# Coins on a chess board

#### Dave

Joined Nov 17, 2003
6,970
Somewhere around Barnard's Star.

Yeah like 6 light years or so. 1e18 was inches not meters. My original estimate was only off by a factor of forty.
So quite a bit beyond Proxima Centuari!

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.
Ok, have a rough stab at the Maths in your head and have a guess.

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.
Really! So get your calculator out and convert that mass to metres.

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.
3.1 light years is pretty precise, care to share how you came to that?

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.
Next conumdrum: What is the area of that piece of paper?!

Oh, and we've another guess at 6 light years.

Hey man - spare change?
Sure do, the bag has an infinite number of coins!

Dave

#### Salgat

Joined Dec 23, 2006
221
At what rate would the money come out of the bag full of infinite coins on earth? Don't use math.

Joined Jan 10, 2006
614
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)
14 if you're superstitious.

#### recca02

Joined Apr 2, 2007
1,214
well i used the forbidden technique 'maths'
log 2 (to the base 10) = .30 almost
no. of coins on 64th square = 2^(64-1) (since we started with 2^0).
2^63=10^(63*.30)=10^18.9
total length = 10^18.9*3.175*10^-3 metres
divided by speed of light 3*10^8 metres*24 * 3600*365.25 (sec per year)
365.25 to account for leap year ;-)

and yes, i m religious not superstitious
but a good one there gadget san

the area of piece of paper (base area) after 50 folds considering original area as 1mX1m
1/(2^50) sq metres = (so if an amoeba lives on it it will have a record breaking density)

#### Dave

Joined Nov 17, 2003
6,970
At what rate would the money come out of the bag full of infinite coins on earth? Don't use math.
It can only be proved with Maths: and the answer is plot the size of bag against the number of coins, and the money comes out when d(size of bag)/d(number of coins) = 0 - i.e. never!

Dave

#### Dave

Joined Nov 17, 2003
6,970
Ok, time to put this baby to bed. Here are the stats for the pile of coins on the last square:

There are 9,223,372,036,854,775,808 coins (a lot of money!)

This equates to a height of:
- 29,284,206,217,013,913,190.4 mm
- 29,284,206,217,013.9131 km
- 18,200,252,465,515.1729 miles
- 3.095 light years

Pretty high I might say.

Dave

#### beenthere

Joined Apr 20, 2004
15,819
For what it's worth, I chose barnard's Star as I thought it was 4.3 LY - or am I confusing that distance with a parsec?

#### Dave

Joined Nov 17, 2003
6,970
A quick net search suggests Barnard's Star is 5.96 light years distant, or 1.8 parsecs.

Dave

#### m4yh3m

Joined Apr 28, 2004
186
Are we stacking these pennies using European or African Swallows? Creeper?