719 Cases To Go
Number Theory
Level
2
Is it possible to rearrange the digits of the number 123456 to form a perfect square ?
Yes
No
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1 solution
Relevant wiki: Application of Divisibility Rules
An integer is divisible by 3 iff the sum of its digits in base 10 is divisible by 3.
An integer is divisible by 9 iff the sum of its digits in base 10 is divisible by 9.
Since the order of digits doesn't affect the sum of digits, any permutation of the digits produces an integer which is divisible by 3, but not by 9.
The answer is No because if a perfect square is divisible by a prime (in this case 3) then it is also divisible by its square (in this case 9).