COVID-19 Restaurant Seating Puzzle

Amie Campbell

You have made a reservation at a restaurant and you managed to book your favourite table out of the 100 available.

When the first person arrives, the booking system is down so they are seated at a random table by the waiting staff. The system then is booted back up. All of the other guests start to arrive. They are seated one by one by the restaurant staff at their originally assigned tables.

In order to reduce the risk of spreading coronavirus, once a guest is seated at a table, they must remain at their table even if it was not the table they were allocated originally on the booking system. If their original table is available, then a guest will be seated there. If not, they will be seated at a random available table. 

You are the last guest to arrive (i.e. the 100th person) and so there is only one table left in the restaurant, which you are seated at. 

What is the probability that the table you are seated at is the same one you had originally booked?

Watch Amie explain the solution here.

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