Nine persons- A, B, C, D, E, F, G, H and I sit around a circular table (but…

2023

Nine persons- A, B, C, D, E, F, G, H and I sit around a circular table (but not necessarily in the same order) in such a way that some are facing the center whereas others are facing away from the center. Not more than two persons sit together are facing in the same direction. No two persons in alphabetical order are sitting together. A sits third to the left of E both face in opposite directions. The person sits immediate left of A sits fourth to the right of D who faces the center. F sits third to the left of C and both face in the same direction. Neither G nor A sits adjacent to C. F sits immediate left of H who faces away from the center. Neither H nor B sits adjacent to E. B sits immediate left of G and faces away from the center. Find how many persons sit between E and B when counted from the right of B?

  1. A.

    Three

  2. B.

    Six

  3. C.

    Four

  4. D.

    One

  5. E.

    Five

Show answer & explanation

Correct answer: D

Concept

In a circular seating puzzle with mixed facing directions, the key idea is that 'left' and 'right' reverse with facing: a person facing the centre has their left towards the clockwise side, while a person facing away has their left towards the anticlockwise side. Fix the most-constrained person first, then propagate each clue, always interpreting 'left/right' through that person's own facing direction.

Building the arrangement

  1. Fix A's seat as a reference. 'A sits third to the left of E, both facing opposite directions' then places E three seats to A's left; testing both facings shows A must face away from the centre and E must face it.

  2. 'The person immediately left of A sits fourth to the right of D, and D faces the centre' fixes D's seat and the seat just left of A; with D facing the centre, its right runs anticlockwise, which uniquely locates that fourth seat.

  3. 'F sits third to the left of C, both facing the same direction' plus 'F sits immediately left of H, and H faces away from the centre' force F, H and C into a single block with F adjacent to H.

  4. 'B sits immediately left of G, and B faces away from the centre' fixes B and G; the negatives 'G and A are not adjacent to C' and 'H and B are not adjacent to E' then rule out the remaining alternative placements.

  5. Imposing the global rules - no two alphabetically consecutive persons adjacent, and no run of three consecutive persons facing the same way - eliminates every remaining case, leaving exactly one valid arrangement.

The unique clockwise order is A, F, H, D, B, G, E, C, I. Facing the centre: F, D, E, C. Facing away: A, H, B, G, I.

Seat

Person

Facing

1

A

Facing away

2

F

Facing centre

3

H

Facing away

4

D

Facing centre

5

B

Facing away

6

G

Facing away

7

E

Facing centre

8

C

Facing centre

9

I

Facing away

Answering the question

B faces away from the centre, so B's right is the clockwise side. Moving clockwise from B, the next seat is G and the one after that is E. Exactly one person, G, lies between B and E on that side.

Cross-check

If one instead counted on B's other (anticlockwise) side, six persons - D, H, F, A, I, C - would fall between B and E; that larger count belongs to the wrong side, confirming that counting from the right of B gives a single person in between.

So the number of persons sitting between E and B, counted from the right of B, is one.

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