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Is there any perfect square whose digits consist of exactly 4 ones, 4 twos and 4 zeros in any order?

Gigili
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user1829537
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  • If I counted correctly there are just 23100 such numbers, assuming leading $0$s aren't allowed. A computer could check them all quickly. There are much easier "by hand" methods. – Jonas Meyer Jul 23 '13 at 07:37

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No because the number will be divisible by $3$ but not by $9$.

Mark Bennet
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  • WOW. I just wrote a little program to generate every combination of those digits, and calculate their square root. Such a waste of time, your way of solving it was much much better :D. – Fabinout Jul 23 '13 at 08:55