Eight friends P, Q, R, S, T, V, W and Y are sitting around a square table. Out…

2023

Eight friends P, Q, R, S, T, V, W and Y are sitting around a square table.

  1. Out of eight, four persons are sitting at the corners of the table and the other four are sitting at the mid-points of each side of the table.

  2. Persons at the corners are facing the centre while the persons at the mid points of side are facing outside.

  3. S is third to the right of P. P is facing the centre.

  4. Y is not sitting beside P or S.

  5. T is third to the right of R.

  6. R is not sitting at the mid-point of any side of the table.

  7. R is also not beside Y.

  8. There is only one person between P and V.

  9. Q is not sitting beside V.


How many people are there between T and Q ?

  1. A.

    1

  2. B.

    2

  3. C.

    3

  4. D.

    none

Attempted by 18 students.

Show answer & explanation

Correct answer: A

Concept: In circular or square seating puzzles, a person's left-right sense depends on which way they face. A person facing the centre has the clockwise direction (as the layout is drawn) as their LEFT, so their RIGHT runs counter-clockwise; a person facing outward has this reversed, with clockwise as their RIGHT. The number of people "between" two seats is counted along the shorter arc joining those two seats.

Application:

  1. Number the eight seats 1 to 8 clockwise, with corners at seats 1, 3, 5, 7 (facing the centre) and mid-points at seats 2, 4, 6, 8 (facing outward). Since P faces the centre, place P at a corner -- seat 1.

  2. P faces the centre, so P's right runs counter-clockwise. S, third to P's right, lands three seats counter-clockwise from seat 1, at seat 6 -- a mid-point.

  3. R never sits at a mid-point, so R must occupy one of the remaining corner seats: 3, 5 or 7.

  4. Only one person separates P and V, so V sits two seats from P along one arc -- seat 3 or seat 7, both corners.

  5. R must be seat 3, 5 or 7, and V must be seat 3 or 7 (clue 6). Testing the four possible pairings against the adjacency clues on Y (clues 2 and 5): V=3 with R=5, V=3 with R=7, and V=7 with R=3 each force Y into a seat that sits beside P, S or R, breaking clue 2 or clue 5. Only V=7 with R=5 leaves a seat for Y that clears every adjacency clue. This pairing also fixes T -- third to R's right, counter-clockwise -- at seat 2.

  6. With P, S, R, T and V fixed, Y cannot sit beside P (seats 8 or 2) or beside S (seats 5 or 7); of the seats still open, Y also cannot sit beside R (seat 4), so Y must take seat 3.

  7. The last two open seats, 4 and 8, remain for Q and W. Since Q cannot sit beside V (seat 8 is beside V's seat 7), Q takes seat 4 and W takes seat 8.

Cross-check: Every clue holds against the seating 1-P, 2-T, 3-Y, 4-Q, 5-R, 6-S, 7-V, 8-W: S is exactly third to P's right, T is exactly third to R's right, Y sits beside neither P nor S, R does not sit beside Y, exactly one person sits between P and V, and Q does not sit beside V.

Result: T occupies seat 2 and Q occupies seat 4; the shorter arc between them (seat 2 to seat 3 to seat 4) passes through only one seat, seat 3. So exactly one person sits between T and Q.

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