5. Determine the largest three-digit number $\overline{a b c}$ such that $\overline{a b c}+\overline{b c a}+\overline{c a b}=1221$. Different letters represent different digits.
5. The equality $\overline{a b c}+\overline{b c a}+\overline{c a b}=1221$ corresponds to the equality:

$(100 a+10 b+c)+(100 b+10 c+a)+(100 c+10 a+b)=1221, \quad 2$ points

which is $111 a+111 b+111 c=1221, \quad 2$ points

or $111 \cdot(a+b+c)=1221, \quad 2$ points

from which $a+b+c=1221: 111=11$. 2 points

Since the largest three-digit number is sought such that

$\overline{a b c}+\overline{b c a}+\overline{c a b}=1221$, and the digits $a, b$ and $c$ must be different,

it follows that $a=8, b=2$ and $c=1$,

so the desired number is 821.

2 points

TOTAL 10 POINTS