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Linear Arrangement (Single Row)

Introduction

Linear Arrangement (Single Row) puzzle सबसे common और basic reasoning patterns में से एक है। यह आपकी क्षमता test करता है कि आप दिए गए positional clues के आधार पर लोगों या objects को एक straight line में कैसे arrange करते हैं।

यह pattern महत्वपूर्ण है क्योंकि यही आगे चलकर double-row, circular और mixed arrangements जैसे advanced puzzles की foundation बनाता है।

Pattern: Linear Arrangement (Single Row)

Pattern

मुख्य concept यह है कि लोगों या items को एक सीधी line में “left of”, “right of”, “between”, “next to” जैसे relational clues के आधार पर सही जगह पर रखा जाए।

Arrangement में सभी का facing direction (आमतौर पर North) एक जैसा हो सकता है, या कभी-कभी opposite directions भी दिए जाते हैं। Facing direction समझना बहुत ज़रूरी है क्योंकि उसी के आधार पर “left” और “right” की interpretation बदलती है।

Step-by-Step Example

Question

पाँच दोस्त - A, B, C, D और E - North की ओर देखकर एक row में बैठे हैं। A, B के immediate left में है; C, D के पास नहीं बैठा है; और D किसी भी end पर नहीं है। Extreme ends पर कौन बैठा है?

  • A. A and B
  • B. C and E
  • C. B and D
  • D. C and A

Solution

  1. Step 1: Total positions पहचानें

    5 लोग हैं, इसलिए positions 1 से 5 तक होंगी (left to right, facing North)。

  2. Step 2: A और B को place करें

    A, B के immediate left में है → दोनों ऐसे साथ होंगे: [A B]।

  3. Step 3: D की position

    D किसी भी end पर नहीं है → D position 2, 3 या 4 में होगा।

  4. Step 4: C का clue

    C, D के पास नहीं बैठ सकता → जहाँ भी D होगा, C उसके बगल में नहीं बैठ सकता।

  5. Step 5: Logical placement

    D को middle position 3 पर रखने पर arrangement possible होता है। तब A-B (1-2) या (4-5) पर रखे जा सकते हैं। C को D के पास नहीं बैठना, इसलिए C को end पर रखना ज़रूरी है।

  6. Step 6: Final arrangement

    सभी clues satisfy करने वाला arrangement है: C - A - B - D - E

  7. Final Answer:

    C और E → Option B

  8. Quick Check:

    A, B के left में है ✅ D end पर नहीं है ✅ C, D के पास नहीं है ✅ सभी conditions satisfy होती हैं ✅

Quick Variations

1. सभी लोग एक ही direction (North) में face करके बैठे हों - simplest form।

2. कुछ North और कुछ South की ओर - complexity बढ़ जाती है।

3. Position + extra attributes (profession, color आदि)।

4. Multi-row versions (Two Rows) इस pattern को extend करते हैं।

Trick to Always Use

  • शुरू में boxes (जैसे 1-5) बनाकर placeholders तैयार करें।
  • Direct clues (जैसे “A left of B”) तुरंत map करें।
  • “Not” वाले clues को elimination के लिए use करें।
  • Facing direction पहले fix करें - इससे left/right decide होता है।

Summary

Summary

  • Total positions और facing direction को पहले समझें।
  • Immediate left/right जैसे fixed relations से शुरू करें।
  • “Not next to” जैसे clues से गलत possibilities हटाएँ।
  • Final order बनाने से पहले सभी conditions cross-check करें।

याद रखने वाला उदाहरण: 5 लोग North की ओर - placeholders बनाकर A-B जैसे fixed pairs को पहले place करें और फिर बाकी fill करें।

Practice

(1/5)
1. Six persons - A, B, C, D, E, and F - are sitting in a row facing North. B is to the immediate right of A. C is two places to the right of B. E is not at any end. Who is sitting exactly between D and C?
easy
A. E
B. B
C. F
D. A

Solution

  1. Step 1: Place A and B

    B is immediately right of A ⇒ a pair [A B].

  2. Step 2: Place C

    C is two places to the right of B ⇒ positions include [A B _ C].

  3. Step 3: Use E’s condition

    E is not at any end ⇒ E occupies one of the middle positions (position 3 or 4 in a 6-person row).

  4. Step 4: Construct a valid arrangement

    One arrangement that satisfies all clues is: D - A - B - E - C - F.

  5. Step 5: Identify the exact middle between D and C

    Between D and C are A, B, and E; the middle of these three is B.

