6. Find all three-digit numbers $\overline{\Pi B \Gamma}$, consisting of distinct digits $\Pi, B$, and $\Gamma$, for which the equality $\overline{\Pi B \Gamma}=(\Pi+B+\Gamma) \times(\Pi+B+\Gamma+1)$ holds.
Answer: 156.

Solution: Note that П+В $\overline{\Pi В \Gamma}$ and (П + В + Г) should give the same remainder when divided by 9. This is only possible when $П+В+\Gamma$ is a multiple of 3. Note that $П+В+\Gamma=9$ - does not work, because (П + В + $\Gamma) \times(П+B+\Gamma+1)=90$-two-digit. By trying $12,15,18,21,24$, we get $\overline{\Pi В \Gamma}=$ $156=12 \times 13$.

## Variant 1-b