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Sunday Times Teaser 2729 – Factorial Fact

by Nick MacKinnon

Published: 11 January 2015 (link)

The “factorials” of numbers are defined by 1! = 1, 2! = 2×1, 3! = 3x2x1, 4! = 4x3x2x1, etc.

It is possible to take eleven of the twelve factorials

1!, 2!, 3!, 4!, 5!, 6!, 7!, 8!, 9!, 10!, 11!, 12!

and to split them into groups of three, four and four so that in each group the product of the factorials in that group is a perfect square.

What are the factorials in the group whose product is the smallest?

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