What digits should be written in place of the individual letters (different letters represent different digits) so that the following double addition is correct:

A B C

| D E F |
| ---: |
| $+\quad \mathrm{G}$ E |
| $\mathrm{G}$ E F |
| $+\quad \mathrm{D}$ E |
| $\mathrm{H}$ F J |
$C=0$, so that $C+F=F$ can be true. $B+E=10$ and $2 F$ is greater than 10, to leave a remainder when added to $E+C$, where $C=0$, so that $E$ is not equal to $F$. From the same, $F=E+1$. $F$ cannot be 9, because in that case both $E$ and $J$ would be 8. $F$ cannot be 6, because in that case both $E$ and $B$ would be 5. Finally, $F$ cannot be 7, because then both $B$ and $J$ would be 4. Since $2 F$ is greater than 10, $F=8, J=6$ and $E=7$. Since $B+E=10$, from this $B=3$. $A+D+1=G$ and $G+D=H$, from this $A+2 D+1=H$, where $H$ must not be less than 5, since $A$ and $D$ are different integers. If $H=9$, then $A$ would be 4, $D=2$ and $G$ would be the already occupied 7. So $H=5$, from which $A=2, D=1, G=4$.