23.2. Validity of Paths in a Square Grid

Try these first

1. 1.

   Define what a valid path is.

   Hint

   Think about the movements allowed.

2. 2.

   How many total moves are there from (0,0) to (n,n)?

   Hint

   Count how many R's and T's are needed.

3. 3.

   What is the total number of moves from (0, 0) to (n, n)?

   • n
   • 2n
   • n^2

   Hint

   Count both direction moves.

4. 4.

   True or False: You can move left or down while traveling from (0,0) to (n,n).

   • True
   • False

   Hint

   Reflect on the definitions of valid paths.

5. 5.

   If n=4, calculate the total valid paths and explain the method used.

   Hint

   Use the formula for the binomial coefficient.

6. 6.

   Visualize a grid of n=3 and list all paths. How many distinct valid paths are there?

   Hint

   Each valid path is formed by ensuring no undesired movements occur.