MathDB
14 wheels of cheese and a scale

Source: 2023 South Russian Girls MO - Assara Juniors p6

February 28, 2024
combinatorics

Problem Statement

Aunt Raya has 1414 wheels of cheese. She found out that out of any 66 wheels, she could choose 44 and put them on the scales so that the scales came into balance. Aunt Raya wants to give Daud Kazbekovich two of these 1414 wheels , and divide the rest equally (by weight) between Pavel and Kirill. Prove that she can make her wish come true.