Introduction

Circular arrangement problems place people (or objects) around a table or circle and ask for their relative positions. These puzzles test spatial reasoning, left-right understanding, and modular counting logic.

This pattern is crucial because it teaches how to visualize rotational relationships and use wrap-around reasoning - a key skill in many reasoning and seating arrangement problems.

Pattern: Rank in Circular Arrangement

Pattern

When people face the centre, Left = Clockwise and Right = Anticlockwise.
The circular setup means positions repeat after n seats - use modulo arithmetic to move left/right around the circle.

  • Fix one person’s seat to remove rotational symmetry.
  • Left and right depend on whether people face the centre or outside.
  • Opposite = n/2 places away (only when n is even).
  • Use modular counting: (current position ± k) mod n.

Step-by-Step Example

Question

Six people A, B, C, D, E and F sit around a circular table facing the centre. A is second to the left of B. C is opposite A. D sits immediately to the left of B and E sits immediately to the left of A. Who sits to the immediate right of C?

Solution

  1. Step 1: Apply direction convention

    All are facing the centre → Left = Clockwise, Right = Anticlockwise.

  2. Step 2: Anchor B

    Fix B at position 1 (12 o’clock). This helps eliminate circular ambiguity.

  3. Step 3: Place A (2nd to the left of B)

    Left = Clockwise → Move two seats clockwise from B. Place A at position 3.

  4. Step 4: Place C (opposite A)

    With 6 seats, opposite = 3 seats away. From A (position 3), opposite is position 6 → C sits at position 6.

  5. Step 5: Place D and E using extra clues

    D is immediately to the left (clockwise) of B → D at position 2.
    E is immediately to the left (clockwise) of A → E at position 4.
    The remaining person F occupies position 5.

  6. Step 6: Determine immediate right of C

    Facing centre, right = anticlockwise → move one step anticlockwise from position 6 → position 5 = F.

  7. Final Answer:

    F

  8. Quick Check:

    A is 2nd left of B ✅, C opposite A ✅, D left of B ✅, E left of A ✅, right of C = F ✅.

Quick Variations

1. When people face outside, left-right directions reverse.

2. For an odd number of people, there is no exact opposite - use nearest position.

3. Some questions mix adjacency and “k-places away” clues - fix one person and propagate step by step.

4. In concentric circles, solve each circle separately before linking inter-circle clues.

Trick to Always Use

  • Step 1: Fix one reference position (e.g., A at top) to simplify directions.
  • Step 2: Convert “left/right” to clockwise/anticlockwise based on facing direction.
  • Step 3: Apply modular counting to find opposite or k-step positions.
  • Step 4: Verify consistency by checking each person’s relative position after completion.

Summary

Summary

  • When facing the centre: Left = Clockwise, Right = Anticlockwise.
  • For even n, opposite = n/2 seats away; for odd n, use nearest seat.
  • Fix one reference point to avoid rotational confusion.
  • Use modulo arithmetic (wrap-around logic) to calculate positions efficiently.

Example to remember:
In a circle of 6 people facing centre, the person opposite position 1 is position 4, and the person to the immediate right of position 6 is position 5.

Practice

(1/5)
1. Six friends A, B, C, D, E, and F are sitting around a circular table facing the centre. A is second to the left of B. C is opposite A. D sits immediately to the left of B and E sits immediately to the left of A. Who is to the immediate right of C?
easy
A. B
B. E
C. F
D. D

Solution

  1. Step 1: State direction convention

    All are facing the centre → Left = Clockwise, Right = Anticlockwise.

  2. Step 2: Anchor B

    Fix B at position 1 (reference). This removes rotational symmetry.

  3. Step 3: Place A (second to the left of B)

    Left = Clockwise → move two seats clockwise from B. Place A at position 3.

  4. Step 4: Place D and E using given adjacency clues

    D is immediately to the left (clockwise) of B → D at position 2.
    E is immediately to the left (clockwise) of A → E at position 4.

  5. Step 5: Place C (opposite A) and remaining person F

    With 6 seats, opposite = 3 seats away. From A (position 3), opposite is position 6 → C at position 6. The remaining person F occupies position 5.

  6. Step 6: Find immediate right of C

    Facing centre, right = anticlockwise → one step anticlockwise from position 6 is position 5 = F.

  7. Final Answer:

    F → Option C

  8. Quick Check:

    Positions: 1=B, 2=D, 3=A, 4=E, 5=F, 6=C. A is 2nd left of B (3rd vs 1st) ✅, D left of B ✅, E left of A ✅, C opposite A ✅, right of C = F ✅
Hint: When circle clues mix 'k-th left' with adjacencies, fix one person and place k-step clues first, then place adjacency clues to force a unique arrangement.
Common Mistakes: Leaving only the initial clues (A second left of B and C opposite A) and assuming uniqueness - adjacency clues are needed to fix remaining seats.
2. Eight persons P, Q, R, S, T, U, V, and W are sitting in a circle facing the centre. If Q is second to the left of P and R is opposite P, who is second to the right of R?
easy
A. Q
B. S
C. V
D. U

Solution

  1. Step 1: Fix a reference and set direction rules

    Facing centre → Left = Clockwise, Right = Anticlockwise. Fix P at position 1 to remove rotation ambiguity.

