MathDB

9

Part of 2021 Durer Math Competition Finals

Problems(1)

rook on a 8x8 chessboard

Source: 2021 Dürer Math Competition Finals Day2 E9 https://artofproblemsolving.com/community/c2749870_

1/8/2022
On an 8×88 \times 8 chessboard, a rook stands on the bottom left corner square. We want to move it to the upper right corner, subject to the following rules: we have to move the rook exactly 99 times, such that the length of each move is either 33 or 44. (It is allowed to mix the two lengths throughout the "journey".) How many ways are there to do this? In each move, the rook moves horizontally or vertically.
combinatoricsChessboard