Problem

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2018 Shortlist LRP5 (Logic Reasoning Probability)

Tags: combinatorics, probability



The Matini company released a special album with the flags of the $ 12$ countries that compete in the CONCACAM Mathematics Cup. Each postcard envelope has two flags chosen randomly. Determine the minimum number of envelopes that need to be opened to that the probability of having a repeated flag is $50\%$.