Probability puzzle: How many balls in the bag?

Written by Michael Fletcher on 14 February 2022.

Last week our village had a fête. One of the competitions on offer was to guess the number of balls in a bag. There were N balls in the bag, and they were numbered 1, 2, 3, …, N. To help competitors make a sensible guess, they were allowed to take out four balls and note the numbers on them.

When I took part, I pulled out balls numbered 24, 87, 14 and 35.

There is a prize for the person who guesses the correct number exactly. How many balls should I estimate are in the bag?

Send your answers to This email address is being protected from spambots. You need JavaScript enabled to view it.. Explain to us how you came up with the solution, as we may publish a selection of correct entries (if received by 7 March 2022).

• Puzzle set by Michael Fletcher and published in the February 2022 issue of Significance.
• Try your hand at Michael's previous puzzle, "Classroom bingo", and read the solution in our latest issue (magazine subscription required).