What is the digit $a$ in $a 000+a 998+a 999=22$ 997?
Performing the addition

| 111 |
| ---: |
| $a 000$ |
| $a 998$ |
| $+a 999$ |
| $\square 997$ |

we find $\square 997=22997$, where $\square=a+a+a+1$. Therefore, $22=a+a+a+1$, and thus, $a=7$.