Difference between revisions of "2017 USAJMO Problems/Problem 6"
(Created page with "==Problem== Let <math>P_1, \ldots, P_{2n}</math> be <math>2n</math> distinct points on the unit circle <math>x^2 + y^2 = 1</math> other than <math>(1,0)</math>. Each point is...") |
(No difference)
|
Revision as of 19:36, 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.