Answer to October 04, 2004 Problem |
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The Greeley, Colorado Problem |
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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?
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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.
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1. Rich Murray | Ridgetown, Ontario, Canada |
2. James Alarie | Universty of Michigan -- Flint, Flint, Michigan |
3. Larry Schwartz | Trumbull, Connecticut |
4. Viktor Logrell | Tullängsskolan, Örebro, Sweden |
5. Jonas Sutinen | Tullängsskolan, Örebro, Sweden |
6. Gustav Nilsson | Tullängsskolan, Örebro, Sweden |
7. Richard Johnson | La Jolla, California |
8. Jeffrey Gaither | Winchester, Virginia |
9. Jonathan Jansson | Tullängen, Örebro, Sweden |
10. Ako Saleh | Tullängen, Örebro, Sweden |
11. Erik Hultgren | Tullängsskolan, Örebro, Sweden |
12. Daniel Kvist | Tullängsskolan, Örebro, Sweden |
13. Sanna Lejegren | Tullängsskolan, Örebro, Sweden |
14. Erik Ekman | Tullängsskolan, Örebro, Sweden |
15. Joakim Berggren | Tullängsskolan, Örebro, Sweden |