Professsor Gamble buys a lottery ticket, which requires that he pick six different integers from 1 -46, 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 winner ticket?
Suppose the winning numbers are: .
The sum of the six logs is an integer: .
This means that the log of the product of the numbers is an integer: .
. . Hence: .
That is, the product of the 6 different numbers is a power of 10.
I found only four cases:
Therefore, the Professor's probability of winning is