Square and Consecutive Settlement (Posted on 2010-09-10)

Determine the probability that for a base 11 perfect squareP chosen at random between 1,000,000,000 (base 11) and A,AAA,AAA,AAA (base 11) inclusively, the five digit number formed by the last five digits of P (reading left to right) is precisely one more than the number formed by the first five digits.