Question 42
(a) Adriano secretly chose five numbers $a$, $b$, $c$, $d$ and $e$ and informed Bruna the ten numbers $24, 28, 30, 30, 32, 34, 36, 36, 40$ and $42$ obtained by calculating all the sums of two numbers among the five chosen. Bruna's goal is to discover $a$, $b$, $c$, $d$, $e$. Can Bruna achieve her goal?
(b) Adriano secretly chose four numbers $m$, $n$, $p$ and $q$ and reported to Carlos the six numbers $10, 20, 22, 24, 26$ and $36$ obtained by calculating all the sums of two numbers among the four chosen. Carlos' goal is to discover $m$, $n$, $p$ and $q$. Can he reach his goal?
(b) Adriano secretly chose four numbers $m$, $n$, $p$ and $q$ and reported to Carlos the six numbers $10, 20, 22, 24, 26$ and $36$ obtained by calculating all the sums of two numbers among the four chosen. Carlos' goal is to discover $m$, $n$, $p$ and $q$. Can he reach his goal?