construct/mc non transitive dice
construct/mc non transitive dice: a task in MathConstructOptimize-Envs-harbor (Harbor dataset). Design 7 dice D 0, ..., D 6, each with 7 faces showing integers from 0..13 (values may repeat). Die D i beats die D j if, among the 49 pairs (a, b) of a face a of D i and a face b of D j, strictly more…
The task
Design 7 dice D_0, ..., D_6, each with 7 faces showing integers from 0..13 (values may repeat). Die D_i beats die D_j if, among the 49 pairs (a, b) of a face a of D_i and a face b of D_j, strictly more than 24 satisfy a > b. The dice must be cyclically intransitive: D_i beats D_(i+1) mod 7 for every i = 0..6.