[tex]\it \overline{xyz}+ \overline{yzx}+ \overline{zxy}=444\Rightarrow100x+10y+z+100y+10z+x+100z+10x+y =444\Rightarrow\\ \\ \Rightarrow 111x+111y+111z=444\Rightarrow 111(x+y+z)=444|_{:111}\Rightarrow x+y+z=4\Rightarrow\\ \\ \Rightarrow \overline{xyz} \in\{112,121,211\}[/tex]
