Since the previous puzzle was very tough, a relatively simpler problem.
Can a number be written with one hundred 0’s, one hundred 1’s and one hundred 2’s be a perfect square. If yes, what is that number, if not, prove it.
For Children: Do the same puzzle with ten 0’s, 1’s and 2’s instead of hundred.
Source: Mathematical Circles, by Dmitri Fomin, Sergey Genkin, Ilia Itenberg