# An Insane Equation!!

Algebra Level 4

Four positive integers $$a, b, c, d$$ are such that

$$abcd+abc+bcd+cda+dab\\+ab+bc+cd+da+ac+bd+a+b+c+d = 2009 .$$

What is the value of $$a+b+c+d$$??

This problem is part of the set Hard Equations

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