Math Is Fun Forum

1a2b3c2212

Member

Registered: 2009-04-04

Posts: 419

Pattern problem

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

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Pattern problem

Hi 1a2b3c2212,

Did you really try this? It's easy!

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"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."

soroban

Member

Registered: 2007-03-09

Posts: 452

Re: Pattern problem

. .

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. .

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gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Pattern problem

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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Pattern problem

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.

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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.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Pattern problem

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."

Shivamcoder301

Guest

Re: Pattern problem

Pattern rule: Term#^2=Term Result.
Example: 3rd term-3^2=9-3rd term=6