Advanced Puzzles & Seating Arrangements — Worked Practice

2A.1 A Fully Worked Circular Arrangement

Consider eight people — A, B, C, D, E, F, G and H — seated around a circular table, all facing the centre. The clues are: A sits third to the right of B. C sits second to the left of A. D sits opposite B. E sits immediately to the right of D. F sits second to the right of C. G sits immediately to the left of B. H occupies the remaining seat.

Working through this systematically: place B at a reference position. A, third to the right of B, occupies the position three seats clockwise from B. C, second to the left of A, sits two seats anticlockwise from A. D is directly opposite B, which in an eight-seat circle means four seats away. E sits immediately clockwise of D. F sits two seats clockwise of C. G sits immediately anticlockwise of B, and H fills the one seat left over. Diagramming each clue in turn, rather than trying to hold the whole arrangement in memory at once, is what makes an eight-person puzzle tractable within exam time limits.

2A.2 A Fully Worked Linear Arrangement with an Attribute

Seven colleagues — P, Q, R, S, T, U and V — sit in a row facing north, and each has a distinct designation: Clerk, Officer, Manager, Assistant, Supervisor, Analyst and Director. The clues are: P sits third from the left end. The Manager sits immediately to the right of P. Q, who is the Analyst, sits at the right end. R sits exactly two seats to the left of the Director. S is the Clerk and sits second from the left end. T sits immediately to the left of the Officer, who is U. V is the Supervisor.

The correct approach is to fix the positional clues first (P third from the left, S second from the left, Q at the right end), then layer in the designation clues one at a time, checking after each addition that no contradiction has been introduced. Puzzles that combine a linear or circular seat order with a second independent attribute are solved fastest when the two clue types are tracked in separate columns of the same working diagram rather than merged into one narrative.

2A.3 A Fully Worked Floor-and-Box Puzzle

Six boxes — J, K, L, M, N and O — are stacked one on top of another, box 1 being the bottommost position and box 6 the topmost. J is placed exactly two positions above L. K is directly above J. M is placed at the very bottom. N is directly below O. The only positions left, once J, K, L, M, N and O are placed according to the above, must be internally consistent — meaning L, sitting two below J, and K sitting directly above J, together fix a contiguous three-box block (L, then a gap, then J, then K), which combined with M fixed at the bottom fully determines the stack when N-below-O is slotted into the remaining two positions.

2A.4 Ranking and Scheduling Worked Example

In a class of 40 students, Meena ranks 14th from the top. Directly computing her rank from the bottom uses the formula: rank from bottom = (total students) − (rank from top) + 1 = 40 − 14 + 1 = 27th. This formula — total minus rank-from-one-end plus one equals rank-from-the-other-end — is the single most useful identity in ranking puzzles and should be applied directly rather than re-derived from a diagram each time.

For scheduling, if a five-day training programme (Monday to Friday) must place Session X exactly two days after Session Y, and Session Y is fixed on Tuesday, then Session X falls on Thursday — counting forward two full days from Tuesday.

2A.5 Practice Set — Advanced Puzzles (14 MCQs)

1. In an 8-person circular arrangement facing the centre, if a person is placed exactly opposite another, how many seats apart are they (counting the shorter way)?
   (a) 4 (b) 3 (c) 5 (d) 2
2. A person ranks 14th from the top in a class of 40. Their rank from the bottom is:
   (a) 27th (b) 26th (c) 28th (d) 25th
3. In a row of 7 people, if a person sits third from the left end, how many people sit to their left?
   (a) 2 (b) 3 (c) 4 (d) 1
4. In a stack of 6 boxes (box 1 at the bottom), if box K is directly above box J, and box J is two positions above box L, how many positions separate K and L?
   (a) 3 (b) 2 (c) 4 (d) 1
5. A training session is scheduled exactly two days after Tuesday. On which day is it held?
   (a) Thursday (b) Wednesday (c) Friday (d) Saturday
6. In a circular arrangement of 10 people facing the centre, two people sitting exactly opposite each other are how many seats apart?
   (a) 5 (b) 4 (c) 6 (d) 3
7. In a linear arrangement of 9 people, a person sitting exactly in the middle is at position:
   (a) 5 (b) 4 (c) 6 (d) 4.5
8. In a floor puzzle with 12 floors (ground = 1, top = 12), a person living exactly midway between floor 2 and floor 12 lives on floor:
   (a) 7 (b) 6 (c) 8 (d) 6.5
9. When a puzzle combines seating order with a second attribute like profession, the recommended method is to:
   (a) Track both clue types in separate columns of one working diagram (b) Solve the attribute first and ignore seating (c) Solve seating first and discard all attribute clues (d) Guess the attribute assignment
10. In a row, if exactly 5 people sit to the right of R and R is 4th from the left end, the total number of people in the row is:
    (a) 9 (b) 8 (c) 10 (d) 7
11. In an 8-person circular arrangement, if C is second to the left of A, and A is third to the right of B, the working method is to:
    (a) Fix B's position first as a reference and place A, then C, relative to it (b) Guess A's position randomly (c) Assume C and B are always adjacent (d) Ignore B's position entirely
12. In box-stacking puzzles, "directly above" means:
    (a) Immediately adjacent in the stack, one position higher (b) Anywhere higher in the stack (c) Two positions higher (d) At the very top only
13. A runner finishes 9th from the last in a race of 30 runners. Their rank from the first is:
    (a) 22nd (b) 21st (c) 23rd (d) 20th
14. In scheduling puzzles, when a clue states an event is "exactly two days after" a fixed day, the correct approach is to:
    (a) Count forward exactly two full days from the fixed day (b) Count backward two days (c) Assume it means the very next day (d) Ignore the "exactly" qualifier

Answer Key

1.(a)

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13.(a) 14.(a)