**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 ?**

Guest Jun 19, 2014

#4**+5 **

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

CPhill
Jun 20, 2014

#1**0 **

Chess board have 64 squares, then the result is 2^{64} = 18.446.744.073.709.551.616

Guest Jun 19, 2014

#2**+5 **

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

CPhill
Jun 19, 2014

#3**+5 **

$${{\mathtt{2}}}^{{\mathtt{63}}} = {\mathtt{9\,223\,372\,036\,854\,775\,808}}$$ 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

Melody
Jun 20, 2014

#4**+5 **

Best Answer

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

CPhill
Jun 20, 2014