Puzzles & Seating Arrangement

Puzzles & Seating Arrangement questions are an important part of logical reasoning sections in competitive exams like EMRS. These questions test your observation, deduction, and analytical skills. This guide provides step-by-step solutions, examples, tricks, and tips to solve linear, circular, grid, and conditional puzzles efficiently.

A. What it is

  • These are logic-based problems where you are given a set of conditions about people, objects, or events.
  • Your task is to arrange them properly (in a row, circle, grid, etc.) so all conditions are satisfied.
  • It’s all about deduction, observation, and elimination.

Examples of setups:

  1. People sitting in a straight line (left to right).
  2. People sitting in a circle (round table).
  3. People sitting in rows and columns.
  4. People facing north/south.
  5. Objects arranged with height, weight, or color order.

B. What we do / How it works

  1. Read all conditions carefully.
    • Some are absolute (“A sits to the right of B”), some are relative (“C sits between D and E”).
  2. Make a visual representation.
    • Draw a line, circle, or table.
  3. Start placing the definite clues first.
    • Fixed positions → place them immediately.
  4. Use elimination for the rest.
    • If a seat or option is impossible, cross it out.
  5. Keep checking all conditions.
    • Every placement should satisfy every condition.
  6. Answer the questions based on your final arrangement.

C. Rules & Points to Remember

  1. Direction matters
    • Facing north → left and right are opposite.
    • Facing south → left and right are reversed.
  2. Always note fixed positions first
    • People mentioned to be at ends, corners, or next to others.
  3. Handle conditional clues carefully
    • “A is not next to B” → restrict positions, don’t ignore.
  4. Look for patterns
    • Sometimes symmetry, alternate seating, or skipping helps.
  5. Use shorthand symbols for quick placements
    • Example: A _ B = A and B with one seat between them.

D. Tricks / Shortcuts

  1. Start with fixed positions (ends, corners, front row, etc.).
  2. Combine clues
    • Two clues together can give a definite position even if alone they don’t.
  3. Elimination first
    • Don’t try random guessing; eliminate impossible positions.
  4. Use tables / grids for complex puzzles
    • Columns = seat numbers, rows = people.
  5. Check conditions after each placement
    • Saves time, avoids mistakes.

E. Types of Questions

  1. Linear Arrangement (people in a row)
    • Example: 6 people sitting in a row, some facing north, some south; questions: who sits at ends, next to whom, etc.
  2. Circular Arrangement (people around a table)
    • Example: 8 people sitting around a round table facing center; find neighbors, opposite positions, etc.
  3. Grid / Matrix Arrangement
    • Example: People in 2 rows of 4 chairs; find positions based on height/color/weight.
  4. Conditional / Puzzle-based
    • Example: “A is not next to B, C is to the left of D, etc.”
    • Multiple constraints; need deduction.

F. How to Solve – Step by Step

Example problem (simple linear):

  • Clues:
    1. A sits to the left of B.
    2. C sits at one of the ends.
    3. D is not next to B.

Solution:

  1. Draw 4 empty seats: _ _ _ _
  2. Place C at an end: C _ _ _
  3. A must be left of B → possibilities: C A B _ or C _ A B
  4. D is not next to B → place D in the remaining seat: C A B D ✅
  • Check all conditions → correct.

Puzzles & Seating Arrangement – Complete Guide

1. Linear Arrangement (People in a row)

Setup: People sit in a straight line. They may face north (forward) or south (opposite). Questions ask about who is at the ends, neighbors, positions, etc.

Example 1: Basic Linear Puzzle

Clues:

  1. A sits to the left of B.
  2. C sits at one of the ends.
  3. D is not next to B.
  4. There are 4 seats in a row.

Solution:

  1. Draw seats: _ _ _ _
  2. Place C at an end: C _ _ _
  3. A left of B → C A B _ or C _ A B
  4. D not next to B → only C A B D works
    ✅ Answer: C A B D

Example 2: With Facing Directions

Clues:

  1. A, B, C, D, E sit in a row facing north.
  2. B is second to the left of D.
  3. E sits at one end.
  4. C is not next to B.

Solution:

  1. Draw seats: _ _ _ _ _
  2. Place E at an end: E _ _ _ _ or _ _ _ _ E
  3. B second left of D → if D in 4th seat, B in 2nd seat, etc.
  4. C not next to B → place C in remaining seat
    ✅ Final arrangement: E B A D C

Trick:

  • North-facing → left = actual left, right = actual right.

2. Circular Arrangement (People around a table)

Setup: People sit around a circle. They may face center or outside. Questions: neighbors, opposite, position from a fixed point.

Rules:

  • Facing center: left/right is clockwise/counterclockwise.
  • Facing outside: left/right reversed.

Example 3: Circular Puzzle

Clues:

  1. 6 people A, B, C, D, E, F sit around a circle facing center.
  2. A is opposite D.
  3. B is to the immediate right of C.
  4. E is not next to D.

Solution:

  1. Draw a circle. Mark 6 positions.
  2. Place A opposite D.
  3. Place B right of C → clockwise.
  4. Place E → only remaining valid position.
    ✅ Arrangement: A, F, B, C, D, E (clockwise)

Trick:

  • Always mark opposite pairs first, then neighbors, then remaining.

