numbers in 3x2023 board (2023 May Olympiad L1 p4)
Source:
March 24, 2024
combinatorics
Problem Statement
There is a board with three rows and columns. In the first row the numbers are written from to , ordered from least to greatest. The devil writes those same numbers in the boxes in the second row, but ordered to his choice. Then, in each box in the third row he writes the difference between the two numbers already written in his own column (the largest minus the smallest). For example, if the first two boxes of a column are the numbers and , in the third box it is written . Explain why, no matter how the devil completed the second row of the board, it will never happen that multiplying them numbers in the third row the result is odd.