MathDB

P5

Part of 2023 China Team Selection Test

Problems(1)

A geometry (combinatorics) problem that is not orz

Source: 2023 China TST Problem 5

3/15/2023
Let △ABC\triangle ABC be a triangle, and let P1,⋯ ,PnP_1,\cdots,P_n be points inside where no three given points are collinear. Prove that we can partition △ABC\triangle ABC into 2n+12n+1 triangles such that their vertices are among A,B,C,P1,⋯ ,PnA,B,C,P_1,\cdots,P_n, and at least n+n+1n+\sqrt{n}+1 of them contain at least one of A,B,CA,B,C.
geometrycombinatoricsChina TST