IMO Shortlist 2002 problem C4


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2. travnja 2012.
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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.
Izvor: Međunarodna matematička olimpijada, shortlist 2002