1. ## Help

Problem:
There are some positive integers with the following properties:
-All are different and smaller than 100
-All their pairwise sums are different.
What is the maximum sum of these positive integers?

Can anyone simply explain what is being asked?
What does "pairwise sums" mean?
Thank you.

2. ## Re: Help

Originally Posted by DenisB
Problem:
There are some positive integers with the following properties:
-All are different and smaller than 100
-All their pairwise sums are different.
What is the maximum sum of these positive integers?
Can anyone simply explain what is being asked?
What does "pairwise sums" mean?
The term pairwise is a very important term in set theory.
In the definition of a partition it is said that the cells are pairwise disjoint. Meaning that any two cells have no elements in common.

Thus "pairwise sums" would be: If any two of the numbers are added together, their sum is different from the sum of any other pair in the collection.

3. ## Re: Help

So if lesser than 6 (instead of 100), then: 5,4,3,1
5+4=9
5+3=8
5+1=6
4+3=7
4+1=5
3+1=4

Thanks.