Discrete Mathematics An Open Introduction, 4th Edition

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.

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?

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?

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?