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

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What is the sum of the digits of the square of 111,111,111?  [#permalink]

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New post 28 Mar 2019, 00:37
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Difficulty:

  65% (hard)

Question Stats:

43% (01:52) correct 57% (01:36) wrong based on 30 sessions

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Re: What is the sum of the digits of the square of 111,111,111?  [#permalink]

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New post 28 Mar 2019, 01:18
111111111 X 111111111= 12345678987654321
Sum =81

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Re: What is the sum of the digits of the square of 111,111,111?  [#permalink]

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New post 28 Mar 2019, 01:27
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Re: What is the sum of the digits of the square of 111,111,111?  [#permalink]

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New post 28 Mar 2019, 01:36
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If you were to lay out the number and multiply the number by itself, it would take a very long time to arrive at the answer.

Look at this neat little pattern here

Sum of digits of 11 = 2.
Sum of digits of its square, 121 = 4.

Similarly.

Sum of digits of 111=3
Sum of digits of its square, 12321 =9.

Using the pattern above:

Count up the number of 1s in the number, you will get 9. Square this. You will get 81.

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Re: What is the sum of the digits of the square of 111,111,111?  [#permalink]

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New post 28 Mar 2019, 01:52
swatato best approach so far, at least better than mine :)
Here is mine

11*11=121
111*111=12321

Note that the answer consists of ascending and descending digits and ascending stops at the value how many 1s have the initial number

111 111 111 has nine 1s so the result after quadratic will be = 12345678987654321

Sum from 1 to 8 = 36
36*2+9=81
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Re: What is the sum of the digits of the square of 111,111,111?   [#permalink] 28 Mar 2019, 01:52
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What is the sum of the digits of the square of 111,111,111?

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