Drunk Passenger Puzzle

The Puzzle: 100 people are boarding a plane with 100 seats.

• The first passenger is drunk and picks a seat completely at random.
• Every subsequent passenger takes their assigned seat if it’s open.
• If their seat is taken, they pick a random seat from the remaining ones. What is the probability that the 100th passenger sits in their own assigned seat?

1. The Strategy: Simplification

Let’s try for $N=2$ passengers.

• Drunk picks seat 1 (Correct): Last person gets seat 2 (Success).
• Drunk picks seat 2 (Wrong): Last person gets seat 1 (Fail).
• Probability = 1/2.

Let’s try for $N=3$ passengers.

• Drunk picks 1: Success.
• Drunk picks 3: Fail.
• Drunk picks 2: Now passenger 2 is “the new drunk” for the remaining 2 seats. We already know that the probability for 2 people is 1/2.
• Probability = 1/2.

2. The General Rule

No matter how many seats there are, the decision always “boils down” to whether Seat 1 or Seat $N$ is picked first.

• If any passenger picks Seat 1, the cycle of “taking someone else’s seat” ends, and the last passenger gets their correct seat.
• If any passenger picks Seat $N$, the last passenger is guaranteed to fail.
• All other seats just “kick the can down the road” to the next person.

Result: The probability is always 1/2.

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Interview-Focused Questions

Key Takeaway

This puzzle tests your ability to simplify a problem using small test cases to find a pattern ($N=2, N=3$) and then prove it logically.