MathDB
Changing 4 consecutive numbers

Source: JOM 2024 P2

February 29, 2024
combinatorics

Problem Statement

The sequence 1,2,,2023,20241, 2, \dots, 2023, 2024 is written on a whiteboard. Every second, Megavan chooses two integers aa and bb, and four consecutive numbers on the whiteboard. Then counting from the left, he adds aa to the 1st and 3rd of those numbers, and adds bb to the 2nd and 4th of those numbers. Can he achieve the sequence 2024,2023,,2,12024, 2023, \dots, 2, 1 in a finite number of moves?
(Proposed by Avan Lim Zenn Ee)