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Omni-MATH / Let T be the set of ordered triples (x,y,z), where x,y,z are integers with 0≤x,y,z≤9. Players A and B play the following guessing game. Player A chooses a triple (x,y,z) in T, and …

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problem

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[i]'s[/i] triple in as few moves as possible. A [i]move[/i] 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[i]'s[/i] triple.
Plain-text mathematical notation (without MathML)
Let T be the set of ordered triples (x,y,z), where x,y,z are integers with 0≤x,y,z≤9. 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[i]'s[/i] triple in as few moves as possible.  A [i]move[/i] consists of the following: B gives A a triple (a,b,c) in T, and A replies by giving B the number |x+y−a−b|+|y+z−b−c|+|z+x−c−a|. Find the minimum number of moves that B needs to be sure of determining A[i]'s[/i]  triple.
Original LaTeX notation
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 $A$[i]'s[/i] triple in as few moves as possible.  A [i]move[/i] 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 $A$[i]'s[/i]  triple.

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Source and history

task_id
8f80dcf0-b24c-5ab1-8c98-27a817e7b9d0
task_key
test--8f80dcf0-b24c-5ab1-8c98-27a817e7b9d0
task_revision_id
1
config / split
/ test

Official source

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