This week Tiny Alice goes on a tiny trip: Can You Race Across the Chess Board?

A very tiny Alice (…) is racing across a 2-by-2 chessboard, as shown below, where each smaller square has a side length of 1 cm. Alice starts at the bottom-left corner of the bottom-left black square and is trying to reach the top-right corner of the top-right black square.

There’s just one catch. Alice moves faster on the white squares than she does on the black squares. Her speed on the white squares is 1 cm per minute (again, she’s very small), while her speed on the black squares is 0.9 cm per minute.

What’s the least amount of time it will take her to reach the finish?

And here’s my proposed solution.

Actually, that link will also take you to a solution to the extra credit puzzle:

Instead of a 2-by-2 chessboard, Alice now wants to traverse an 8-by-8 chessboard, as shown below. Again, she’s going from the bottom-left corner of the bottom-left black square to the top-right corner of the top-right black square.

As before, her speed on the white squares is 1 cm per minute, while her speed on the black squares is 0.9 cm per minute.

What’s the least amount of time it will take her to reach the finish?