Answer :
So, in general, the number of routes for the checker to reach the bottom of the board in an m x n checkerboard is [tex]2^{(m-1)}.[/tex]
To determine the number of routes for the checker to reach the bottom of the board, we need to consider the dimensions of the checkerboard and the possible moves the checker can make.
Let's assume the checkerboard has dimensions of m rows and n columns. Since the checker starts at the top right corner, it needs to reach the bottom row. The checker can only move diagonally downward, either to the left or to the right.
To reach the bottom row, the checker must make m-1 moves. Since each move can be either diagonal-left or diagonal-right, there are two options for each move. Therefore, the total number of routes can be calculated as 2 raised to the power of (m-1).
In mathematical notation, the number of routes is given by:
Number of routes = [tex]2^{(m-1)}[/tex]
For example, if the checkerboard has 8 rows, the number of routes would be:
Number of routes = [tex]2^{(8-1)[/tex]
= [tex]2^7[/tex]
= 128
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