Probability puzzle: Classroom bingo

Classroom

A primary schoolteacher is playing a game with her class. She has two identical dice, with the numbers on the six faces of each die being 1, 2, 2, 3, 3 and 3. The teacher tells the class that she will throw the pair of dice, add up the two numbers showing, and call out that number in a game of bingo. She then asks each member of the class to make their own bingo card consisting of five numbers of their own choosing.

The teacher explains that the children can repeat a number on their card if they wish (and then delete just one occurrence of the number whenever it is called).

Most of the class chose the five possible different totals as their bingo numbers, but one clever pupil made a better selection.

Can you figure out what her five numbers might have been? And is this the best possible selection? 

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 4 January 2022).

  • Puzzle set by Michael Fletcher and published in the December 2021 issue of Significance.
  • Try your hand at Michael's previous puzzle, "A certain bet", and read the solution in our latest issue (magazine subscription required).