Logical reasoning · Day 10
Seating Arrangement
Place the most definite clue first (someone at an end, someone facing the centre), then fill around it. Draw every time.
Why this topic matters
Seating puzzles look long, but they are just clues placed one at a time. Start with the clue that fixes a seat, and draw after every clue.
Seating sets carry 3 to 5 questions. A clean drawing method turns a 5-minute puzzle into 2 minutes.
Linear: facing north or south
Number the seats from the left of your page. If people face north, their left is your left. If they face south, their left is YOUR right.
'Immediately right' means the next seat. 'Second to the right' means skip one.
Example 1P, Q, R, S, T sit in a row facing north. R is in the middle. P is at the right end. S is immediately left of R. Q is not at an end. Who is at the left end?
- Seats 1 to 5 from the left. R = 3, P = 5.Fixed seats first.
- S is immediately left of R: S = 2.Facing north, left is your left.
- Q is not at an end: Q = 4.Seats 1 and 5 are the ends.
- T takes seat 1.
Answer: T
Circular: facing the centre
Put the most mentioned person at the top. For people facing the centre, their right is anticlockwise on your drawing, their left is clockwise.
In a table of n (n even), the person opposite is n/2 seats away.
Example 1Six people sit around a table facing the centre. A is at the top. B is second to the right of A, C is opposite A, D is immediately left of A. Who is opposite B?
- A at the top. Right of A (facing centre) is anticlockwise.Draw the circle first.
- C opposite A. D one seat clockwise from A. B two seats anticlockwise.
- The seat opposite B is the one just clockwise of A, which is D.
Answer: D
Formula summary
Linear, facing north
Your left = the reader's left.
Circular, facing centre
Seen from above: your left is clockwise, your right is anticlockwise.
Immediate neighbours
'Sits second to the right' means skip one seat.
Count check
n people round a table: each has exactly 2 neighbours; opposite exists only when n is even.
Shortcuts and tricks
Anchor and branch
Use it when: When a clue allows two places, draw BOTH sketches and let a later clue kill one.
- Place the fixed clue first (a named seat, an end).
- When a clue gives two options, copy the sketch and try each.
- Apply the remaining clues to both sketches. Cross out the one that breaks a clue.
ExampleP, Q, R, S, T sit in a row facing north. Q is second from the left. R sits next to Q. T is at one end. S is not at an end, and P sits immediately to the right of S. R is not at an end. Who is in the middle?
- Number the seats 1 to 5 from the left. Q = seat 2.'Second from the left' is a fixed seat, so it is the anchor.
- R is next to Q, so R = 1 or R = 3. Draw two sketches: (a) R Q _ _ _ and (b) _ Q R _ _.The clue allows two places, so we keep both alive instead of guessing.
- 'R is not at an end' kills sketch (a), because seat 1 is an end.A later clue removes one branch; that is the whole trick.
- In sketch (b), S is not at an end and P is right after S, so S = 4 and P = 5.Seats 1, 2, 3 are either taken or an end; S = 4 is the only seat left that is not an end and has a free seat to its right.
- T takes the last free seat, 1, which is an end, as the clue says. Row: T Q R S P.Always finish by checking every clue against the final row.
- The middle seat (3) is R.
Answer: R
Circle: fix one person, then count
Use it when: Round-table questions. Fix any one person at the top; the circle has no 'first seat' otherwise.
- Draw the circle with n seats and put the most mentioned person at the top.
- Facing the centre: their right is anticlockwise on your drawing, their left is clockwise.
- 'Second to the right' means move two seats, not one.
ExampleA, B, C, D, E, F sit around a round table facing the centre, equally spaced. B is second to the right of A. C is opposite A. D is immediately left of A. E is not next to C. Who sits opposite D?
- Six seats, numbered 0 to 5 anticlockwise on paper. Put A at seat 0.Facing the centre, a person's right is anticlockwise when you look down on the table.
- B is second to the right of A: seat 2. C is opposite A: seat 3.Opposite in a table of 6 is 3 seats away.
- D is immediately left of A: one step clockwise, which is seat 5.Left of a centre-facing person is clockwise.
- E and F take seats 1 and 4. Seat 4 is next to C (seat 3), so E = 1 and F = 4.'E is not next to C' decides which of the two free seats E gets.
- Opposite D (seat 5) is seat 2, which is B.
Answer: B
Common mistakes
Treating 'second to the right' as the next seat.
Skip one seat.
Forgetting to mirror left and right for people facing south.
Their left is your right.
Before you move on, you should be able to...
- draw after every clue
- turn left/right correctly for north, south and centre facing
- keep two sketches when a clue allows two places
Practice questions (3)
Try each one before opening the solution. Or practise them one by one so your score is saved.
easy Eight people around a round table, equally spaced. How many different people can sit directly opposite a given person?
- With 8 seats, exactly one seat is opposite.
Answer: 1
medium A, B, C, D, E, F sit around a round table facing the centre. A is opposite D. B is to A's immediate right (from A's view, i.e. anticlockwise when drawn). C is opposite B. Who is opposite E?
- Six seats: A and D, B and C, so E and F are the remaining opposite pair.
Answer: F
hard P, Q, R, S, T sit in a row facing north. R is in the middle. P is at the right end. S is immediately left of R. Q is not at an end. Who is at the left end?
- Seats 1-5: R=3, P=5, S=2.
- Q not at an end → 4. T = 1.
Answer: T
Class plan (2 hours, for trainers)
A tested order for teaching this topic in one 2-hour session. Present mode follows the same order.
| 10 min | Warm-up. |
| 30 min | Linear: north and south facing, with the row picture. |
| 30 min | Circular: centre-facing, opposite, second to the right. |
| 15 min | Anchor and branch: keep two sketches alive. |
| 30 min | Practice set. |
| 5 min | Recap. |