A positive integer x consists of the following digits: 100 zeros, 100 ones, and 100 twos. Can x be a perfect square (x = n^2)?

Answer 1

All numbers that are squares, have digital roots that are 0,1,4,7, or 9. To find the digital root of a number, add all the digits of a number successively, until you have a single digit number. For example:

Finding the digital root of 74938273

7+4+9+3+8+2+7+3=43

4+3=7

Because the digital root of 74938273 is 7, we know it has a perfect square. Apply this to your hypothetical number. I am assuming this number has no other digits besides the ones explicitly listed.