Puzzle: Non-transitive dice


Consider six dice, each with six numbers on them. The numbers 1 to 36 are distributed between the faces of the six dice. The sum of the numbers on each dice is 111. The six dice are labelled a, b, c, d, e, and f. If I throw two of the dice, X and Y say, and X is more likely to have a higher number than Y, then we say X > Y.

Your challenge is to construct a set of dice so that a < b < c < d < e < f < a.

Send your answers to This email address is being protected from spambots. You need JavaScript enabled to view it.. Explain how you came up with the solution, as we may publish a selection of correct entries (if received by 11 July 2022).