Gridtown USA Route Calculations

The video tutorial explores the concept of shortest routes in a grid system, using Gridtown as an example. It covers calculating the number of shortest paths between two points using combinations, considering stops at donut shops, and avoiding obstacles like potholes. The tutorial also applies the principle of inclusion-exclusion to determine routes passing through multiple points of interest.

What is the primary feature of Gridtown USA's street layout?

• Circular roads

• Diagonal avenues

• Precisely laid out grids

• Randomly placed streets

If you live at (2, 3) and work at (8, 10), how many blocks do you need to move right?

• 7 blocks

• 8 blocks

• 5 blocks

• 6 blocks

How many shortest routes are there from home to work?

• 2048

• 1024

• 1716

• 2560

What is the location of the donut shop you stop at on the way to work?

• (6, 8)

• (7, 9)

• (8, 10)

• (5, 7)

How many shortest routes are there if you stop at the donut shop?

• 756

• 500

• 1000

• 1200

Where is the pothole located that you need to avoid?

• 4th Avenue between 5th and 6th Street

• 5th Avenue between 6th and 7th Street

• 6th Avenue between 7th and 8th Street

• 7th Avenue between 8th and 9th Street

How many shortest routes avoid the pothole?

• 1500

• 1200

• 1296

• 1000

What principle is used to calculate routes passing by both donut shops?

• Principle of Superposition

• Principle of Inclusion-Exclusion

• Principle of Least Action

• Principle of Maximum Likelihood

What is the new location of the donut shop?

• (2, 6)

• (3, 7)

• (4, 8)

• (5, 9)

How many shortest routes pass by one or both donut shops?

• 800

• 916

• 1000

• 1100