Arrangement puzzles give a set of clues and several questions. The winning method is the same every time: start from the most concrete clue, place it, and add others only when they are forced.
Setup for the worked example & drill
Five friends — P, Q, R, S, T — sit in a row facing north. R is second from the left. P is immediately to the right of R. Q is to the left of T. S is at one end. Working it out gives the order, left to right: Q, R, P, T, S.
Seating rules
Find a clue that fixes an absolute position ('X sits at the left end') and start there. Convert 'immediate left/right' into adjacency before placing anyone. In a circle facing the centre, a person's left is your right as you look at the page — flip carefully.
- Find a clue that fixes an absolute position ('X sits at the left end') and start there.
- Convert 'immediate left/right' into adjacency before placing anyone.
- In a circle facing the centre, a person's left is your right as you look at the page — flip carefully.
How to Approach It
- Anchor the most fixed clue — Find the clue that pins an absolute position — an end seat or a definite slot — and place that first. It becomes the foundation everything else hangs on.
- Draw numbered blanks, then names — Sketch the seats as numbered empty positions and drop names in only where the clues force them. This simple habit prevents the classic error of double-booking a seat.
- Settle the facing direction — In a circle facing the centre, a person's left is your right as you look at the page. Decide the facing before you interpret any left-or-right clue.
- Abandon impossible branches — The moment a placement violates any clue, discard that entire arrangement rather than trying to patch it. Backtracking cleanly is faster than forcing a broken layout.
Techniques & Methods
- Anchor a fixed clue — Start from an absolute position — an end seat or a definite slot.
- Blanks, then names — Draw numbered empty seats first; drop names only where forced.
- Facing flips left/right — In a circle facing the centre, a person's left is your right on the page.
- Filter branches — Discard any whole layout the moment it breaks a clue.
The Edge
Write the empty seats as numbered blanks first, then drop names in. Looking at _ _ _ _ _ stops you from double-booking a seat — the most common puzzle error under time pressure. Treat each clue as a filter: if a placement violates any clue, discard that whole branch immediately instead of patching it.Worked example
In the arrangement above, who sits in the middle seat?
- From the clues, the row from left to right is Q, R, P, T, S.
- There are 5 seats, so the middle is the 3rd seat.
- Counting in from the left: seat 1 is Q, seat 2 is R, seat 3 is P.
- The person in the middle is therefore P.
Answer: P is in the middle
Worked example
How many people sit between Q and S?
- Q is at the left end (seat 1) and S is at the right end (seat 5).
- Everyone seated strictly between them occupies seats 2, 3 and 4.
- Those seats hold R, P and T.
- That makes three people between Q and S.
Answer: Three people
Worked Drills
Worked example
(Order Q, R, P, T, S) Who is second to the right of R? (a) P b) T c) S d) Q)
- R is in seat 2.
- Two seats to the right is seat 4.
- Seat 4 holds T.
Answer: T — option b)
Worked example
Counting from the right end, T is in which position? (a) first b) second c) third d) fourth)
- From the right, the order is S(1), T(2), P(3), R(4), Q(5).
- So T is second from the right.
Answer: second — option b)
Worked example
If P and T swap seats, who is now in the middle? (a) P b) R c) T d) S)
- Original order: Q, R, P, T, S. After swapping P and T: Q, R, T, P, S.
- The middle is seat 3.
- Seat 3 now holds T.
Answer: T — option c)
Worked example
(Six students sit in a row facing north; order Y, X, W, U, V, Z) Who sits at the left end? (a) U b) V c) W d) Y)
- The order left to right is Y, X, W, U, V, Z.
- The left end is seat 1.
- Seat 1 is Y.
Answer: Y — option d)
Worked example
Who is third from the right? (a) W b) U c) V d) X) [order Y, X, W, U, V, Z]
- From the right, the order is Z(1), V(2), U(3), W(4), X(5), Y(6).
- Third from the right is U.
Answer: U — option b)
Worked example
Who sits between X and U? (a) W b) V c) Z d) Y) [order Y, X, W, U, V, Z]
- X is seat 2 and U is seat 4.
- The seat strictly between them is seat 3.
- Seat 3 holds W.
Answer: W — option a)
Worked example
How many persons sit between Y and V? (a) 2 b) 3 c) 4 d) 5) [order Y, X, W, U, V, Z]
- Y is seat 1 and V is seat 5.
- Seats 2, 3 and 4 lie between them, holding X, W and U.
- That is 3 persons.
Answer: 3 — option b)
Worked example
If U and X interchange seats, who then sits third from the left? (a) W b) X c) U d) V) [order Y, X, W, U, V, Z]
- Swapping U and X gives Y, U, W, X, V, Z.
- Third from the left is seat 3.
- Seat 3 (W) is unchanged, so W is still third.
Answer: W — option a)
⚠ Watch out
- 'Facing centre' flips left and right versus 'facing out' — decide the facing first.
- Don't assume an order the clues never state; keep branches open until forced.
- Re-read each clue against your final layout before answering.
Takeaways
- Anchor the most concrete clue first and build outward from it.
- Sketch numbered blank seats before dropping in any names.
- Settle the facing direction before reading any left/right clue.
- Discard a whole layout the instant it breaks a clue — don't patch it.