13. A nine-digit number is odd. The sum of its digits is 10 . The product of the digits of the number is non-zero. The number is divisible by seven.
When rounded to three significant figures, how many millions is the number equal to?
SOLUTION
112
None of the digits in the number may be zero since we know that their product is non-zero. As they sum to 10 , we know the digits must be eight $1 \mathrm{~s}$ and one 2 , in some order. It remains to check the eight possible odd integers for divisibility by seven. Of those, only 112111111 has zero remainder when divided by seven, and to three significant figure this number is 112 million. Therefore the answer is 112 .