1.1. Introduction to Grid Paths

Try these first

1. 1.

   How many total moves are needed to reach (5, 10) from (0, 0)?

   Hint

   Add the right and up moves together.

2. 2.

   If you can only move right (R) and up (U), which sequences are valid?

   Hint

   Think of different arrangements.

3. 3.

   How many steps are required to go from (0, 0) to (5, 10)?

   • 10
   • 15
   • 20

   Hint

   Add right and up moves.

4. 4.

   True or False: If an intersection is blocked, it can still be part of a valid path.

   • True
   • False

   Hint

   Think about blocked paths.

5. 5.

   Given a grid of size (n, m), derive the number of paths if points (i, j) and (k, l) are blocked.

   Hint

   Break it down into sections and compute step by step.

6. 6.

   Create a grid-based scenario illustrating how many paths are available if an entire column of intersections is blocked.

   Hint

   Use combinatorial principles for disconnected components.