Problem 8 · The ten pairwise sums
Each number appears in four pairs: $4S = 28$.
Integer answer, at most 4 digitsCarles writes five integers on a piece of paper. Adding them in pairs, the results are $-3, -1, 0, 2, 3, 3, 4, 5, 6$ and $9$. What is the sum of the five numbers?
Copa Cangur · SCM
Easy
Closed answer
Reasoned solution
Key idea: in the $\binom{5}{2} = 10$ pairwise sums, each number appears exactly $4$ times (once with each companion).
Adding the ten sums:
$$-3 - 1 + 0 + 2 + 3 + 3 + 4 + 5 + 6 + 9 = 28 = 4S \;\Longrightarrow\; S = 7.$$
Answer: 7