1. Find the sum of all three-digit numbers that contain only odd digits in their decimal representation.
1. Since there are a total of 5 odd digits: $1,3,5,7$ and 9, from them we can form a total of $125\left(=5^{3}\right)$ three-digit numbers. For each of the 5 odd digits, there are a total of 25 observed three-digit numbers that have that digit in the units place. The same applies to the tens and hundreds digits. Therefore, grouping the sums in the hundreds, tens, and units places, we calculate that the desired sum is: $100 \cdot 25 \cdot(1+3+5+7+9)+10 \cdot 25 \cdot(1+3+5+7+9)+25 \cdot(1+3+5+7+9)=62500+6250+625=69375$.