# Coins on a chess board

#### Dave

Joined Nov 17, 2003
6,970
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

#### m4yh3m

Joined Apr 28, 2004
186

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

#### thingmaker3

Joined May 16, 2005
5,084
As high as the appropriate parabola.

#### Dave

Joined Nov 17, 2003
6,970

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

As high as the appropriate parabola.
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

#### Salgat

Joined Dec 23, 2006
221
Somewhere in the vacuum of space.

#### Papabravo

Joined Feb 24, 2006
14,393
About the distance to a relatively close star. On the order of 1e18 meters
Estimating 61 * log(2) = 18 * log(10)

#### Distort10n

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

#### Salgat

Joined Dec 23, 2006
221
This is similar to, would you rather have a million dollars or the money from 1 penny after it doubles everyday for one month.
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.

#### recca02

Joined Apr 2, 2007
1,214
i believe uncle scrooge can answer that after he joins hands with bruce wayne and of course mr Bill Gates

#### Dave

Joined Nov 17, 2003
6,970
Somewhere in the vacuum of space.
So higher than the atmosphere. Care to have a more accurate stab at it?

About the distance to a relatively close star. On the order of 1e18 meters
Estimating 61 * log(2) = 18 * log(10)
Interesting approach to this. So we are saying somewhere near Proxima Centauri (the closest star)?

This is similar to, would you rather have a million dollars or the money from 1 penny after it doubles everyday for one month.
This probably demonstrates why people get themselves into debt with culmulative interests on loans - but then this is a completely different question.

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.
Did he have enough rice?

i believe uncle scrooge can answer that after he joins hands with bruce wayne and of course mr Bill Gates
Funny you should mention Bill Gates, he lent me the infinite supply of coins I needed for this conumdrum

Dave

#### Salgat

Joined Dec 23, 2006
221
Haha I just said Outter space because I'm guessing its more than I can think in my head.

#### Dave

Joined Nov 17, 2003
6,970
Haha I just said Outter space because I'm guessing its more than I can think in my head.
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

#### beenthere

Joined Apr 20, 2004
15,819
Somewhere around Barnard's Star.

#### Papabravo

Joined Feb 24, 2006
14,393
Yeah like 6 light years or so. 1e18 was inches not meters. My original estimate was only off by a factor of forty.

#### thingmaker3

Joined May 16, 2005
5,084
Don't use software or maths to calculate the height, because that defeats the point of this.
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.

#### kender

Joined Jan 17, 2007
264
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.

#### recca02

Joined Apr 2, 2007
1,214
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.

Joined Jan 10, 2006
614
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.

#### recca02

Joined Apr 2, 2007
1,214
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.
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)

#### beenthere

Joined Apr 20, 2004
15,819
Hey man - spare change?