Problem

Source: 2023 South Russian Girls MO - Assara Juniors p6

Tags: combinatorics



Aunt Raya has $14$ wheels of cheese. She found out that out of any $6$ wheels, she could choose $4$ and put them on the scales so that the scales came into balance. Aunt Raya wants to give Daud Kazbekovich two of these $14$ wheels , and divide the rest equally (by weight) between Pavel and Kirill. Prove that she can make her wish come true.