The puzzle
Varun, Sanjay, Divya, Uma, Meera, Sneha 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.
- Uma sits somewhere to the left of Divya.
- Uma sits somewhere to the right of Sneha.
- Exactly 2 people sit between Varun and Uma.
- Sneha sits somewhere to the right of Meera.
- Varun sits immediately to the left of Meera.
- Exactly 2 people sit between Divya and Sneha.
- Uma sits somewhere to the left of Sanjay.
Question: What is the seating order from far-left to far-right?
Reveal the answer
Answer: Varun, Meera, Sneha, Uma, Sanjay, Divya (left to right).
Seat 1VarunSeat 2MeeraSeat 3SnehaSeat 4UmaSeat 5SanjaySeat 6Divya
- Start: 720 possible left-to-right orders of 6 people.
- Clue 1 — "Uma sits somewhere to the left of Divya." leaves 360 possibilities.
- Clue 2 — "Uma sits somewhere to the right of Sneha." leaves 120 possibilities.
- Clue 3 — "Exactly 2 people sit between Varun and Uma." leaves 28 possibilities.
- Clue 4 — "Sneha sits somewhere to the right of Meera." leaves 7 possibilities.
- Clue 5 — "Varun sits immediately to the left of Meera." leaves 3 possibilities.
- Clue 6 — "Exactly 2 people sit between Divya and Sneha." leaves 1 possibility.
- Clue 7 — "Uma sits somewhere to the left of Sanjay." leaves 1 possibility.
- Exactly one order survives every clue — that is the answer.