As we all know that there are 64 sq in a chess board ,if i place one penny in the first one and double of it in the second one and double in the third how much would i need in the 64 square...???1...2...4....8.....16....32......
2006-10-02 06:42:06 · 16 answers · asked by S S 1 in Science & Mathematics ➔ Mathematics
You'd need 2^0 + 2^1 + ... + 2^63 =
2^64 - 1 = 18,446,744,073,709,550,912 pennies.
2006-10-02 06:46:41 · answer #1 · answered by James L 5 · 1⤊ 1⤋
The answer is 2^63=9.223372037x10^18. It's a pretty huge number! How do you do it? Well, you know that there is one penny in the first square, and then each subsequent square contains double the number of pennies in the square immediately before it. So in the second sqaure, there are 1x2=2 pennies, in the third square 2x2=2^2, in the fourth 2x2x2=2^3 etc. Thus, in the nth sqaure, there are 2^(n-1) pennies. Hence, in the 64th square, there are 2^(64-1)=2^63 pennies. I hope that this helps!
2006-10-02 07:36:38 · answer #2 · answered by friendly_220_284 2 · 0⤊ 0⤋
It is geometric progression with
a=first term=1
r=commonratio=2
n=number of terms=64
sum=number pennies needed
=a(r^n-1)/(r-1)
=1*(2^64-1)/1
=2^64-1
=1.844674407371*10^19-1
2006-10-02 06:51:11 · answer #3 · answered by openpsychy 6 · 0⤊ 0⤋
2^64-1
2006-10-02 06:48:09 · answer #4 · answered by Anonymous · 1⤊ 0⤋
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2016-10-18 08:54:50 · answer #5 · answered by Anonymous · 0⤊ 0⤋
This would not work - a stack of over a hundred pennies would fall over. By the 64th square you would have so many that you wound need to remove the roof of your house to fit the stack in, also you would have to order a wheel barrow full of pennies from the bank and have enough savings to afford them!
2006-10-02 07:00:11 · answer #6 · answered by monkeymanelvis 7 · 0⤊ 0⤋
Easy!!!
9223372036854780000.00
but did you know where the question comes from??
hundereds of years ago a poor chinease field worker was able to perform a small favour for the emperor. the emperor offered him a small token of his appreciation and the worker polietly asked for one grain of rice in the corner of a chess board, twice as much on the next sqaure and so on. the emperor laughed and granted his wish only to later find himself bankcrupt!!
dont know exactly how true to detail that was, but it was the way i was told the story.
the question specifically asked how many on the 64th sqaure, not the total of all squares which is the value provided by some (18446744073709600000.00). honestly, some people just dont look.
2006-10-02 07:02:48 · answer #7 · answered by Anonymous · 2⤊ 1⤋
It would far exceed the worlds monetary system as it is 2 to the power of 64
The log of 2 is 0.30103 therefore 64x 0.30103 =19.27 if this is antilogged you end up with a figure of Xx 10 to the power of18
it is such a staggering amount that it begs belief !!!!!!!!!!!
2006-10-03 10:51:19 · answer #8 · answered by xenon 6 · 0⤊ 1⤋
2^63
simple geometric progression with a = 1, r = 2, n = 64
Tn = 2^(n-1)
2006-10-02 11:22:39 · answer #9 · answered by vish 2 · 0⤊ 0⤋
2^63 = 9.2 x 10^18
which is about £92,000,000,000,000,000 or 92 million billion pounds, or 92 thousand trillion pounds, or 92 quadrillion pounds.
2006-10-02 10:41:48 · answer #10 · answered by THJE 3 · 0⤊ 0⤋