Seating Arrangement

Introduction

Seating arrangements combine clues into one consistent picture. Rows and circular tables are most common.

Key concepts

Linear arrangement

People in a row facing north: their right is east (your right on the page); facing south, their right is your left. 'Immediately to the right' means adjacent; 'to the right' means anywhere on that side.

Circular arrangement

• Facing the centre: a person's left is clockwise and right is anticlockwise.
• Facing outwards: the reverse.
• In a circle of n, the person opposite is n/2 seats away (n even).
• Rotations of the same arrangement count as one.

Order of clues

1. Start with definite clues: 'A is at an end', 'B is opposite C', 'D is immediately left of E'.
2. Then blocks: pairs or triples that must sit together.
3. Then negative clues: 'F is not next to G'.
4. When a clue allows two cases, draw both and eliminate with later clues.

Typical questions

Who sits at the ends or in the middle; who is between two people; how many sit between two people; which pair are neighbours.

Solved examples

Example 1

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

(a) C (b) E (c) D (d) F

Example 2

Six people A–F sit around a circular table facing the centre. F sits directly opposite B. B sits immediately to the left of A. D sits second to the left of A. E sits directly opposite A. Who sits immediately to the right of F?

(a) E (b) A (c) C (d) D

Example 3

5 friends A, B, C, D and E sit in a row facing north (so their left is west). D sits at one of the ends. B sits somewhere to the left of E. E does not sit at either end. B does not sit at either end. A sits at one of the ends. D sits somewhere to the left of B. Exactly one person sits between E and B. Who sits in the middle of the row?

(a) C (b) D (c) E (d) A

Example 4

5 friends A, B, C, D and E sit in a row facing north (so their left is west). Exactly one person sits between A and E. C sits at one of the ends. E sits immediately to the right of B. A does not sit at either end. B does not sit at either end. C sits somewhere to the left of A. E does not sit at either end. Who sits second from the left end?

(a) C (b) A (c) E (d) B

Example 5

5 friends A, B, C, D and E sit in a row facing north (so their left is west). C sits somewhere to the left of D. C sits somewhere to the left of E. B sits somewhere to the left of E. D sits second to the right of C. C sits immediately to the left of B. A sits at one of the ends. A sits somewhere to the left of B. Who sits second from the left end?

(a) D (b) C (c) A (d) E

Example 6

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

(a) C (b) D (c) A (d) F

Example 7

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

(a) D (b) B (c) F (d) C

Example 8

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

(a) D (b) E (c) A (d) F

Practice set

Attempt all 10 questions (about 90 seconds each), then check the worked solutions below.

Q1. 6 friends A, B, C, D, E and F sit in a row facing north (so their left is west). Exactly one person sits between F and E. B does not sit at either end. F sits at one of the ends. E sits somewhere to the left of F. E sits between B and D, next to both. C sits somewhere to the left of A. Exactly one person sits between D and C. Who sits at the right end?

(a) A (b) E (c) F (d) C

Q2. 5 friends A, B, C, D and E sit in a row facing north (so their left is west). D does not sit at either end. A sits somewhere to the left of C. D sits second to the right of B. A sits immediately to the right of B. D sits immediately to the left of C. B sits immediately to the right of E. Who sits in the middle of the row?

(a) A (b) D (c) C (d) B

Q3. 5 friends A, B, C, D and E sit in a row facing north (so their left is west). B sits immediately to the left of A. A sits immediately to the left of E. C sits at one of the ends. B sits somewhere to the left of D. D sits at one of the ends. Who sits in the middle of the row?

(a) A (b) E (c) C (d) D

Q4. 5 friends A, B, C, D and E sit in a row facing north (so their left is west). A sits somewhere to the left of B. D sits somewhere to the left of B. C sits immediately to the left of D. Exactly one person sits between C and A. B sits at one of the ends. E sits somewhere to the left of D. E sits at one of the ends. Who sits immediately to the right of C?

(a) C (b) B (c) E (d) D

Q5. Six people A–F sit around a circular table facing the centre. D sits directly opposite B. B sits immediately to the right of A. C sits immediately to the right of D. F sits second to the left of C. Who sits opposite D?

(a) E (b) B (c) A (d) F

Q6. Six people A–F sit around a circular table facing the centre. F sits immediately to the left of B. E sits immediately to the left of F. D sits immediately to the right of B. A sits directly opposite F. Who sits opposite E?

(a) C (b) F (c) D (d) A

Q7. 5 friends A, B, C, D and E sit in a row facing north (so their left is west). Exactly one person sits between E and C. B sits somewhere to the left of D. Exactly one person sits between A and E. C sits somewhere to the left of A. Who sits in the middle of the row?

(a) D (b) E (c) C (d) A

Q8. Six people A–F sit around a circular table facing the centre. A sits immediately to the left of D. B sits second to the left of D. D sits directly opposite E. D sits immediately to the left of C. Who sits opposite D?

(a) C (b) F (c) A (d) E

Q9. 5 friends A, B, C, D and E sit in a row facing north (so their left is west). B does not sit at either end. A sits immediately to the left of C. A does not sit at either end. B sits immediately to the left of A. Exactly one person sits between B and E. Who sits immediately to the right of B?

(a) B (b) A (c) D (d) E

Q10. Six people A–F sit around a circular table facing the centre. D sits immediately to the left of F. C sits second to the left of E. F sits immediately to the left of B. Who sits opposite B?

(a) E (b) C (c) A (d) D