  2. Step 2: Place Q (second to the left of P)

    Second left of P means move two seats clockwise from P → Q is at position 3.

  3. Step 3: Place R (opposite P)

    With 8 people, opposite = 4 seats away. From P (position 1) → R is at position 5.

  4. Step 4: Find second to the right of R

    Right = anticlockwise. From R at position 5: first right → position 4, second right → position 3 = Q.

  5. Final Answer:

    Q → Option A

  6. Quick Check:

    Positions (clockwise): 1=P, 2=(adj), 3=Q, 4=(adj), 5=R, 6=(adj), 7=(adj), 8=(adj). Second right of R (anticlockwise two steps) is position 3 → Q ✅
Hint: Fix one person, convert 'k-th left' to clockwise steps, find opposite with n/2, then move anticlockwise for 'right'.
Common Mistakes: Mixing clockwise/anticlockwise directions or forgetting that 'second to the right of R' may land on an already-placed person if the circle is anchored incorrectly.
3. Seven people A, B, C, D, E, F, and G sit around a circular table facing the centre. D is third to the right of B. C is third to the right of D. E is immediately to the right of B. F sits immediately to the left of C. Who sits to the left of C?
easy
A. G
B. E
C. F
D. B

Solution

  1. Step 1: Set direction convention

    Facing centre → Left = Clockwise, Right = Anticlockwise. Fix B at position 1 to remove rotational symmetry.

  2. Step 2: Place D (3rd to the right of B)

    Right = anticlockwise. From B(pos1) move 3 anticlockwise: pos7 (1st), pos6 (2nd), pos5 (3rd) → D = pos5.

  3. Step 3: Place C (3rd to the right of D)

    From D(pos5) move 3 anticlockwise: pos4 (1st), pos3 (2nd), pos2 (3rd) → C = pos2.

  4. Step 4: Place E (immediate right of B)

    Immediate right = one step anticlockwise from B(pos1) → E = pos7.

  5. Step 5: Apply the added clue: F immediate left of C

    Left = clockwise. Immediate left of C(pos2) is pos3 → F = pos3.

  6. Step 6: Fill remaining seats

    Remaining people A and G occupy pos4 and pos6 (order not needed for this question).

  7. Step 7: Identify left of C

    Left of C (clockwise next seat from pos2) = pos3 → occupied by F.

  8. Final Answer:

    F → Option C

  9. Quick Check:

    Positions (clockwise): pos1=B, pos2=C, pos3=F, pos4=A (or G), pos5=D, pos6=G (or A), pos7=E. Verify: D is 3rd right of B (pos5 from pos1) ✅; C is 3rd right of D (pos2 from pos5) ✅; E immediate right of B (pos7) ✅; F immediate left of C (pos3) ✅ → left of C = F ✅
Hint: Fix one reference seat, convert right/left using facing-direction, place k-step offsets first, then fill adjacency clues to pin remaining seats.
Common Mistakes: Assuming the arrangement is unique without adding the minimal adjacency that fixes remaining seats; forgetting to convert 'right' as anticlockwise when facing centre.
4. Ten people sit around a circular table facing the centre. If A is 4th to the right of B and C is opposite A, how many people sit between B and C (clockwise)?
medium
A. 3
B. 4
C. 5
D. 6

Solution

  1. Step 1: A is 4th right of B

    → Move 4 anticlockwise from B to place A.

  2. Step 2: C opposite A

    → Opposite = 10/2 = 5 seats away → place C 5 seats from A.

  3. Step 3: Count between B and C clockwise

    Between count = 5 (positions between them).

  4. Final Answer:

    5 → Option C

  5. Quick Check:

    10 seats → opposite = 5 apart ✅
Hint: Use n/2 step rule for opposite positions.
Common Mistakes: Counting wrong direction or missing one seat.
5. Eight friends A, B, C, D, E, F, G, and H sit around a circular table facing the centre. A is opposite D. C is to the immediate right of A. B sits immediately to the left of A. G sits second to the left of H. E sits immediately to the left of G. Who is opposite G?
medium
A. F
B. E
C. H
D. B

Solution

  1. Step 1: Fix A and D

    Place A at position 1. Opposite (n/2=4) → D at position 5.

  2. Step 2: Place C and B

    C is immediate right (anticlockwise) → C at position 8.
    B is immediate left (clockwise) → B at position 2.

  3. Step 3: Apply G-E-H relation

    Left = clockwise → H → G → E in clockwise order.

  4. Step 4: Determine valid placement

    G must be at position 6 to maintain clockwise H→G→E without colliding with A, B, C, D. Then E is at position 7 and H at position 4.

  5. Step 5: Opposite of G

    Opposite of pos6 = pos2 → pos2 is B.

  6. Final Answer:

    B → Option D

  7. Quick Check:

    Positions: 1=A, 2=B, 4=H, 5=D, 6=G, 7=E, 8=C → All clues satisfied; opposite of G is B.
Hint: Add a minimal anchoring adjacency around A to force a unique opposite seat.
Common Mistakes: Skipping the anchoring adjacency results in multiple possible opposites.

Mock Test

Ready for a challenge?

Take a 10-minute AI-powered test with 10 questions (Easy-Medium-Hard mix) and get instant SWOT analysis of your performance!

10 Questions
5 Minutes