Sum of the digits of the square

What is the sum of the digits of the square of 111,111,111 ?

(1)18
(2) 27
(3) 45
(4) 63
(5) 81

Ah, very interesting question Kevin, the solution is quite simple.

Any number when divided by 9 if it yield remainder as 0 then the sum is 9 else its digit sum of the remainder

For example: 100 mod 9 will yield 1 and the sum of digit of 100 is 1.

For this question: 111,111,111 mod 9 yields 9 and square would yield 9^2 = 81, option 5

Alternatively you can also check the answer by looking at the pattern

1^2 = 1
11^2 = 121
111^2 = 12321
1111^2 = 1234321

similarly 111,111,111 ^2 will be 12, 345, 678, 987, 654, 321 and the sum is 81 option 5.

Hope it helps.

thanks, much appreciated.

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