76 numbere cards in a circle
Source: III Soros Olympiad 1996-97 R2 10.6 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics
May 31, 2024
combinatorics
Problem Statement
There are cards with different numbers written on them. These cards are laid out on the table in a circle, number down. Try to find some three cards in a row such that the number written on the middle of these three cards is greater than on each of the two neighboring ones. You can turn over no more than cards in succession. How should one proceed to be sure to find three cardboard boxes for which the specified condition is met?