Question 6
Axel and Franco play the following game. First Axel thinks of a natural number $N$. From then on, in each move, Franco chooses 4 distinct numbers $a, b, c, d$ from the set $\{1, 2, 3, 4, 5, 6, 7, 8\}$ and tells them to Axel. Then Axel announces one of the sums $N+a, N+b, N+c, N+d$, of his choice. (For example, if Axel thought of 2007 and in one move Franco chooses 1, 3, 4, 6, Axel must announce one of the numbers 2008, 2010, 2011, 2013, of his choice.)
Franco's goal is to know the number $N$ with certainty. Determine the minimum number of moves that always allows Franco to achieve his goal.
Franco's goal is to know the number $N$ with certainty. Determine the minimum number of moves that always allows Franco to achieve his goal.