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Problem of the Week
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.

character one penguin two fish one fish two fish two penguins
one fish one fish three fish three penguins one penguin two fish
one penguin two fish one penguin one penguin one fish two penguins
three fish two penguins two penguins two fish one penguin one fish
three penguins two fish one penguin two penguins one penguin two fish
three fish one fish three penguins two fish one fish house

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.