2024 Cayley Problem 24

A park has four paths, as shown in the map below. It takes 2 minutes to walk along the path from A to B, 3 minutes to walk along the path from B to A, 3 minutes to walk along the path from B to C, and 3 minutes to walk around the path that begins and ends at B. Rasheeqa goes for a walk, starting at A, walking only in the directions indicated along the paths, never stopping to rest, and finishing at C.

If the walk takes a total of t minutes, how many possible values of t are there with t \le 100?

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.