The puzzle
Omkar, Kiran, Deepak, Varun, Chetan, Arjun sit in a single row, all facing north. Seat 1 is the far-left end and seat 6 is the far-right end. Using the clues below, work out the order from left to right.
- Omkar sits somewhere to the left of Kiran.
- Chetan sits somewhere to the right of Varun.
- Exactly 1 person sits between Omkar and Arjun.
- Kiran sits somewhere to the left of Deepak.
- Arjun sits immediately to the left of Deepak.
- Exactly 2 people sit between Kiran and Chetan.
Question: What is the seating order from far-left to far-right?
Reveal the answer
Answer: Varun, Omkar, Kiran, Arjun, Deepak, Chetan (left to right).
Seat 1VarunSeat 2OmkarSeat 3KiranSeat 4ArjunSeat 5DeepakSeat 6Chetan
- Start: 720 possible left-to-right orders of 6 people.
- Clue 1 — "Omkar sits somewhere to the left of Kiran." leaves 360 possibilities.
- Clue 2 — "Chetan sits somewhere to the right of Varun." leaves 180 possibilities.
- Clue 3 — "Exactly 1 person sits between Omkar and Arjun." leaves 48 possibilities.
- Clue 4 — "Kiran sits somewhere to the left of Deepak." leaves 14 possibilities.
- Clue 5 — "Arjun sits immediately to the left of Deepak." leaves 3 possibilities.
- Clue 6 — "Exactly 2 people sit between Kiran and Chetan." leaves 1 possibility.
- Exactly one order survives every clue — that is the answer.