A3. For the numbers $a, b, c, d$ and $e$, it holds that:

$$
a+b+1=b+c-2=c+d+3=d+e-4=e+a+5 \text {. }
$$

Which of these five numbers is the largest?
A) $a$
B) $b$
C) $c$
D) $d$
E) $e$
A3. B) $b$

For the sums of pairs, we see that

$$
e+a<c+d<a+b<b+c<d+e .
$$

Every sum of four numbers can be obtained by adding two of these pairs. For example, $a+b+c+e$ is equal to $(e+a)+(b+c)$. Of all the quartets, the quartet $a, c, d, e$ has the smallest sum, because $a+c+d+e=(e+a)+(c+d)$ is the sum of the two smallest pairs. The remaining number, namely $b$, is thus the largest of the five. Indeed, the largest number is the number for which the remaining four numbers have the smallest sum.