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 possible solution by Ady TZIDON)

Interesting idea, but two of the pairs have a digit in common: 5
So you'd have to erase one of these.  I'm not sure about the soundness of your logic otherwise, but if it holds the probability is actually 1/2=.5

Posted by Jer on 2014-10-06 14:13:49