# Two Questions

Discussion in 'Community Discussion' started by asherman13, Feb 23, 2006.

1. ### asherman13 macrumors 6502a

Joined:
Jul 31, 2005
Location:
SF Bay Area, CA
#1
These questions have always stimulated my mind:

If you give somebody a penny for their thoughts, and they give you their two cents, where does the extra cent go?

And can I put it in a bank account to accumulate millions of dollars over the years?

2. ### kretzy macrumors 604

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Sep 11, 2004
Location:
Canberra, Australia
3. ### grapes911 Moderator emeritus

Joined:
Jul 28, 2003
Location:
Citizens Bank Park
#3
I'll give you are quarter if you never post anything this ridiculous again.

4. ### asherman13 thread starter macrumors 6502a

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Jul 31, 2005
Location:
SF Bay Area, CA

### Staff Member

Joined:
Sep 19, 2002
Location:
Los Angeles
#5
I'll tell you the answer if you do one simple thing for me first:

Give me a penny today, double that tomorrow, double that the next day, and so on for 2 months.

That's all. I'll even give you \$100 as a reward!

6. ### w_parietti22 macrumors 68020

Joined:
Apr 16, 2005
Location:
Seattle, WA
#6
I heard somewhere that if you stacked a penny on a chess board in one square and then doubled it in the next square (2 pennies) and then doubled it again (4 pennies) and so on that you would end up with more money than the US treasurery or something like that. I think it was in some math book.

7. ### asherman13 thread starter macrumors 6502a

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Jul 31, 2005
Location:
SF Bay Area, CA
#7
I think that would amount to 2^60 or so pennies, which is a lot more than \$100. If only I was on a Mac, then I'd hit F12 and find out what that is. I hate seven-year-old Dell Inspirons.

I also think that that originated with a peasant and grains of rice? Something like that...

EDIT Are we talking cumulative here, like 2 + 4 + 8 + 16 + 32, etc? 'Cause then I'd have to bust out my calculator...

8. ### Chundles macrumors G4

Joined:
Jul 4, 2005
#8
11,529.215046 TRILLION dollars!!!!!

Holy snapping ducks!!! That's a ****load of cash!!!

EDIT: Hang on, that's 2^60.

It's:

184,467 Trillion dollars!!!

Just put a formula into excel, doubling the previous number, starting at "1" and ending 64 operations later, then summed the lot.

Then I divided by 100 to give the dollar amount, then by 1,000,000,000,000 to give the amount in trillions.

9. ### asherman13 thread starter macrumors 6502a

Joined:
Jul 31, 2005
Location:
SF Bay Area, CA
#9
Should the right amount be 2^60 + 2^59 + 2^58 + .... + 2^2 + 2^1 + 2^0 (1) ?

Don't forget to divide by 100!

10. ### xsedrinam macrumors 601

Joined:
Oct 21, 2004
#10
I'd pick July and August for the 62 maximum days. My little calculator couldn't stand the pressure and went in to "error" mode, but I suspect one would fare as well or better than the Nebraska meat housers on that little venture.

11. ### Deepdale macrumors 68000

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May 4, 2005
Location:
New York
#11
Cheap tipper.

### Staff Member

Joined:
Sep 19, 2002
Location:
Los Angeles
#12
OK, I'll throw in a Rubik's Cube.

### Staff Member

Joined:
Aug 16, 2005
Location:
New England
#13
NOTE: The chess board has 8x8 = 64 squares, so it's essentially the same as 62 days. Also note that Sum(2^(0..n))=2^(n+1)-1, so you don't need to actually do the sum to get the answer.

You can see this rule in action if you consider binary representation of numbers. 1+2+4+8+16+32+64+128 = 255 = 0b1111 1111. 2^8 -1 = 256 -1.

Now extend this to 62 or 64 binary 1s!

B

14. ### Deepdale macrumors 68000

Joined:
May 4, 2005
Location:
New York
#14
Great - another paperweight. A few weeks ago on an episode of "Beauty and the Geek 2," there was a young guy who had been one of the recordholders for solving that. He demonstrated by holding it behind his back and within 15 seconds or so it was all done. Even the "beauties" were in awe!

15. ### robbieduncan Moderator emeritus

Joined:
Jul 24, 2002
Location:
London
#15
OK. First you have to find a chess board capable of supporting the weight of all the pennies. And then some way of stopping them from all falling over. Then I'll go and get all my pennies