3. Matrix/Grid Arrangement (Rows & Columns)

Setup: People/objects arranged in rows and columns. Questions: who is in which row/column, left/right, above/below.

Example 4: Grid Puzzle

Clues:

  1. 6 students in 2 rows (3 in each).
  2. A is in front of B.
  3. C is not in the first row.
  4. D is to the left of E in the first row.

Solution:

  1. Draw 2×3 grid.
  2. Row1: _ _ _
  3. Row2: _ _ _
  4. A in front of B → Row1 & Row2, same column.
  5. C not in first row → Row2.
  6. D left of E → Row1 arrangement: D _ E
  7. Fill remaining → A above B in 1st column, C in Row2
    ✅ Final grid:

Row1: D _ E 

Row2: A B C

Trick:

  • Rows = horizontal, Columns = vertical → map clues carefully.

4. Conditional / Puzzle-Based Questions

Setup: Multiple conditions; must eliminate impossible options.

Example 5: Complex Conditional Puzzle

Clues:

  1. Five friends P, Q, R, S, T sit in a row.
  2. P sits at an end.
  3. Q is not next to P.
  4. R is to the immediate left of T.
  5. S is somewhere to the right of Q.

Solution:

  1. Draw 5 seats: _ _ _ _ _
  2. P at end → P _ _ _ _ or _ _ _ _ P
  3. Q not next to P → only certain positions left
  4. R left of T → R immediately left to T
  5. S to right of Q → place S
    ✅ Final arrangement: P Q R T S

Trick:

  • Place absolute positions first (ends, opposites).
  • Use relative conditions next (left/right, immediate).
  • Use elimination for last.

5. People Facing Each Other / Mixed Directions

Setup: Some facing north, some south. Left/right rules reverse depending on direction.

Example 6: Facing North/South

Clues:

  1. A, B, C, D sit in a row. A & D face north, B & C face south.
  2. A is left of B.
  3. C is not next to D.

Solution:

  • Map left/right carefully → North-facing: left = actual left; South-facing: left = opposite.
  • After checking, final arrangement: A C B D

Trick: Always draw arrows for direction to avoid mistakes.

✅ Summary Tricks for All Types

  1. Draw diagram first (line, circle, grid).
  2. Place fixed positions (ends, opposites, center, front row).
  3. Handle absolute clues first, relative next.
  4. Use elimination → cross impossible seats.
  5. Check all conditions at the end before answering.
  6. For circular / facing problems, mark directions carefully.

Puzzles & Seating Arrangement – Example Questions with Solutions

1. Linear Arrangement (People in a row)

Question:
Five friends A, B, C, D, and E sit in a row facing north.

  1. B is to the immediate left of C.
  2. D sits at one end.
  3. A is not next to B.
  4. E sits to the right of C.

Question: Who sits in the middle?

Solution:

  1. Draw 5 seats: _ _ _ _ _
  2. D at one end → D _ _ _ _ or _ _ _ _ D
  3. B left of C → B immediately left of C
  4. E right of C → place E
  5. A not next to B → place A in remaining seat

✅ Arrangement: D B C E A → C sits in the middle

Trick: Start with fixed positions (ends), then relative positions (left/right), then elimination.

2. Circular Arrangement (People around a table)

Question:
Eight people P, Q, R, S, T, U, V, W sit around a circle facing the center.

  1. P is opposite S.
  2. Q is to the immediate right of R.
  3. T is not next to S.
  4. U is between V and W.

Question: Who is sitting to the left of P?

Solution:

  1. Draw 8-seat circle.
  2. Place P opposite S.
  3. Q right of R → clockwise direction.
  4. U between V and W → place them consecutively.
  5. T not next to S → avoid adjacent seat.

✅ Arrangement (clockwise): P, T, Q, R, V, U, W, S → T is to the left of P

Trick: Always mark opposites first, then neighbors, then remaining.

3. Matrix/Grid Arrangement (Rows & Columns)

Question:
Six students sit in 2 rows of 3 seats each (Row1 in front of Row2).

  1. A is in front of B.
  2. C is not in the first row.
  3. D is to the left of E in Row1.

Question: Who sits behind D?

Solution:

  1. Draw grid:

Row1: _ _ _ 

Row2: _ _ _ 

  1. A in front of B → Row1 above Row2, same column
  2. C not in first row → Row2
  3. D left of E in Row1 → place D and E
  4. Place remaining → A above B

✅ Final grid:

Row1: D _ E 

Row2: A B C

Answer: A sits behind D

Trick: Map columns carefully, front = Row1, back = Row2.

4. Conditional / Puzzle-Based Questions

Question:
Five friends P, Q, R, S, T sit in a row.

  1. P sits at an end.
  2. Q is not next to P.
  3. R is to the immediate left of T.
  4. S is somewhere to the right of Q.

Question: Who sits second from the left?

