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Direction: Study the information given below and answer the question that follows.

Six people — Sonu, Monu, Jim, Akash, Anvesha and Kapil — are sitting around a circular table.
All of them are facing towards the center of the circle.
Anvesha is not sitting between Monu and Akash.
Some people are sitting between Monu and Akash.
Sonu sits just left of Kapil.
Jim is fourth to the right of Sonu.

Question: Who is sitting opposite to Jim?

(inferred — the clue "some people are sitting between Monu and Akash" is read as "Monu and Akash are not neighbours", and "Anvesha is not sitting between Monu and Akash" is read on the shorter of the two arcs separating them. Applying the second clue to both arcs at once leaves no valid seating at all, so the shorter-arc reading is the one under which the setup is satisfiable. The answer is the same under either left/right orientation convention for people facing the center.)

1d:Td32,# Editorial ## Overview Six people sit around a circular table facing the center, and four clues constrain the arrangement. The task is to name the person seated directly opposite Jim. The answer is `Kapil`. ## Key Insight Only two of the four clues matter. `Sonu sits just left of Kapil` and `Jim is fourth to the right of Sonu` chain together into a fixed offset between Jim and Kapil, and on a circle of six that offset happens to be exactly three seats — the diameter. The clues about Monu, Akash and Anvesha narrow down which seating occurs but cannot change who faces Jim across the table. ## Approach Number the seats `0` through `5` going clockwise. For people facing the center, the left hand points clockwise and the right hand points anticlockwise, so `just left of Kapil` places Sonu one seat clockwise from Kapil, and `fourth to the right of Sonu` places Jim four seats anticlockwise from Sonu. Composing the two gives Jim at `Kapil + 1 - 4`, which modulo six is `Kapil + 3`. Since `3` is half of `6`, Jim and Kapil are diametrically opposite. To confirm nothing was missed, pin Sonu at seat `0` to remove rotational symmetry, generate all `5! = 120` orderings of the remaining five people, keep the seatings satisfying every clue, and read off who sits three seats from Jim in each. ## Why This Works Enumeration is complete, so no case is assumed away. Three seatings survive the filters — `Sonu, Monu, Jim, Akash, Anvesha, Kapil`, `Sonu, Akash, Jim, Monu, Anvesha, Kapil` and `Sonu, Akash, Jim, Anvesha, Monu, Kapil`, read clockwise. The arrangement is therefore not unique, but all three place Kapil opposite Jim, which matches the algebraic argument. Flipping the left/right convention produces a different set of three seatings — `Sonu, Kapil, Anvesha, Monu, Jim, Akash`, `Sonu, Kapil, Akash, Anvesha, Jim, Monu` and `Sonu, Kapil, Anvesha, Akash, Jim, Monu` — and Kapil is again the one facing Jim, so the item is orientation-proof. Checking the options one by one: `Sonu` is the result of counting `fourth to the right` inclusively, a three-step move that lands the wrong seat; `Akash` and `Monu` are Jim's flanking neighbours in most surviving seatings rather than the seat across from him; `Kapil` is opposite Jim in every seating consistent with the clues, so `Kapil` is the answer. ## Complexity Enumerating `5!` seatings and testing a constant number of clues on each costs `O(n!)` time with `n = 6`, which is `120` checks — instant. Done by hand, the deduction is `O(1)`: compose the two positional clues and take the offset modulo six. ## Common Pitfalls The most frequent error is reversing left and right: seated people facing the center have their left toward the clockwise direction, the opposite of the map-style convention used when they face outward. Here that mistake is harmless, but on most seating items it is fatal, so it is worth getting right. A second trap is inclusive counting — `fourth to the right` means four moves from Sonu, not three, and the off-by-one lands on `Sonu` himself as the seat facing Jim. A third is forgetting that `fourth to the right` wraps around a six-seat circle, so positions must be taken modulo six. Finally, do not burn time forcing a unique seating: the clues pin three arrangements, not one, and the question is still answerable because every one of them agrees on who faces Jim. 13:[["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"LearningResource\",\"learningResourceType\":\"Coding Question\",\"name\":\"Circular Seating: Opposite Jim\",\"description\":\"Six people — Sonu, Monu, Jim, Akash, Anvesha and Kapil — are sitting around a circular table, all facing towards the center of the circle. Anvesha is not sitting between Monu and Akash. Some people are sitting between Monu and Akash. Sonu sits just left of Kapil. 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Circular Seating: Opposite Jim

Problem Statement

Question 1