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BALTIC-WAY 2006 Problem 4

  • Answer

Let a,b,c,d,e,fa, b, c, d, e, f be non-negative real numbers satisfying a+b+c+d+e+f=6a+b+c+d+e+f=6. Find the maximal possible value of

abc+bcd+cde+def+efa+faba b c+b c d+c d e+d e f+e f a+f a b

and determine all 6-tuples (a,b,c,d,e,f)(a, b, c, d, e, f) for which this maximal value is achieved.

Dataset text NuminaMath olympiads. Quoted with source.

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