Holiday Contest 2025 - Team Round - Problem 8

Vi, Powder, Caitlyn, Jayce, and Maddie each have one distinct hat and one distinct crystal. They are trying to put their crystals in hats. Maddie lost her hat, and Caitlyn's hat can hold at most two crystals. The other three hats can hold at most five crystals. Compute the number of ways for the people to put their crystals in the hats.