MathDB
"n-interesting" meeting

Source: 2018 China Southeast MO Grade 11 P6

July 31, 2018
combinatorics

Problem Statement

Assume integer m≥2.m \geq 2. There are 3m3m people in a meeting, any two of them either shake hands with each other once or not.We call the meeting "nn-interesting", only if there exists n(n≤3m−1)n(n\leq 3m-1) people of them, the time everyone of whom shakes hands with other 3m−13m-1 people is exactly 1,2,⋯ ,n,1,2,\cdots,n, respectively. If in any "nn-interesting" meeting, there exists 33 people of them who shake hands with each other, find the minimum value of n.n.
Back to ProblemsView on AoPS