1.2. Counting Paths without Blocks

Try these first

1. 1.

   How many total moves do you need to reach (3,4)?

   Hint

   Add up the right and up moves.

2. 2.

   What is the binomial coefficient for (5,3)?

   Hint

   Count total moves needed.

3. 3.

   How many distinct paths from (0,0) to (5,10)?

   • 100
   • 3003
   • 5000

   Hint

   Think about how many total moves you need.

4. 4.

   True or False: A blocked intersection increases the number of valid paths.

   • True
   • False

   Hint

   Consider how blocked paths affect counts.

5. 5.

   How many paths are there from (0,0) to (6,4) with blocked points at (2,2) and (4,3)?

   Hint

   Break this down into segments, computing each segment's paths separately.

6. 6.

   Describe a complex grid scenario involving three blocked points and outline the process to compute valid paths.

   Hint

   Use clear steps for each block, ensuring you count each way to navigate between them.