Find all four-digit numbers that, after scratching out the middle two digits, decrease by 120 times.

(S. Bednářová)
If the number after scratching out the middle two digits is reduced by 120 times, the units place must be 0 (the original number is divisible by 120). This also means that the two-digit number formed by scratching out is a multiple of 10. We will list all such possibilities in the table and select those that meet the conditions.

| $120 \cdot 10=1200$ | satisfies |
| :--- | :--- |
| $120 \cdot 20=2400$ | satisfies |
| $120 \cdot 30=3600$ | satisfies |
| $120 \cdot 40=4800$ | satisfies |
| $120 \cdot 50=6000$ | does not satisfy |
| $120 \cdot 60=7200$ | does not satisfy |
| $120 \cdot 70=8400$ | does not satisfy |
| $120 \cdot 80=9600$ | does not satisfy |
| $120 \cdot 90=10800$ | does not satisfy |

The numbers that satisfy are: 1200, 2400, 3600, 4800.