MathDB

11.4

Part of 2003 All-Russian Olympiad Regional Round

Problems(1)

vector numbering

Source: Russia 2003

4/29/2008
Points A1,A2,...,An A_1,A_2,...,A_n and B1,B2,...,Bn B_1,B_2,...,B_n are given on a plane. Show that the points Bi B_i can be renumbered in such a way that the angle between vectors AiAj⟶ A_iA_j^{\longrightarrow} and BiBj⟶ B_iB_j^{\longrightarrow} is acute or right whenever i≠j i\neq j.
vectorcombinatorics unsolvedcombinatorics