MathDB

2.4

Part of 2019 Belarus Team Selection Test

Problems(1)

Colorings of a table

Source: 2019 Belarus Team Selection Test 2.4

9/2/2019
Cells of 11×1111\times 11 table are colored with nn colors (each cell is colored with exactly one color). For each color, the total amount of the cells of this color is not less than 77 and not greater than 1313. Prove that there exists at least one row or column which contains cells of at least four different colors.
(N. Sedrakyan)
combinatorics