# Coins on a chess board

Discussion in 'Off-Topic' started by Dave, Apr 3, 2007.

1. ### Dave Thread Starter Retired Moderator

Nov 17, 2003
6,960
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Here's a little conundrum that someone asked me the other day and it really demonstrates the power of the exponential.

If you have a 64-square chess boards and an infinite supply of coins (if only) that are 1/8" (3.175mm) thick, and you placed 1 coin on the 1st square, doubled it and placed 2 coins on the 2nd square, doubled it again and placed 4 coins on the 3rd square, doubled it again and placed 8 coins on the 4th square, doubled it again and placed 16 coins on the 5th square, and continued doubling thereafter...

...How high would the pile of coins be on the final square?

Now the trick here is to have a qualitative guess at the height, for example "as high as my house". Don't use software or maths to calculate the height, because that defeats the point of this.

Dave

2. ### m4yh3m Senior Member

Apr 28, 2004
186
42

VERY FREAKIN HIGH! I can't remember if it was somewhere along the lines of a mile long or something to that extent.

3. ### thingmaker3 Retired Moderator

May 16, 2005
5,072
6
As high as the appropriate parabola.

4. ### Dave Thread Starter Retired Moderator

Nov 17, 2003
6,960
145
So we have one guess at a mile.

And in millimetres/inches/metres/feet/kilometres/miles that is?

I reiterate to those reading don't calculate it on a computer then post up your "guess", the idea is to have a qualitative guess.

Dave

5. ### Salgat Active Member

Dec 23, 2006
215
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Somewhere in the vacuum of space.

6. ### Papabravo Expert

Feb 24, 2006
10,338
1,850
About the distance to a relatively close star. On the order of 1e18 meters
Estimating 61 * log(2) = 18 * log(10)

7. ### Distort10n Active Member

Dec 25, 2006
429
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This is similar to, would you rather have a million dollars or the money from 1 penny after it doubles everyday for one month.

8. ### Salgat Active Member

Dec 23, 2006
215
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Haha ya, I remember my teacher asking that in 8th grade. When your young it can be quite amazing how doubling something so small relatively few times can lead to quite a large value. Another one is the story of the man who asked the king for the amount of rice equal to 1 grain doubled for every square on the chess board.

9. ### recca02 Senior Member

Apr 2, 2007
1,211
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i believe uncle scrooge can answer that after he joins hands with bruce wayne and of course mr Bill Gates

10. ### Dave Thread Starter Retired Moderator

Nov 17, 2003
6,960
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So higher than the atmosphere. Care to have a more accurate stab at it?

Interesting approach to this. So we are saying somewhere near Proxima Centauri (the closest star)?

This probably demonstrates why people get themselves into debt with culmulative interests on loans - but then this is a completely different question.

Did he have enough rice?

Funny you should mention Bill Gates, he lent me the infinite supply of coins I needed for this conumdrum

Dave

11. ### Salgat Active Member

Dec 23, 2006
215
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Haha I just said Outter space because I'm guessing its more than I can think in my head.

12. ### Dave Thread Starter Retired Moderator

Nov 17, 2003
6,960
145
To the Hubble Space Station? To the moon? To the Sun? To Mars? To Pluto? Beyond?

There are no numbers required here, its a qualitative guess.

Dave

13. ### beenthere Retired Moderator

Apr 20, 2004
15,815
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Somewhere around Barnard's Star.

14. ### Papabravo Expert

Feb 24, 2006
10,338
1,850
Yeah like 6 light years or so. 1e18 was inches not meters. My original estimate was only off by a factor of forty.

15. ### thingmaker3 Retired Moderator

May 16, 2005
5,072
6
I remember the last time my father and I were in the hardware store. He wanted to re-paint his living room, and was checking to see how many square feet a gallon of paint would cover. Once we had the number, we both started babbling - he in "old math" and I in "new math." We came to the same answer at the same time.

It's how he taught me, it's how I do things. "Don't guess" he said, "you'll be wrong." If I'm not allowed to run the math (at least in my head) then I'm stuck at square one.

16. ### kender Senior Member

Jan 17, 2007
263
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The cumulative mass of the coins will be comparable to that of Jupiter. The stacks of coins will colapse into a ball under their own gravitational pull.

17. ### recca02 Senior Member

Apr 2, 2007
1,211
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if one coin is 3.175mm thick
so my guess is abt 3.1 light years ,
lets go see it for ourself, your car got enough fuel
i bought potato chips with the money on the 64th square.

18. ### Gadget Distinguished Member

Jan 10, 2006
613
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Well, I know that if you fold paper over 50 times it will reach to the sun.. (Actually THAT is our closest star)... so accounting for the different thickness's and the extra 14 doublings, I would think Papabravo's estimate to be fairly close.

19. ### recca02 Senior Member

Apr 2, 2007
1,211
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so thats why i saw something burning on sun that day. btw it was my million dollar lottery ticket that you folded and burned

gadget san (jap for mr.),doesnt it has to be 13 extra doublings since first square is having only single coin (2^0) hence 64th sq will corr to (2^63)

20. ### beenthere Retired Moderator

Apr 20, 2004
15,815
283
Hey man - spare change?