Friday, March 7, 2008

Akbar and Birbal

Akbar used to play chess with Birbal almost every evening. One evening when Birbal won , Akbar was very pleased with Birbal's game and so offered him a grand reward.

"Ask and thou shall recieve. I am rich enough to satisfy thy most cherished wish," snapped Akbar.
Birbal was hesistant but, on being forced by the emperor, said, "Sir, I will like to have one grain of wheat for the first square on the chessboard, two for second, four for third, and so on for all the 64 squares."

"Is that all?" retorted Akbar. "birbal, thy request is not worthy of my generosity. Anyhow, thou shall have thy sack of grain."

What do you think was the size of this sack ?

For the uninitiated, Birbal

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16 Comments:

Anonymous Steve said...

US equivalencies:
18 Quintillion grains
2 Quadrillion pounds
900 metric tons
33 Trillion Bushels
US$330 Trillion
25 times the US annual GDP

March 7, 2008 10:39 AM  
Anonymous Anonymous said...

That was hilarious

thanks steve for the calculation i stopped after 8 chess square

March 7, 2008 10:53 AM  
Anonymous Anonymous said...

ok calculating that he got all the tiles not just the last one
36,893,488,147,419,103,231 grains
10,167,027,312,562,755 tons
$2,663,761,155,891,442,124.00
513,143,144,005,931 cubic miles
or 87 cubic light years
or 26.76 parsecs
granted thats in a perfect world
where the grains are exactly the same and theres no space between them.

March 7, 2008 12:14 PM  
Anonymous Anonymous said...

thats cheating you have to show the intermediate steps of the calculations hahahaha

March 7, 2008 12:17 PM  
Anonymous Anonymous said...

2 to the power 64
18,446,744,073,709,551,616

March 7, 2008 3:57 PM  
Anonymous Steve said...

2^64-1 Don't overestimate the number anon ;)

Fills 1.16 million Empire State buildings
13 billion standard "high" freight cars
Train 114 million miles long
Passes the sun by 21 million miles
Stretches from the earth to the moon 481 times.

March 7, 2008 6:28 PM  
Anonymous Patrick A. said...

What an idiot Birbal was!!

I would have asked Akbar for malt grains instead of wheat.

At least when you finished with the malt grains you could get drunk together ;)

March 7, 2008 9:53 PM  
Blogger abdeali said...

Tis is one of the oldest questions ever!
This even came in the 10th Matriculation text for maths!
And it really isnt a akbar birbal question

March 7, 2008 11:36 PM  
Anonymous Anonymous said...

ok second post, i was the post that clamed the 87 cubic light years. everyone keeps say 2 to the 64th power is the answer, but what i see is thats only the last square, theres 63 other squares....?

March 8, 2008 5:07 AM  
Anonymous Steve said...

2^(n-1) = Amount just in square n.
sq 1 = 1 grain = 2^0
sq 2 = 2 grains = 2^1
sq 3 = 4 grains = 2^2

(2^n)-1 = Total of all previous squares.
sq 1 = 2^1-1 = 1 grain
sq 2 = 2^2-1 = 2+1 grains = 3
sq 3 = 2^3-1 = 4+2+1 grains = 7
etc

And, no, it would not come anywhere near filling up 87 LY^3 :)

March 8, 2008 6:26 AM  
Anonymous Anonymous said...

2^0 + 2^1 + 2^2 .... + 2^64

calculus professor mentioned this a couple weeks ago

March 8, 2008 8:46 AM  
Anonymous mo said...

2^65 - 1 grains of wheat, which will need a pretty big sack.

March 8, 2008 11:42 AM  
Anonymous Anonymous said...

it will have to be giant, the amount of grains of wheat to be put in it is 9223372036854775808

March 8, 2008 9:40 PM  
Anonymous mo said...

Whoops, got that wrong. The answer should be

2^0 + 2^1 + ... +2^63 = 2^64 - 1

which is 18,446,744,073,709,551,615. Assuming an average wheat grain has a size of 3.5mm³, the sack would need to be 64.56 cubic kilometers in size, which is 15.49 cubic miles. No idea how half of that is supposed to fit on the last chess board square.

March 10, 2008 5:31 AM  
Anonymous Euclid's Brother said...

yeah.. i'll go with 18446744073709551615. (2^64)-1 which is the same as summing 2^0 + .. + 2^63.

I like the version about a penny a day doubled each day for 1 month.. even in feb non leap year gives you 268435455 pennies. or $2,684,354.55

March 10, 2008 7:17 AM  
Anonymous subhasish said...

the sack's size will be according to the weight of the grain.

March 13, 2009 10:43 PM  

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