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.
- Puzzle set by Michael Fletcher and published in the June 2022 issue of Significance.
- Try your hand at Michael's previous puzzle, "Oh no! Puncture!", and read the solution in our latest issue (magazine subscription required).