1.4. More Complex Blockages

Try these first

1. 1.

   How many total paths are there from (0,0) to (3,2)?

   Hint

   Consider how many total moves and how you can arrange them.

2. 2.

   What is '4 choose 2'?

   Hint

   Think about how you can choose 2 moves from a total of 4.

3. 3.

   How many unique paths are there from (0,0) to (3,3)?

   • 6
   • 20
   • 10

   Hint

   Think about total steps and how to arrange vertical and horizontal moves.

4. 4.

   True or False: The number of paths going through (1,1) in a 3x3 grid is always the same as going through (2,2).

   • True
   • False

   Hint

   Consider how each point's distance affects available paths.

5. 5.

   Design a larger grid path model where various points are blocked. Calculate the remaining valid paths using inclusion-exclusion principles.

   Hint

   Draw a smaller grid to visualize blocked paths and use known combinations.

6. 6.

   Create a scenario with multiple paths and suggest how you might compute the benefits or drawbacks of various paths in a real-world situation.

   Hint

   Think about traffic flows and how to avoid congestion.