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Rank in Circular Arrangement

Introduction

Circular arrangement के प्रश्न लोगों (या वस्तुओं) को किसी table या चक्र के चारों ओर place करते हैं और उनके आपसी स्थान पूछते हैं। ये puzzles spatial reasoning, left-right understanding और modular counting logic को परखते हैं।

यह pattern ज़रूरी है क्योंकि यह सिखाता है कि rotational संबंधों को कैसे visualize किया जाए और wrap-around reasoning कैसे इस्तेमाल की जाए - जो कि कई reasoning और seating arrangement प्रश्नों के लिए मुख्य skill है।

Pattern: Rank in Circular Arrangement

Pattern

जब लोग centre की ओर face करते हैं, Left = Clockwise और Right = Anticlockwise होता है।
Circular setup का मतलब है कि positions n seats के बाद repeat करते हैं - left/right घूमने के लिए modulo गणित का उपयोग करें।

  • Rotational symmetry हटाने के लिए किसी एक व्यक्ति की सीट fix करें।
  • Left और right इस बात पर निर्भर करते हैं कि लोग centre की ओर face कर रहे हैं या बाहर।
  • Opposite = n/2 seats दूर (केवल तब जब n even हो)।
  • Modular counting का प्रयोग करें: (current position ± k) mod n।

Step-by-Step Example

Question

छह लोग A, B, C, D, E और F एक circular table के चारों ओर centre की ओर face करके बैठे हैं। A, B के बाएँ से दूसरी सीट पर है। C, A के opposite है। D B के तुरंत बाएँ बैठता है और E A के तुरंत बाएँ बैठता है। C के immediate right पर कौन बैठा है?

Solution

  1. Step 1: Apply direction convention

    सभी centre की ओर face कर रहे हैं → Left = Clockwise, Right = Anticlockwise।

  2. Step 2: Anchor B

    घुमाव की ambiguity हटाने के लिए B को position 1 (12 o’clock) पर रख लें।

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

    Left = Clockwise → B से दो सीटें clockwise घुमकर A को position 3 पर रखें।

  4. Step 4: Place C (opposite A)

    6 सीट होने पर opposite = 3 seats दूर। A (position 3) से opposite position 6 है → C position 6 पर बैठता है।

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

    D, B के तुरंत बाएँ (clockwise) बैठता है → D position 2 पर।
    E, A के तुरंत बाएँ (clockwise) बैठता है → E position 4 पर।
    बाकी बचा व्यक्ति F position 5 लेता है।

  6. Step 6: Determine immediate right of C

    centre की ओर facing होने पर right = anticlockwise → position 6 से एक कदम anticlockwise = position 5 = F।

  7. Final Answer:

    F

  8. Quick Check:

    A, B के बाएँ दूसरी पर है ✅, C opposite A ✅, D B के बाएँ ✅, E A के बाएँ ✅, C के right पर F ✅.

Quick Variations

1. जब लोग बाहर की ओर face कर रहे हों तो left-right उलट जाते हैं।

2. Odd संख्या में लोगों के लिए exact opposite नहीं होता - नज़दीकी सीट देखें।

3. कुछ प्रश्न adjacency और "k-places away" clues mix करते हैं - पहले किसी एक को fix करके step-by-step आगे बढ़ें।

4. Concentric circles में पहले हर circle अलग से हल करें और फिर inter-circle clues जोड़ें।

Trick to Always Use

  • Step 1: किसी एक reference position (जैसे A को top) पर fix करें ताकि directions सरल हों।
  • Step 2: "left/right" को facing direction के आधार पर clockwise/anticlockwise में बदलें।
  • Step 3: opposite या k-step positions निकालने के लिए modular counting लागू करें।
  • Step 4: पूरा क्रम बन जाने पर हर व्यक्ति की relative position जांचकर consistency verify करें।

Summary

Summary

  • Centre की ओर face करने पर: Left = Clockwise, Right = Anticlockwise.
  • Even n में opposite = n/2 seats दूर; Odd n में nearest seat लें।
  • Rotational confusion हटाने के लिए एक reference fix करें।
  • Positions निकालने के लिए wrap-around logic यानी modulo arithmetic का उपयोग करें।

याद रखने के लिए उदाहरण:
6 लोगों के circle में centre facing पर position 1 का opposite position 4 है, और position 6 का immediate right position 5 है।

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

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