An Insane Equation!!
Four positive integers are such that
What is the value of ??
This problem is part of the set Hard Equations
The answer is 73.
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1 solution
abcd+abc+bcd+cda+dab+ab+bc+cd+da+ac+bd+a+b+c+d=2009
(a+1)(b+1)(c+1)(d+1)-1=2009
(a+1)(b+1)(c+1)(d+1)=2010
Expressing 2010 as a product of primes, 2010=2x3x5x67.
Therefore, a+b+c+d=(2-1)+(3-1)+(5-1)+(67-1)
=73