The sum of all 3-digit numbers whose digits are all odd is ?

Question

HIX Tutor · Accepted Answer

undefined Great question! Let's think step by step about this.

1. **Identify Odd Digits**: The odd digits are 1, 3, 5, 7, and 9. How many odd digits do we have?

2. **Count Choices for Each Digit**: Since we have 5 odd digits, how many choices do we have for each place in a 3-digit number (hundreds, tens, units)?

3. **Calculate Total Combinations**: How many total 3-digit numbers can we create with these choices?

4. **Sum Each Digit Place**: Each digit has a place value (hundreds, tens, units). How do we calculate the contribution of each digit in each position?

5. **Add Everything Together**: Finally, how can we sum up what we found for each digit place?

Let's start with the first step! How many odd digits do you see?

Savannah Anderson · Answer

#69375#

The only odd digits are #1, 3, 5, 7, 9#, all of which are non-zero.

The number of ways of forming a three digit number from these digits is #5^3 = 125#, since there are #5# choices for the first digit, #5# for the second, and #5# for the third.

In these #125# ways, each digit has the same frequency.

The average digit value is #1/5(1+3+5+7+9) = 5#.

A linear combination of digits makes up every possible three-digit number.

Hence the average value of one of the three digit numbers is #555#.

Thus, the total is:

#5^3 * 555 = 125 * 555 = 69375#

Isaiah Anthony · Answer

undefined The sum of all 3-digit numbers whose digits are all odd is 124,875.