# Too Many Solutions!

**Algebra**Level 5

\[\large a+b+c+d=12\] \[\large abcd = 27+ab+ac+ad+bc+bd+cd\]

Given that \(a,b,c\) and \(d\) are all positive integers, find the sum of all possible values of \(a\).

\[\large a+b+c+d=12\] \[\large abcd = 27+ab+ac+ad+bc+bd+cd\]

Given that \(a,b,c\) and \(d\) are all positive integers, find the sum of all possible values of \(a\).

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