Difference between revisions of "2009 UNCO Math Contest II Problems/Problem 6"
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m (moved 2009 UNC Math Contest II Problems/Problem 6 to 2009 UNCO Math Contest II Problems/Problem 6: disambiguation of University of Northern Colorado with University of North Carolina) |
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Revision as of 21:14, 19 October 2014
Problem
Let each of 
distinct points on the positive
-axis be joined to each of 
distinct points on
the positive 
-axis. Assume no three segments
are concurrent (except at the axes). Obtain
with proof a formula for the number of interior
intersection points. The diagram shows that
the answer is 
when 
and 
![[asy] draw((0,0)--(0,3),arrow=Arrow()); draw((0,0)--(4,0),arrow=Arrow()); for(int x=0;x<4;++x){ for(int y=0;y<3;++y){ D((x,0)--(0,y),black); }} dot(IP((2,0)--(0,1),(1,0)--(0,2))); dot(IP((3,0)--(0,1),(1,0)--(0,2))); dot(IP((3,0)--(0,1),(2,0)--(0,2))); [/asy]](http://latex.artofproblemsolving.com/9/a/4/9a4f1e83e4540dd6d84dee9c1a84b446076fed15.png)
