2002 IMO Shortlist S18

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.

令 $T$ 为有序三元组 $(x,y,z)$ 的集合，其中 $x,y,z$ 是具有 $0\leq x,y,z\leq9$ 的整数。玩家$A$和$B$玩以下猜谜游戏。玩家 $A$ 在 $T$ 中选择一个三元组 $(x,y,z)$ ，而玩家 $B$ 必须在尽可能少的移动中发现 $A$ * 的* 三元组。 *移动*由以下部分组成：$B$在$T$中给$A$一个三元组$(a,b,c)$，$A$通过给$B$数字$\left|x+y-a-b\right |+\left|y+z-b-c\right|+\left|z+x-c-a\right|$来回复。求 $B$ 确定 $A$ * 的 * 三倍所需的最小移动次数。