41. (MON 2) Let points be given arbitrarily in the plane, no three of them collinear. Let us draw segments between pairs of these points. What is the minimum number of segments that can be colored red in such a way that among any four points, three of them are connected by segments that form a red triangle?
Track / Stage 4 / 188 of 340 #448 of 1964
Problem 448
AMC 12 late, AIME early Combinatorics Difficulty 4.9 Find the answer
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Official solution
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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.