Perfect Square

A 10-digit number has one 1, two 2's, three 3's and four 4's as its digits in some order. Prove that it can never be a perfect square.

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2305
Shaswata Roy ·

Sum of the digits of the given number is 30.
Hence it is divisible by 3 but not by 9(i.e 32).

Therefore it can never be a perfect square.

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