Mathematical Enigma - XX

Algebra Level 3

If \(a,b,c,d,e,f\) are positive real numbers which satisfy \[a+b+c+d+e+f=7 \ , \] find the minimum value of \[\frac { 1 }{ a } +\frac { 4 }{ b } +\frac { 9 }{ c } +\frac { 16 }{ d } +\frac { 25 }{ e } +\frac { 36 }{ f } . \]

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