Question 24
Let $T$ be the set of ordered triples $(x, y, z)$, where $x, y, z$ are integers with $0 \leq x, y, z \leq 9$. Players $A$ and $B$ play the following guessing game. Player $A$ chooses a triple $(x, y, z)$ in $T$, and Player $B$ has to discover $A$'s triple in as few moves as possible. A move consists of the following: $B$ gives $A$ a triple $(a, b, c)$ in $T$, and $A$ replies by giving $B$ the number $|x + y - a - b| + |y + z - b - c| + |z + x - c - a|$. Find the minimum number of moves that $B$ needs to be sure of determining $A$'s triple.