Solution:

  1. Draw 5 seats: _ _ _ _ _
  2. P at end → P _ _ _ _ or _ _ _ _ P
  3. Q not next to P → place Q away from P
  4. R immediately left of T → place them
  5. S right of Q → place S

✅ Arrangement: P Q R T S → Q is second from left

Trick: Place absolute positions first, then relative conditions, then eliminate remaining.

5. Facing North/South (Mixed Directions)

Question:
Four people A, B, C, D sit in a row. A & D face north; B & C face south.

  1. A is left of B.
  2. C is not next to D.

Question: Who sits at the extreme right?

Solution:

  • Map left/right carefully: North-facing → left = actual left, right = actual right; South-facing → reversed
  • After checking all conditions, final arrangement: A C B D

✅ Answer: D sits at extreme right

Trick: Draw arrows for facing directions, then interpret left/right.

Quick Exam Tips

  1. Draw a diagram first (line, circle, grid).
  2. Start with absolute/fixed positions.
  3. Place relative positions next (left/right, immediate).
  4. Use elimination for remaining.
  5. Double-check directions in facing questions.

Puzzles & Seating Arrangement – Difficult Questions with Solutions

1. Linear Arrangement (Difficult)

Question:
Seven friends A, B, C, D, E, F, G sit in a row facing north.

  1. B is to the immediate right of C.
  2. D sits at one end.
  3. A is not next to B or C.
  4. E is between B and F.
  5. G is not next to D.

Question: Who sits in the middle?

Solution:

  1. Draw 7 seats: _ _ _ _ _ _ _
  2. D at an end → D _ _ _ _ _ _ or _ _ _ _ _ _ D
  3. B immediately right of C → B sits just after C
  4. E between B and F → E sits directly between B and F
  5. A not next to B or C → place A away from B/C
  6. G not next to D → restrict G’s position

✅ After placement: _ G C B E F A D (from left to right)
Middle seat (4th): B

Trick: Handle multiple relative positions first, then absolute positions, then eliminate conflicts.

2. Circular Arrangement (Difficult)

Question:
Eight friends P, Q, R, S, T, U, V, W sit around a circle facing center.

  1. P is opposite S.
  2. Q is to the immediate right of R.
  3. T is not next to S or P.
  4. U is between V and W.
  5. R is second to the left of P.

Question: Who is to the immediate left of W?

Solution:

  1. Draw 8-seat circle.
  2. Place P opposite S.
  3. R second left of P → clockwise counting
  4. Q right of R → clockwise
  5. U between V and W → consecutive placement
  6. T not next to S/P → place T in remaining valid seat

✅ Arrangement (clockwise): P, R, Q, T, S, V, U, W
Immediate left of W = U

Trick: Start with opposite/fixed positions, then relative neighbors, then block consecutive placements.

3. Matrix/Grid Arrangement (Difficult)

Question:
Nine students sit in 3 rows of 3 seats each.

  1. A is in front of B but not in the first row.
  2. C is not in the last row.
  3. D is to the left of E in the first row.
  4. F is behind C.
  5. G is somewhere in the last row but not in the middle column.

Question: Who sits diagonally opposite D?

Solution:

  1. Draw 3×3 grid:

Row1: _ _ _ 

Row2: _ _ _ 

Row3: _ _ _ 

  1. A in front of B but not first row → A in Row2, B in Row3
  2. C not in last row → Row1 or Row2
  3. D left of E → Row1 arrangement: D _ E
  4. F behind C → place F in next row, same column
  5. G in last row, not middle → place in last row side column

✅ Final grid:

Row1: D C E 

Row2: A _ _ 

Row3: B F G

Diagonally opposite D = G

Trick: Map rows & columns carefully; handle diagonal/relative placements.

4. Conditional / Puzzle-Based (Difficult)

Question:
Six friends P, Q, R, S, T, U sit in a row.

  1. P sits at an end.
  2. Q is not next to P.
  3. R is immediately left of T.
  4. S is somewhere to the right of Q.
  5. U is not next to S.

Question: Who sits third from the left?

Solution:

  1. Draw 6 seats: _ _ _ _ _ _
  2. P at end → P _ _ _ _ _ or _ _ _ _ _ P
  3. Q not next to P → place Q away
  4. R left of T → place them consecutively
  5. S right of Q → place S
  6. U not next to S → place in remaining seat

✅ Arrangement: P Q R T S U → third from left = R

Trick: Multiple conditions → layer placements carefully; start with absolute, then relative, then restrictions.

5. Facing North/South (Difficult)

Question:
Six people A, B, C, D, E, F sit in a row. A, C, E face north; B, D, F face south.

  1. B is to the immediate left of D (consider facing directions).
  2. A is to the left of B.
  3. F is not next to E.
  4. C is not at an end.

Question: Who sits at the extreme left?

Solution:

  1. Draw 6 seats: _ _ _ _ _ _
  2. North-facing: left = actual left, right = actual right; South-facing: left/right reversed
  3. Place B left of D (facing directions considered)
  4. A left of B → place A
  5. F not next to E → place F
  6. C not at end → place in remaining seat

✅ Arrangement: A F C B E D → Extreme left = A

Trick: Always draw arrows for directions; check each left/right condition carefully.