Q23 from AMC 2012 If $abc+ab+bc+ac+a+b+c=104$, and $a,b,c>0$, what is the value of  $ a^2 + b^2 +c^2$?
I tried to make $a,b,c$ the subject of the equation and tried to add them up but it's weird...
I also have lots of more questions which I will ask later from AMC 2012, it's more difficult than what I usually do...

Given, $abc+ab+bc+ac+a+b+c=104$, and $a,b,c>0$
$abc+ab+bc+ac+a+b+c=104$
$(a+1)(b+1)(c+1)-1=104$
$(a+1)(b+1)(c+1)=105$
$(a+1)(b+1)(c+1)=3\cdot5\cdot7$
Without the loss of generality, let $a\leq b\leq c$
$a+1=3, b+1=5, c+1=7$
$a=2, b=4, c=6$
$\;\therefore\;a^2+b^2+c^2=2^2+4^2+6^2$
Hence, $a^2+b^2+c^2=56$
