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2009 UNCO Math Contest II Problems/Problem 6

Revision as of 17:50, 19 October 2014 by Timneh (talk | contribs) (Created page with "== Problem == Let each of <math>m</math> distinct points on the positive <math>x</math>-axis be joined to each of <math>n</math> distinct points on the positive <math>y</math>-...")
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Problem

Let each of $m$ distinct points on the positive $x$-axis be joined to each of $n$ distinct points on the positive $y$-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 $3$ when $m=3$ and $n=2.$

[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]


Solution

See also

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