# Thread: SETS - (k+1)-element subset S

1. ## SETS - (k+1)-element subset S

There is a natural number $k$. Prove that from any set consisting of integer numbers that has more than $3^k$ elements we can take a subset S that has $(k+1)$ elements and:
For any two different subsets $A, B \subseteq S$ the sum of all elements of set $A$ is different from the sum of all elements of set $B$. (We assume that the sum of all elements of an empty set equals 0).

I would be really grateful if anyone could help me with this assignment.

2. Maybe we can try to prove it inductively...

But I don't know how do get down to it anyway.