construct/mc non transitive dice
construct/mc non transitive dice: a task in MathConstructOptimize-Envs-harbor (Harbor dataset). Design 8 dice D 0, ..., D 7, each with 8 faces showing integers from 0..15 (values may repeat). Die D i beats die D j if, among the 64 pairs (a, b) of a face a of D i and a face b of D j, strictly more…
The task
Design 8 dice D_0, ..., D_7, each with 8 faces showing integers from 0..15 (values may repeat). Die D_i beats die D_j if, among the 64 pairs (a, b) of a face a of D_i and a face b of D_j, strictly more than 32 satisfy a > b. The dice must be cyclically intransitive: D_i beats D_(i+1) mod 8 for every i = 0..7.