Can anyone answer this puzzle?

Question

If you put a penny on the first square of a chessboard, 2 pennies on the second square, 4 pennies on the third square, 8 pennies on the fourth square etc, etc. How high would the pile be on the 64th square? (In miles or k/ms)

Put it in light years if you like

Answer 1

there will be 2^63 pennies, that is 9.223372X10^18

by measuring 10 pennies i have found that the average penny is 1.6mm, this means that 9.223372X10^18X1.6 =1.475739X10^19mm high, divide this by 1000 to get meters then again by 1000 to get km

=1.475739X10^13km high or
=9.223372X10^12 miles high

and if you really want to know, that is about 1.55984589X10^-3 light years, or 0.00155984589 light years

Answer 2

Ah, the chess board...

So to start we want to know how many pennies there are in the 64th square right?

If we look at the pattern we can see that the number of pennies on any particular square can be found using this expression:

2^(n-1), where n is the nth square.

So on the 64th square we have 2^63 pennies (that's about 9.22 * 10^18)

Now we need to find how thick a penny is, so after a little research I found that a penny is about 1.27mm.

So now we multiply:

2^63 * 1.27

This is about 1.17 x 10^19

But wait, this is in millimeters, we need km or miles, so we convert:

(2^63 * 1.27) * 1*10^-6 >>> for km
(2^63 * 1.27) * 6.2*10^7 >>> for miles

This gives us about 1.17*10^13 km or 7.27*10^12 miles.

Answer 3

Tricky question since there is no standard thickness for pennies. If you look closely, they are all different (but close!) thicknesses.

Well...it would be 2^32 power tall in pennies if I figured that right. Multiply that by lets approximate a 1/16 of an inch (0.0625) and that is still a really big number.

I get 268,435,456 inches, which is just under 4,237 miles high.

Answer 4

if we assume that a penny is .050" thick then

2^63 + 1 = 9223372036854775809

so 0.050* 9223372036854775809 = 461168601842738790 inches

convert to miles
461168601842738790 * 1foot/12 inches * 1 mile/5280 feet =

7278544852315 miles

Answer 5

Accepting that there is variation to the thickness, but assuming an average thickness of just 1mm

2^63 = 9223372036854780000mm = 922337203685478000 cm = 9223372036854780m = 5,764,607,523,034.24 miles.

I think that may be past the point where it would need to be accepted as legal tender.....

Answer 6

The piile of pennies will touch the moon.

Answer 7

2^64

Answer 8

2^63 * (width of penny)

Answer 9

In miles it should be somewhere around 30.

Answer 10

3 miles high?