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IMO ShortList 2002, combinatorics problem 4

Source: IMO ShortList 2002, combinatorics problem 4

September 28, 2004
combinatoricsgamegame strategyalgorithmIMO Shortlist

Problem Statement

Let TT be the set of ordered triples (x,y,z)(x,y,z), where x,y,zx,y,z are integers with 0≤x,y,z≤90\leq x,y,z\leq9. Players AA and BB play the following guessing game. Player AA chooses a triple (x,y,z)(x,y,z) in TT, and Player BB has to discover AA's triple in as few moves as possible. A move consists of the following: BB gives AA a triple (a,b,c)(a,b,c) in TT, and AA replies by giving BB the number ∣x+y−a−b∣+∣y+z−b−c∣+∣z+x−c−a∣\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 BB needs to be sure of determining AA's triple.
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