Question

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

Answer 1

`69375`

Explanation:

• 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`.

• Each possible three digit number is a linear combination of digits.

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

So the sum is:

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