I'll try my best.
ok lets use some numbers here.
The example given by maxn was: a "10" and two "1"s. So the sum of these three numbers is 12. This set of numbers then will start like this:
10,1,1,A,B,C,D,E,F,G,H,I,J,K,L whereas the letters are any numbers.
now you'd have to chose numbers for the letters, such as 10 + A + B =12
But also that 1 + A + B = 12...
so you can see.. by definition, the ONLY way that these equations can be true, if A=B=C=D=E... and son on...
They must all be the same, because 10 + E + L = 12 and 1 + E + L = 12
It applies to all. Thus, all must be equal.
To put differently: Prove the statement wrong by picking numbers. You will see, you wont be able to find numbers to fulfill statement 2.