1.3. Paths with a Blocked Intersection

Try these first

1. 1.

   How many total paths exist in a 3 by 2 grid?

   Hint

   Use the combination formula for paths.

2. 2.

   What does $C(n,k)$ represent?

   Hint

   Think about how you choose items.

3. 3.

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

   • 100
   • 1500
   • 3003

   Hint

   Think of the total steps needed.

4. 4.

   Is it possible to move from (0,0) to (5,10) without encountering a blocked intersection?

   • True
   • False

   Hint

   Consider valid pathways.

5. 5.

   You have a 6 by 6 grid and a blocked intersection at (3,3). Calculate the valid paths from (0,0) to (6,6).

   Hint

   Use the combination formula to solve.

6. 6.

   In a 7 by 7 grid with blockages at (4,5) and (5,4), find how many valid paths still exist.

   Hint

   Count paths through each block then adjust for overlaps.