Odd-Odd Numbers

[collegekid]

Odd-odd numbers are numbers that not only end in an odd digit – all of their digits are odd. For example,, 3,515; 73; 1; and 97,757,931 are odd-odd numbers, while 3,576; 64,428; and 997,553,121 are not. How many odd-odd numbers are there between 1 and 1,000,000?

Is anyone aware of a formula/equation to help me solve this problem?

 

[mmm4444bot]

When they say "between 1 and 1,000,000", I think they actually want you to include 1, even though 1 is not between 1 and 1,000,000.

I mean, I think they intend for you to find the number of odd-odd numbers from 1 through 999,999.

We count these possibilities like so:

There are five different odd digits; therefore, there are 5 one-digit odd-odd numbers.

For two-digit odd-odd numbers, there are five possibilities for the first digit and five possibilities for the second digit. That's 5^2 two-digit odd-odd numbers.

For three-digit odd-odd numbers, there are five possibilies for each of the three digits. That's 5^3 three-digit odd-odd numbers.

So far, we have 5 + 5^2 + 5^3 odd-odd numbers from 1 through 999.

Keep going.