Hey there I need some help again. Hope you guys can help me out.

The numbers 1-50 are written on the blackboard. Then two numbers

a and b are chosen and replaced by the single number |a-b|: After 49 operations

a single number is left. Prove that it is is odd.

So far what I got is that since there is an odd number of odd numbers(25) we can say that no matter what combination of numbers you use, it will always come out odd because of this.

Dont think this will work as a proof, was hoping if someone can guide me through this problem better thanks.