Answer to the October 04, 2004 Problem of the Week

The Greeley, Colorado Problem

• Home
• Meet Mr. P
• What's New
• Humor
• Lesson Plans
• Quotes
• Links
• Puzzles & Games
• Problem of the Month
• Math Facts
• Poetry
• Videos

While traveling through Greeley, Colorado this past summer, I noticed that the city is laid out in a grid with numbered Avenues running in a North-South direction and numbered Streets running in an East-West direction. It is a mathematician's delight because you can never get lost! I couldn't help but notice how many times we would be at 7th Avenue and 7th Street or 10th Avenue and 10th Street, or 27th Avenue and 27th Street.

Greeley is set up like the third quadrant with the Avenues descending from left to right (West to East) and the streets descending from top to bottom (North to South). See the diagram below:

In how many ways can you drive from the North Colorado Medical Center (at the corner of 18th Avenue and 16th Street) to the Rio Grande Mexican Restaurant (at the corner of 10th Avenue and 9th Street) and still satisfy the conditions below?

1. You must always travel North and East.
2. You can not travel through any corners where the Avenue and Street have the same numerical value (like 3rd Avenue and 3rd Street).
3. 12th Street is one-way going East to West.
   11th Street is one-way going West to East.
   16th Avenue is one-way going North to South.
   15th Avenue is one-way going South to North.
4. You must obey traffic laws (you can not drive the wrong way on a one-way street).

 

---

Solution to the Problem:

There are 268 different ways to get there!

Using a table similar to Pascal's triangle, the numbers in the following diagram show how many different ways you can get to a particular corner. Remember, you can only travel north and east and you can not go the wrong way on a one-way street and you can not travel through an intersection where the Avenue and Street are of the same value.