ISL 2002 C4

Let $T$ be the set of ordered triples $(x,y,z)$ , where $x,y,z$ are integers with $0\leq x,y,z\leq9$ . 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 $\left|x+y-a-b\right |+\left|y+z-b-c\right|+\left|z+x-c-a\right|$ . Find the minimum number of moves that $B$ needs to be sure of determining $A$ 's triple.

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