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# Musical chairs...sort of

Updated: Jun 22, 2022

On my flight to Reykjavik this morning - it was an early one but at least it actually departed, and on time - I remembered a maths puzzle. It goes as follows.

A plane has a hundred seats, and the flight is full. The first passenger to board however has lost his boarding pass so picks a seat at random. Subsequent passengers attempt to take their own seat but take one at random if theirs is taken. If you are the last to board, what is the probability you will get your assigned seat?

The puzzle is unambiguous from a mathematical perspective. Don’t look for any sleight of hand with respect to the language used because there isn’t one. In other words, for those of you who are chronically suspicious, there are 100 passengers and they have been assigned 100 different seats. It's just that one and only one of them has lost his boarding pass. And he just happens to be the first to board.

If you are still suspicious, pretend he had a paper boarding pass, lost it, could not remember his seat number, and had no record of it on his phone, laptop or elsewhere on his person, that he is on his own, and that the cabin crew cannot look at the passenger manifest to tell him his seat. Finally, the hundred seats mentioned are passenger seats and do not include seats for the crew either in the cockpit or the cabin. That should cover it. You know who you are…

Type your answer in a comment box by 5pm today. Closest to the correct answer gets an Amazon Fresh voucher for a box of bananas.

© Chimp Investor Ltd

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## 10 Comments

50%

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https://medium.com/i-math/solving-an-advanced-probability-problem-with-virtually-no-math-5750707885f1

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99%

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Alex if you and Charlie teamed up you’d do well hint hint

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All I can say Charlie is that if yours is the only entry you win the bananas!

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Good thinking Charlie! Sadly you will have to share the bananas with Alex but then lots of halves of bananas still equates to lots of bananas!

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