Birgit has a list of four numbers. Luciano adds these numbers together, three at a time, and gets the sums 415, 442, 396, and 325. What is the sum of Birgit's four numbers?
Suppose Birgit's four numbers are $a, b, c, d$.

This means that the totals $a+b+c, a+b+d, a+c+d$, and $b+c+d$ are equal to 415,442 , 396 , and 325 , in some order.

If we add these totals together, we obtain

$$
\begin{aligned}
(a+b+c)+(a+b+d)+(a+c+d)+(b+c+d) & =415+442+396+325 \\
3 a+3 b+3 c+3 d & =1578 \\
a+b+c+d & =526
\end{aligned}
$$

since the order of addition does not matter.

Therefore, the sum of Luciano's numbers is 526 .

ANSWER: 526