Kourovka Problem 18.50 - Prescribed Permuted-Product Cardinality

Given $n$ and $1 \le c \le n!$, can $n$ distinct group elements be chosen so that their $n!$ ordered products take exactly $c$ distinct values? Constructions realize every $c$.

Result

Proved

Status

Resolved

AI contribution

AI-discovered

Method

Argument

Field

Group theory

Posed by

—

Year posed

2014

Years open

12y

Solved

2026-07-20

Model

Aristotle

Vendor

Harmonic

Collaborators

—

Verification

Lean-verified

Publication

Preprint

Significance

15 / 100*

Disclosed cost

—

Wikipedia

No dedicated article