MathDB
Maximal value when a+b+c+d+e+f=6

Source: Baltic Way 2006

December 4, 2010
inequalitiesinequalities proposed

Problem Statement

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
\color{white}\ .  \ \color{black}\   abc+bcd+cde+def+efa+fab
and determine all 66-tuples (a,b,c,d,e,f)(a,b,c,d,e,f) for which this maximal value is achieved.
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