MathDB
cards lies beautifully

Source: 2024 South Russian Girls MO - Assara Juniors p1 (Assara 2024 J1)

October 14, 2024
combinatorics

Problem Statement

There is a set of 5050 cards. Each card on both sides is colored in one of three colors — red, blue or white, and for each card its two sides are colored in different colors. The cards were laid out on the table. The card lies beautifully if at least one of two conditions is met: its upper side — red; its underside is blue. It turned out that exactly 2525 cards are lying beautifully. Then all the cards were turned over. Now some of the cards are lying beautifully on the table. How many of them can there be? K.A.Sukhov