Sunday Times Teaser 2729 – Factorial Fact

by Nick MacKinnon

Factorial(n) is written as n! and is defined as the product of the integers from 1 to n inclusive.

Eleven of the twelve factorials from 1! to 12! inclusive can be grouped into two groups of four and a group of three in such a way that the products of the factorials in each group are all perfect squares.

What factorials are in the group with the smallest product?