My first thoughts had to do with the one's place digit.
The one's place of any square number is as follows, in the form of One's digit of X : One's digit of X^2
0:0 1:1 2:4 3:9 4:6 5:5 6:6 7:9 8:4 9:1
So, out of these 10 possibilities, a 9 for the squared number shows up twice. So how about the answer being a 1/5 probability of the 19 digit number being a perfect square?
This is probably too simple and naive of an approach, but I thought it was possible that all the other information was supposed to be distracting/misleading. I figured this idea was worth embarassing myself =)
Otherwise, I like Charlie's approach with the 1(even digit)49 concept.
Posted by nikki
on 2004-03-23 16:07:58