[tex]\displaystyle\\
\text{Se cer numerele de forma }~\overline{xyz}~\text{ stiind ca } ~ \overline{xy}+\overline{yz}+\overline{zx}=66\\\\
\text{Rezolvare:}\\\\
\text{Descompunem in zeci si unitati numerele de 2 cifre.}\\\\
\overline{xy}+\overline{yz}+\overline{zx}=66\\\\
10x+y+10y+z+10z+x=66\\\\
10x+x+10y+y+10z+z=66\\\\
11x+11y+11z=66\\\\
11(x+y+z)=66\\\\
x+y+z = \frac{66}{11}\\\\
\boxed{\bf x+y+z=6}[/tex]
[tex]\Longrightarrow~~\text{Numerele de forma }~\overline{xyz}~\text{ au suma cifrelor egala cu 6.}\\\\
\Longrightarrow~~\overline{xyz}\in\{114;~123;~132;~141;~213;~222;~ 231;~312;~321;~411\}[/tex]