Difference between revisions of "2008 AIME II Problems/Problem 10"
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Revision as of 19:42, 3 April 2008
Problem
The diagram below shows a 
rectangular array of points, each of which is 
unit away from its nearest neighbors.
![[asy] unitsize(0.25inch); defaultpen(linewidth(0.7)); int i, j; for(i = 0; i < 4; ++i) for(j = 0; j < 4; ++j) dot(((real)i, (real)j)); [/asy]](http://latex.artofproblemsolving.com/1/6/e/16ed1460ee16eabb872eb9645928df7b6cf2f60a.png)
Define a growing path to be a sequence of distinct points of the array with the property that the distance between consecutive points of the sequence is strictly increasing. Let 
be the maximum possible number of points in a growing path, and let 
be the number of growing paths consisting of exactly points. Find 
.
Solution
See also
| 2008 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
