Each of A and B is a (base 15) positive integer , with A containing precisely 201 digits and, B containing precisely 202 digits, where:

A = 77…..779 (the digit 7 is repeated precisely 200 times followed by 9), and:
B= 77…..779 (the digit 7 is repeated precisely 201 times followed by 9)

Determine the distinct digits in the base 15 representation of A^{2}. What are the distinct digits in the base 15 representation of B^{2}?

*** For an extra challenge, solve this puzzle without the help of a computer program.

2A (base 15) = 100..003 where there are precisely 200 zeroes.

4A^{2 }(base 15) = 100..00600..009 where there are precisely 200 zeroes between the 1 and the 6 and 200 more between the 6 and the 9.

I haven't checked, but I assume that dividing by 4 (base 15) gives Charlie's answer.

And a similar approach should suffice for B.