MathDB
How Many Puddings?

Source: 2019 Taiwan TST Round 2

April 1, 2020
combinatorics

Problem Statement

There are n≥3 n \ge 3 puddings in a room. If a pudding A A hates a pudding B B , then B B hates A A as well. Suppose the following two conditions holds:
1. Given any four puddings, there are two puddings who like each other.
2. For any positive integer m m , if there are m m puddings who like each other, then there exists 3 3 puddings (from the other n−m n-m puddings) that hate each other.
Find the smallest possible value of n n .
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