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**1a2b3c2212****Member**- Registered: 2009-04-04
- Posts: 419

What is the 2011th digit of the number sequence 1,4,9,16,25,36,49,64,81,100,121,144.....?

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,481

Hi 1a2b3c2212,

Did you really try this? It's easy!

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**soroban****Member**- Registered: 2007-03-09
- Posts: 452

. .

. .

. .

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,481

Oh, ok.

Thanks!

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi all;

You can generate soroban's first table by using this formula:

So put n = 3 and you get 22, so there are 22 squares with 3 digits. Plug in n = 5 and you get 217 so there are 217 squares with 5 digits.

Or:

How about taking advantage of the computational power available at Wolfram Alpha.

We can rephrase the problem as:

Now for computation just bring the following over to Wolfram and play with b using interval bisection you will zero in on 411 quickly.

Copy this exactly into the input box.

Sum[Floor[Log[10,k2]+1],{k,1,b}]

Start by using b = 100 ( that is too low) then use b = 1000 ( that is too high) so take the average (1000 + 100 ) / 2 = 550. Continue in this manner using the closest one that is lower and the closest one that is higher. You will eventually get to b = 411. The result of the sum will be 2008 that means take the 3rd digit in 412^2.

You will now be able to compute much larger ones without all the headache of counting.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,481

Hi bobbym,

Good solution!

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**Shivamcoder301****Guest**

Pattern rule: Term#^2=Term Result.

Example: 3rd term-3^2=9-3rd term=6

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