MathDB

The sequence

1, 2, \dots, 2023, 2024

is written on a whiteboard. Every second, Megavan chooses two integers

a

and

b

, and four consecutive numbers on the whiteboard. Then counting from the left, he adds

a

to the 1st and 3rd of those numbers, and adds

b

to the 2nd and 4th of those numbers. Can he achieve the sequence

2024, 2023, \dots, 2, 1

in a finite number of moves?
(Proposed by Avan Lim Zenn Ee)

2