1.
The 6 in the square in the 3rd row and column represents that there are 6 different paths to that square, even though there are only four squares the rook must move through to get there. One path is DDRR (down down right right). List all 6 paths.
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Let’s find some of the numbers of paths that the rook can take to get to various squares in the chessboard.
2.
How many paths are there to the square in row 4, column 2 (diagonally down and to the left of the 6)? List out all the paths as D/R strings.
How many paths is this? That is, what number goes in that square of the chessboard?
3.
Now let’s find the paths to the square in row 4, column 3 (directly below the 6).
First, list all the paths that end with an R.
Next, list all the paths that end with a D.
Are there any other paths? In total, how many paths are there to this square?
4.
Continue filling in the chessboard, either counting D/R strings directly or using your observation from the previous task. What is the number in the lower right corner of the chessboard?
