MathDB

Pooki Sooki has

8

hoodies, and he may wear any of them throughout a 7 day week. He changes his hoodie exactly

2

times during the week, and will only do so at one of the

6

midnights. Once he changes out of a hoodie, he never wears it for the rest of the week. The number of ways he can wear his hoodies throughout the week can be expressed as

\frac{8!}{2^k}

. Find

k

.
Proposed by Minseok Eli Park (wolfpack)

Problem Statement