## Good Puzzles Are the Reason I Check Facebook

Here’s one by Sergei Luchinin, designed for 7th graders.

Puzzle.We have an 8-by-8 chessboard, but it’s not colored in the usual checkerboard pattern. Instead, all cells in odd-numbered columns are black, and all cells in even-numbered columns are white. A limping rook is placed in the lower-left corner and can only move one cell to the right or one cell up. The rook’s goal is to reach the upper-right corner.

The question is: Are there more paths that pass through more white cells, or more that pass through more black cells?

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## Zarunias:

You can group the paths into pairs: Every path is paired with the path you get if you rotate the whole path by 180°. In this way every path that passes through more black cells is paired with a path that passes through more white cells and vice versa. As there is no middle cell in the grid no path is paired with itself. So the numbers must be the same.

2 November 2024, 9:41 am