43  Arrangements and Puzzle Solving

43.1 Introduction

Arrangement and puzzle questions test logical reasoning, sequencing, and deduction. They involve organizing people, objects, or data according to rules, conditions, and constraints. These are common in IPMAT, CAT, and other competitive exams, and require structured thinking rather than guesswork.

43.2 1) Types of Arrangement Problems

43.2.1 1.1 Linear Arrangement

  • People/objects arranged in a straight line (row/queue).
  • Conditions specify positions like “to the left of”, “between”, “at ends”.

Example:
Six students sit in a row. A is left of B, C is at right end. Who sits in the middle?

43.2.2 1.2 Circular Arrangement

  • People seated around a table facing inside (toward center) or outside (away from center).
  • Relative positions: “second to the left”, “immediate right”.

43.2.3 1.3 Rectangular / Square Arrangement

  • Variations of circular problems with fixed corners and sides.

43.2.4 1.4 Floor Arrangement

  • People living on different floors of a building.
  • Conditions: “X lives above Y but below Z”.

43.2.5 1.5 Scheduling / Day–Month Arrangement

  • People assigned tasks on different days, months, or time slots.

43.2.6 1.6 Distribution / Attribute Puzzle

  • Assigning multiple attributes (color, city, profession) to different people.

Example:
Five friends live in five houses of different colors, own different pets, and drive different cars. Who owns the dog?

43.3 2) Strategies for Solving

  1. Create table/diagram: Rows = people/objects, Columns = attributes (color, floor, etc.).
  2. Fill definite clues first: “X is at extreme left.”
  3. Handle relative clues next: “Y sits second to the right of Z.”
  4. Eliminate contradictions systematically.
  5. Use possibilities: In tough puzzles, create two cases and eliminate wrong one.

43.4 3) Key Words and Meanings

  • “Immediate left/right” = exactly next.
  • “Second to the left” = skip one seat.
  • “Between X and Y” = in the middle of them.
  • “Adjacent” = next to each other.
  • “Opposite” = directly facing (in circular seating).

43.5 4) Solved Examples

43.5.1 Example 1 (Linear)

Six people A–F sit in a row facing North.
- A is left of B.
- C is at right end.
- D is between A and E.

Arrangement: A–D–E–B–F–C.
Answer: E sits between D and B.

43.5.2 Example 2 (Circular)

Eight people sit around a circular table facing center.
- P is second to the right of Q.
- R is between P and S.
- T is opposite Q.

By drawing, positions can be fixed.
Answer: T is opposite Q.

43.5.3 Example 3 (Floor Puzzle)

Five people live on 5 floors (1 lowest, 5 top).
- A lives above B.
- C lives below D.
- E lives on top floor.

Arrangement: E–A–D–C–B (top to bottom).
Answer: A lives on 4th floor.

43.5.4 Example 4 (Scheduling)

Four lectures (Math, English, Reasoning, GK) scheduled Mon–Thu.
- Math before GK.
- English after Reasoning.
- GK not on Thursday.

Possible arrangement: Mon–Math, Tue–Reasoning, Wed–English, Thu–GK (invalid since GK≠Thu).
Correct: Mon–Math, Tue–Reasoning, Wed–GK, Thu–English.

43.5.5 Example 5 (Distribution)

Three friends have different cars: Honda, Ford, Toyota.
- X doesn’t own Honda.
- Y owns Toyota.

So X = Ford, Y = Toyota, Z = Honda.

43.6 5) Practice Questions

  1. Six people A–F sit in a row facing North. D is right of C but left of A. B is right of A. Who is at extreme right?
  2. Eight friends sit around a table, facing center. P is opposite Q, and R is immediate left of Q. Who is immediate right of P?
  3. Four people live on different floors. X above Y, Z above X, W below Y. Who lives on top?
  4. Five subjects (Math, Physics, Chemistry, English, Biology) scheduled Mon–Fri. Physics is before Biology, English is after Math. If Chemistry is on Wednesday, which subject is on Friday?
  5. Three people wear different colored shirts: Red, Blue, Green. A does not wear Red, B does not wear Blue. Who wears what?

43.7 6) Answer Key

  4. Physics–Mon, Math–Tue, Chem–Wed, Eng–Thu, Bio–Fri.
  5. A–Blue, B–Green, C–Red.

43.8 Summary

  • Arrangement problems require structured diagrams.
  • Always start with definite clues, then relative clues.
  • Use tables/trees for multi-attribute puzzles.
  • Eliminate impossible cases systematically.
  • With practice, puzzles can be solved faster than by trial and error.