Problem #PRU-64427

Problems Discrete Mathematics Set theory and logic Mathematical logic Mathematical logic (other)

Problem

In an attempt create diversity the government of the planet hired $100$ truth tellers and $100$ liars. Each of them has at least one friend. Once exactly $100$ members said: “All my friends are honest” and exactly $100$ members said: “All my friends are liars.” What is the smallest possible number of pairs of friends, one of whom is honest and the other a liar?

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