Professor Gamble buys a lottery ticket, which requires that he pick six different integers from through , inclusive. He chooses his numbers so that the sum of the base-ten logarithms of his six numbers is an integer. It so happens that the integers on the winning ticket have the same property— the sum of the base-ten logarithms is an integer. What is the probability that Professor Gamble holds the winning ticket?
This problem is copyrighted by the American Mathematics Competitions.
Instructions for entering answers:
For questions or comments, please email firstname.lastname@example.org.