MathDB

Several positive integers are written in a row. Iteratively, Alice chooses two adjacent numbers

x

and

y

such that

x>y

and

x

is to the left of

y

, and replaces the pair

(x,y)

by either

(y+1,x)

(x-1,x)

. Prove that she can perform only finitely many such iterations.
Proposed by Warut Suksompong, Thailand

Problem Statement