Problems(2)
14 wheels of cheese and a scale
Source: 2023 South Russian Girls MO - Assara Juniors p6
2/28/2024
Aunt Raya has wheels of cheese. She found out that out of any wheels, she could choose and put them on the scales so that the scales came into balance. Aunt Raya wants to give Daud Kazbekovich two of these wheels , and divide the rest equally (by weight) between Pavel and Kirill. Prove that she can make her wish come true.
combinatorics
gray cells in 5x9 table (senior version of 5x5 junior)
Source: 2023 South Russian Girls MO - Assara Seniors p6
3/1/2024
In a checkered rectangle, the middle row and middle column are colored gray. You leave the corner cell and move to the cell adjacent to the side with each move. For each transition from a gray cell to a gray one you need to pay a ruble. What is the smallest number of rubles you need to pay to go around all the squares of the board exactly once (it is not necessary to return to the starting square)?
combinatoricsColoring