Eleven friends M, N, O, P, Q, R, S, T, U, V and W are sitting in a single row,…

2023

Eleven friends M, N, O, P, Q, R, S, T, U, V and W are sitting in a single row, all facing the same direction. Study the following conditions and answer the question that follows.

  • T is immediately to the left of P, and third to the right of U.

  • V is the immediate neighbour of both M and N, and third to the left of S.

  • M is second to the right of Q, who is sitting at one of the ends of the row.

  • R is sitting immediately to the right of P, and P is second to the right of O.

Who is sitting in the center of the row?

  1. A.

    N

  2. B.

    O

  3. C.

    S

  4. D.

    U

Attempted by 6 students.

Show answer & explanation

Correct answer: D

In a linear seating-arrangement puzzle, every condition fixes one person's seat only relative to a seat that is already known: an end position, an "immediate neighbour of two people" condition (which places someone directly between them), or an "nth to the left/right of" count. Applying the conditions in an order where each new seat locks onto an already-fixed seat, starting from the person anchored at an end, fixes every seat in the row - after which the row's middle seat can simply be read off.

  1. Q sits at one of the ends, and M is second to the right of Q. A seat two places to the right of the far end would fall outside the row, so Q must be at the left end - this fixes M two seats to its right.

  2. V is the immediate neighbour of both M and N, so V sits directly between them. Testing the seat immediately to the left of M fails, since its other neighbour would be Q, not N - so V sits immediately to the right of M, with N on V's other side.

  3. V is third to the left of S, so S's seat is three places to the right of V's seat.

  4. T is immediately left of P, and third to the right of U - so U, T and P form a fixed run of seats, three and four places to the right of U respectively.

  5. R sits immediately right of P, and P is second to the right of O - extending the same run to O, T, P and R at two, three, four and five places to the right of U respectively.

  6. Fitting this five-seat run (U, O, T, P, R) into the seats that remain open, without clashing with the already-fixed seats of Q, M, V, N and S, pins down exactly one seat for U - and with it, every remaining friend's seat.

  7. The one seat left over once every other friend is placed belongs to W.

Reading the seats left to right gives the complete row:

Q, W, M, V, N, U, S, O, T, P, R

  • Q sits at the left end, and M is exactly two seats to its right - satisfies the third condition.

  • V sits directly between M and N, and S sits exactly three seats to the right of V - satisfies the second condition.

  • T sits immediately left of P, and exactly three seats to the right of U - satisfies the first condition.

  • R sits immediately right of P, and O sits exactly two seats to the left of P - satisfies the fourth condition.

With eleven friends in the row, the middle seat is the 6th seat, since (11 + 1) / 2 = 6. In the confirmed arrangement, the 6th seat is occupied by U - so U is sitting in the center of the row.

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