Difference between revisions of "2017 USAJMO Problems/Problem 6"
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Revision as of 20:38, 20 April 2017
Problem
Let 
be 
distinct points on the unit circle 
other than 
. Each point is colored either red or blue, with exactly 
of them red and exactly of them blue. Let 
be any ordering of the red points. Let 
be the nearest blue point to 
traveling counterclockwise around the circle starting from . Then let 
be the nearest of the remaining blue points to 
traveling counterclockwise around the circle from , and so on, until we have labeled all the blue points 
. Show that the number of counterclockwise arcs of the form 
that contain the point is independent of the way we chose the ordering of the red points.
Solution
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
See also
| 2017 USAJMO (Problems • Resources) | ||
| Preceded by Problem 2 |
LastProblem | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAJMO Problems and Solutions | ||
