Question

abc+bca+cab=222 caluculati ab+bc+ca.

Answer 1

a•100+b•10+c+b•100+c•10+a+c•100+a•10+b= 111a +111b+111c=222

Answer 2

Deoarece avem numerele :

$\it \overline{abc},\ \overline{bca},\ \overline{cab} \Rightarrow a,\ b,\ c \neq0$

$\it \overline{abc} +\overline{bca}+\overline{cab} =222 \Rightarrow \\ \\ \Rightarrow 100a+10b+c+100b+10c+a+100c+10a+b=222 \Rightarrow \\\\\Rightarrow 111a+111b+111c=222\Rightarrow 111(a+b+c) =222\Rightarrow a+b+c=2$

Deoarece a, b, c sunt cifre nenule, ultima egalitate este falsă.