Problem E

Feeding Penguins

Sabrina is playing a video game that uses a \(6\) by \(6\) grid. Her character starts in the top-left square and needs to get to the house in the bottom-right corner. All the other squares contain either fish or penguins, as shown in the following grid.

Sabrina can move only right or down through the grid. When she gets to a square with fish, she picks up all the fish. When she gets to a square with penguins, she must feed one fish to each penguin.

If Sabrina starts with \(5\) fish, what is the maximum possible number of fish she could have with her when she arrives at the house?

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