<s>[INST] If $x$, $y$ and $z$ are distinct positive integers and $x+y+z=11$ then what is the maximum value of $(xyz+xy+yz+zx)$? 
If $x$, $y$ and $z$ are distinct positive integers and $x+y+z=11$ then what is the maximum value of $(xyz+xy+yz+zx)$?

We know that product is maximum when difference between $x$, $y$ and $z$ is minimum.
So, I assumed $x=3$, $y=4$ and $z=4$. 
Now putting this value in $xyz+xy+yz+zx$ I got my answer $88$. But actual answer is $78$. Where am I doing it wrong?
 [/INST] the way the question is worded, $x$ and $y$ and $z$ cannot be equal (they must instead be distinct) so $y$ and $z$ cannot be $4$.
so the correct answer is choosing $5$, $4$ and $2$ for $x$, $y$ and $z$.
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