Let

be the set of ordered triples

, where

are integers with

. Players

and

play the following guessing game. Player

chooses a triple

in

, and Player

has to discover

's triple in as few moves as possible. A move consists of the following:

gives

a triple

in

, and

replies by giving

the number

. Find the minimum number of moves that

needs to be sure of determining

's triple.
%V0
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.