1. Grid Paths

Try these first

1. 1.

   What is the total number of paths from (0,0) to (1,1)?

   Hint

   Count the combinations of rights and ups.

2. 2.

   How many unique paths exist in a 2x2 grid?

   Hint

   You will have to move right and up once each.

3. 3.

   What is the formula for combinations?

   • n! / (k!(n-k)!)
   • k! / (n!(k-n)!)
   • k! * (n+k)!

   Hint

   Focus on the factorial notation.

4. 4.

   The inclusion-exclusion principle helps avoid what?

   • True
   • False

   Hint

   Remember how overlaps can lead to double counting.

5. 5.

   Consider a grid from (0,0) to (7,5). If points (3,2) and (5,4) are blocked, what is the number of valid paths?

   Hint

   Break down each segment into path counts.

6. 6.

   In a 10x10 grid, if the path must avoid (5,5) and (6,6), formulate a counting strategy.

   Hint

   Create combinations for segments before and after blockages.