The puzzle
Arjun, Isha, Harsh, Chetan, Bhavna, Esha 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.
- Bhavna sits somewhere to the left of Chetan.
- Exactly 2 people sit between Chetan and Esha.
- Harsh sits at the far-left (extreme) end of the row.
- Exactly 4 people sit between Arjun and Harsh.
- Exactly 1 person sits between Harsh and Bhavna.
- Isha sits somewhere to the left of Chetan.
Question: What is the seating order from far-left to far-right?
Reveal the answer
Answer: Harsh, Esha, Bhavna, Isha, Chetan, Arjun (left to right).
Seat 1HarshSeat 2EshaSeat 3BhavnaSeat 4IshaSeat 5ChetanSeat 6Arjun
- Start: 720 possible left-to-right orders of 6 people.
- Clue 1 — "Bhavna sits somewhere to the left of Chetan." leaves 360 possibilities.
- Clue 2 — "Exactly 2 people sit between Chetan and Esha." leaves 72 possibilities.
- Clue 3 — "Harsh sits at the far-left (extreme) end of the row." leaves 12 possibilities.
- Clue 4 — "Exactly 4 people sit between Arjun and Harsh." leaves 2 possibilities.
- Clue 5 — "Exactly 1 person sits between Harsh and Bhavna." leaves 1 possibility.
- Clue 6 — "Isha sits somewhere to the left of Chetan." leaves 1 possibility.
- Exactly one order survives every clue — that is the answer.