[tex]\text{Daca sunt submultimi ordonate,e clar ca ne gandim la aranjamente:}\\
\text{Notam cu x numarul de elemente si obtinem:}\\
A_x^2=42\\
\dfrac{x!}{(x-2)!}=42\\
\dfrac{(x-2)!(x-1)\cdot x}{(x-2)!}=42\\
(x-1)x=42\\
x^2-x-42=0\\
\Delta=1+4\cdot 42=169\Rightarrow \sqrt{\Delta}=13\\
x_1=\dfrac{1+13}{2}=\dfrac{14}{2}=7\\
x_2=\dfrac{1-13}{2}=-6(\text{solutia aceasta nu convine})\\
\text{Prin urmare:}\\
S=7[/tex]
