## 3. Three-digit Ending

Sum all odd four-digit numbers for which the sum of the digits is equal to 4. What are the last three digits of this sum, starting with the hundreds digit?

Result: $\quad 449$
## Solution.

Let's represent the number 4 as the sum of four numbers:

$$
4+0+0+0=3+1+0+0=2+2+0+0=2+1+1+0=1+1+1+1
$$

From the digits $4,0,0,0$ and 2,2,0,0, it is not possible to form an odd number.

The odd four-digit numbers whose sum of digits is 4 are:

$$
3001,1003,2101,2011,1201,1021 \text{ and } 1111
$$

Their sum is 11449, and the last three digits of this sum are 449.