(In reply to Solution (as interpreted)
by ed bottemiller)
I think you interpreted correctly up to the point where you stopped.
Your set of bases, 12, 11, 14, 16 and 13, indeed do not include duplicates and so each "is unique to itself". However they add up to 66, which is not a perfect square. The next step is to find a set of bases that adds up to a perfect square. Then, further, to make that the smallest perfect square given the conditions imposed.
Posted by Charlie
on 2010-07-06 18:08:09