[Jazza]

cool problem, i appreciate posts like these

the first thing you have to realize is that either all the numbers are odd, or all the numbers are even, if this were not the case you could pick 12 numbers whose total sum is odd, and therefore when you split them into two equal groups, one odd, one even, and therefor not equal

if they are all even, you could divide them all by 2 and it shouldn't change whether or not all the numbers worked to begin with

if they are all odd, you could add 1 to all of the numbers, and then divide by two, and it should not change whether or not the numbers work

if at any time you end up with a mixture of odd and even numbers you know these numbers and hence the original numbers will not work

now you could repeat both of these processes, and as long as all of the numbers were finite to begin with, you will figure out the numbers don't work, or you will evenutally end up with all 1's

and the only way to end up with all 1's is to have all the numbers the same to start with