Hello, agrabham!

We need some clarification . . . Some of it is not clear.

The collection is: .You are given a finite collection of distinct quantities and told thier sum.

And their sum is: .

One of them is chosen (you are not told which one),

and you are told the sum of every pair of distinct quantities that contains it.

Suppose the chosen number is

The sums are: .

Their total is: .

. . . . . . . . . . .

. . . . . . . . . . .

You deduce that the chosen quantity is equal to

the difference between this sum of pairs and the first given pair ??

divided by two less that the total number of quantities.

Do this mean: . ?

If so, it doesn't work out . . .