Edward starts in his house, which is at (0,0) and needs to go point (6,4), which is coordinate for his school. However, there is a park that shaped as a square and has coordinates (2,1),(2,3),(4,1), and (4,3). There is no road for him to walk inside the park but there is a road for him to walk around the perimeter of the square. How many different shortest road routes are there from Edward's house to his school?
Problem
Source:
Tags: analytic geometry, geometry, perimeter
Silverfalcon
27.01.2006 03:01
Your answer is correct. Mind on showing "how" you counted them?
LordoftheMorons
27.01.2006 03:30
1 5 15 25 40 66 110 1 4 10 10 15 26 44 1 3 |6 ....| 11 18 1 2 |3 4 5| 6 7 S 1 .1 .1 .1 .1 .1 As you may or may not be able to tell by this terrible diagram, there is a bounded region (the park) and a starting point (S). the number of routes to that number is found by adding the two numbers numbers leading to it (kind of like a Pascals triangle, except with a top of S, a bounded region, and opening to the right and up.) At the destination, there are 110 unique shortest paths.
JesusFreak197
27.01.2006 04:51
Yeah, same thing I did. It's kind of hard to explain without a diagram, but you basically draw a 6x4 grid with a 2x2 square rather than a 1x1 at the specified spot. From there, it's the standard counting thing.
LordoftheMorons
27.01.2006 23:09
Yah... I was trying to draw a grid with autocad, but it was screwing up, so I gave up and drew that crappy ASCII drawing =p