if you put 1 grain of rice on one square of a chess board and 2 on the next, then 4, then 16 ect. how many grains of rice would be on the last square ?
Let me point out that the website makes a slight error.....well, not THAT slight...!!
It claims that 2^63 = 18,446,744,070,000,000,000
Actually, it's only 9,223,372,036,854,775,808....but, like I always say, what's a few quintillion (U.S.) amongst friends??
The Earth to AC and back again applies to ALL the rice grains on the chess board laid end to end......
The sum of this is:
Thus we have
(.2in x 1ft/12in x 1mile/5280ft) x 18,446,744,073,709,551,615 = 58,228,358,819,161 miles
Chess board have 64 squares, then the result is 264 = 18.446.744.073.709.551.616
On the first square we would have 2^0 = 1.
On the second square we would have 2^1 = 2
So, on the nth square, we would have 2^(n-1) grains.
So, on the 64th square, we would have 2^(64-1) = 2^(63) grains
263=9223372036854775808 GRAINS.
(And that is just on the last square - it is NOT the total of all the rice grains)
THAT IS A LOT OF RICE!!!
A grain of rice is approximately .2 inches long. Converting .2 inches to feet (divide by 12 inches to a foot) and then dividing that number by 5,280 feet in one mile, we get the length of the grains of rice, placed end-to-end, to be approximately 60,000,000,000,000 miles. How far is that? Alpha Centauri, the nearest star, is located 25,000,000,000,000 miles from Earth. Placed end to end, these grains of rice would reach farther than from the Earth, across space to the nearest star, Alpha Centauri, and back to Earth again!
Reference: http://mathforum.org/sanders/geometry/GP11Fable.html
Let me point out that the website makes a slight error.....well, not THAT slight...!!
It claims that 2^63 = 18,446,744,070,000,000,000
Actually, it's only 9,223,372,036,854,775,808....but, like I always say, what's a few quintillion (U.S.) amongst friends??
The Earth to AC and back again applies to ALL the rice grains on the chess board laid end to end......
The sum of this is:
Thus we have
(.2in x 1ft/12in x 1mile/5280ft) x 18,446,744,073,709,551,615 = 58,228,358,819,161 miles