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2016 CNMO Grade 11 P8

Source: 2016 China Northern MO Grade 11, Problem 8

February 25, 2020
combinatorics

Problem Statement

Given a set I={(x1,x2,x3,x4)∣xi∈{1,2,⋯ ,11}}I=\{(x_1,x_2,x_3,x_4)|x_i\in\{1,2,\cdots,11\}\}. A⊆IA\subseteq I, satisfying that for any (x1,x2,x3,x4),(y1,y2,y3,y4)∈A(x_1,x_2,x_3,x_4),(y_1,y_2,y_3,y_4)\in A, there exists i,j(1≤i<j≤4)i,j(1\leq i<j\leq4), (xi−xj)(yi−yj)<0(x_i-x_j)(y_i-y_j)<0. Find the maximum value of ∣A∣|A|.
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