Gavin buys a lottery ticket, and in accordance with the rules he picks six different integers from through 1 to 46 inclusively. He chooses his numbers so that the sum of the base-ten logarithms of his six numbers is an integer.

By coincidence, the integers on the winning ticket have the same property - that is: the sum of the base-ten logarithms of the six numbers is an integer.

What is the probability that Gavin holds the winning ticket?

(In reply to re: computer aided solution by Ady TZIDON)

I've corrected my solution (in my own reply) to eliminate the 50's.

Edited on October 6, 2014, 2:28 pm

Posted by Charlie on 2014-10-06 14:28:04