  6. Final Answer:

    B → Option B

  7. Quick Check:

    B is immediately right of A ✅ C is two places right of B ✅ E not at an end ✅
Hint: Start from immediate pairs, place the two-step relation, then fill the remaining middles respecting 'not at end' clues.
Common Mistakes: Counting 'between' people incorrectly - when there are three people in between, pick the middle one (not the first or last).
2. Seven people - P, Q, R, S, T, U, and V - are seated in a line facing North. P is to the left of R. Only two people sit between R and T. S sits to the immediate right of Q. How many persons sit between Q and T?
easy
A. 2
B. 3
C. 4
D. 5

Solution

  1. Step 1: Use R-T relation

    Two persons between R and T → pattern [R _ _ T].

  2. Step 2: Place Q and S

    S immediately right of Q → pair [Q S].

  3. Step 3: Place P

    P is left of R → [P ... R].

  4. Step 4: Combine logically

    Possible order: P - Q - S - R - U - V - T.

  5. Step 5: Count between Q and T

    Between Q and T lie S, R, U, and V → 4 persons.

  6. Final Answer:

    4 → Option C

  7. Quick Check:

    S right of Q ✅ R-T gap two ✅ P left of R ✅
Hint: Count gaps after full arrangement; do not assume one person 'exactly between' if even count.
Common Mistakes: Interpreting 'exactly between' when the count is even - always verify numerically.
3. Five students - J, K, L, M, and N - are sitting in a row facing North. M is to the immediate right of L. N is not at any end. K is to the left of J but not adjacent. Who sits exactly in the center?
easy
A. L
B. M
C. N
D. K

Solution

  1. Step 1: Place L and M

    M immediately right of L → [L M].

  2. Step 2: N’s condition

    N not at any end → must occupy a middle position.

  3. Step 3: K-J relation

    K left of J but not adjacent → [K _ J].

  4. Step 4: Build order

    Final order: K - L - M - N - J.

  5. Step 5: Identify center

    In a 5-person row, the 3rd position is center → M.

  6. Final Answer:

    M → Option B

  7. Quick Check:

    M right of L ✅ N not at end ✅ K left of J non-adjacent ✅
Hint: Always test central positions explicitly for odd counts to verify the exact middle person.
Common Mistakes: Selecting the wrong middle when counting from both ends.
4. Seven persons - A, B, C, D, E, F, and G - are sitting in a straight line facing North. A sits second to the right of D. C sits to the immediate left of E. F is not at any end and is to the left of B. Who sits exactly between D and E?
medium
A. A
B. F
C. C
D. B

Solution

  1. Step 1: Decode A-D relation

    A second to right of D → [D _ A].

  2. Step 2: Decode C-E relation

    C immediately left of E → pair [C E].

  3. Step 3: F’s position

    F not at any end and sits to the left of B → [F ... B].

  4. Step 4: Combine logically

    Valid sequence: D - F - A - C - E - B - G.

  5. Step 5: Identify person between D and E

    Between D and E are F, A, and C → the exact middle is A.

  6. Final Answer:

    A → Option A

  7. Quick Check:

    A 2nd right of D ✅ C left of E ✅ F not at end, left of B ✅
Hint: When multiple people lie between two persons, the 'exactly between' person is the middle of those.
Common Mistakes: Choosing the first person between instead of finding the middle one.
5. Eight persons - P, Q, R, S, T, U, V, and W - are sitting in a row facing North. Q is second to the left of S. R sits to the immediate right of T. V is not at any end. U sits third to the right of Q. Who sits at the extreme right end?
medium
A. P
B. U
C. W
D. S

Solution

  1. Step 1: Translate Q-S and U position

    Q is second to the left of S ⇒ if S is at position p, Q is at p-2. U is third to the right of Q ⇒ U is at (Q+3) = p+1.

  2. Step 2: Determine feasible S positions

    For an 8-seat row, p can be 3..7 so that Q and U fall within 1..8.

  3. Step 3: Place T-R pair

    R is immediate right of T ⇒ place an adjacent pair [T R] in any available adjacent slots.

  4. Step 4: Respect V’s condition

    V is not at an end, so V must occupy one of positions 2-7.

  5. Step 5: Build one valid arrangement

    Choosing S = 3 gives Q = 1 and U = 4. Placing [T R] at positions 5-6 and placing V at position 7 yields a valid seating: Q - P - S - U - T - R - V - W (here P fills the remaining slot).

  6. Step 6: Identify extreme right

    The extreme right end (position 8) is W.

  7. Final Answer:

    W → Option C

  8. Quick Check:

    Q is 2 left of S (pos1 & 3) ✅ U is 3 right of Q (pos4) ✅ R right of T (pos6 right of pos5) ✅ V not at end (pos7) ✅
Hint: Place the fixed-distance pair (Q & S) first, compute dependent positions (U), then fit adjacency pairs and non-end constraints.
Common Mistakes: Assuming the first valid fill is unique - multiple valid orders may exist but the extreme-right person can still be determined in the example above.

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