Problem D

Arranging Cards

Delphine has cards that each contain two pictures; one on the left side of the card and one on the right side of the card. Delphine arranges some of these cards in a row according to the following rules.

The picture on the right side of any card in the row is the same as the picture on the left side of the card to its right.

Cards can not be rotated.

The following diagram shows all of Delphine’s cards. Arrows out of a card indicate the possible card(s) that could be placed to its right.

By following the rules, what is the maximum number of cards Delphine can arrange in a row?

This problem was inspired by a past Beaver Computing Challenge (BCC) problem.