Question 17
Arnaldo chooses a number $a$, $a \ge 0$, and Bernaldo chooses a number $b$, $b \ge 0$. They both secretly tell their chosen number to Cernaldo, who writes on a blackboard the numbers $5$, $8$ and $15$, one of them being the sum $a + b$.
Cernaldo rings a bell and Arnaldo and Bernaldo, individually, write on separate pieces of paper whether or not they know which of the numbers on the board is the sum of $a$ and $b$ and hand them to Cernaldo.
If NO is written on both pieces of paper, Cernaldo rings the bell again and the process is repeated.
Arnaldo and Bernaldo are known to be sincere and intelligent.
What is the maximum number of times you could ring the bell until one of them writes that they know the value of the sum?
Cernaldo rings a bell and Arnaldo and Bernaldo, individually, write on separate pieces of paper whether or not they know which of the numbers on the board is the sum of $a$ and $b$ and hand them to Cernaldo.
If NO is written on both pieces of paper, Cernaldo rings the bell again and the process is repeated.
Arnaldo and Bernaldo are known to be sincere and intelligent.
What is the maximum number of times you could ring the bell until one of them writes that they know the value of the sum?