6

Part of 2024 Caucasus Mathematical Olympiad

Problems(1)

Permuting numbers in a table

Source: Caucasus MO 2024, Juniors P6

The integers from

1

320000

are placed in the cells of a

8 \times 40000

board. Prove that it is possible to permute the rows of the table so that the numbers in each column will not be sorted from the top to the bottom in increasing order.