## Odd Product

#### Problem

It can be seen that the product of the digits in 38, 3 8 = 24, is even and the product of the digits in 57, 5 7 = 35, is odd.

How many 2-digit numbers have an odd product?

#### Solution

The only way the product of the digits in a 2-digit number can be odd, is if the two digits are odd. The first digit can be 1, 3, 5, 7 and 9, as can be the second digit. Hence there are 5 5 = 25 combinations of 2-digit numbers comprising two odd digits.

For how many numbers less than one thousand is the product of their digits odd?

Problem ID: 61 (Jan 2002) Difficulty: 1 Star