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# If n^2 = 123456787654321, what is n? 1. 12344321 2.

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CEO
Joined: 15 Aug 2003
Posts: 3454
If n^2 = 123456787654321, what is n? 1. 12344321 2. [#permalink]

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14 Sep 2003, 07:24
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If n^2 = 123456787654321, what is n?

1. 12344321
2. 1235789
3. 11111111
4. 1111111

thanks
Intern
Joined: 06 Sep 2003
Posts: 19
Location: island

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14 Sep 2003, 18:18
I got 3, is it right?

Check each last three digits.

1. 321*321=103,041
2. 789*789=622,521
3. 111*111=12,321
4. 111*111=12,321

The answer may be 3 or 4, then check there is 15 digits,
111*111=12,321, there is 5 digits, so we can got 15+1/2=8,
N may be 8 digits.

Mystery
Intern
Joined: 12 Sep 2003
Posts: 31
Location: Peru

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14 Sep 2003, 18:31
[quote="praetorian123"]If n^2 = 123456787654321, what is n?

1. 12344321
2. 1235789
3. 11111111
4. 1111111

thanks[/quote]

Hello, I think (3) is the answer.

There is a pattern when squaring "all 1-digited" numbers such as 1,11,111, and so on. It depends on the number of digits you are squaring.

For example, 11^2= 121
111^2=12321
1111^2=1234321

As you can see, the digit-numbers increase consecutively from 1 to the number of "all 1-digited" you are using and then they decrease following the same pattern, so if you square an eight-digited "all 1" number, such as 11111111, you will get 123456787654321.

I hope I have been clear enough in spite of my poor writing skills.

Regards,
Re: PS : Squares   [#permalink] 14 Sep 2003, 18:31
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