A number and its square both have the same last three digits. What are the possibilities for those digits?
Just carrying forward with VL's post, and noting, as Charlie pointed out, that all larger numbers will work provided the rightmost 3 digits are the proper ones...
there are 4 ways that work keeping the same order of digits,
there are 6 ways that work with the same digits in different order.
So for all integers, the probability that an integer chosen at random and its square have the same last three digits is:
1 % if order doesn't matter, or
0.4 % if order matters.

Posted by Larry
on 20070830 20:42:39 