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 Forum index » Diversions » Perplex City Puzzle Cards » PXC: Green Puzzle Cards
Green #116 The Rice Gambit
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ChalcoDoror
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Joined: 12 Oct 2005
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 		Green #116 The Rice Gambit
The Rice Gambit wrote:

According to legend, the game of chess was invented hundreds of years ago by the Grand Vizier Sissa Ben Dahir, for King Shirham of India. King Shirham was so delighted with the new game that he offered his Grand Vizier any reward he wished for.

"Majesty, I desire but one grain of rice on the firest square, two grains on the second, four on the third, eight on the fourth and son on, until every square on the board is covered."

"Is that all you wish, Sissa, you fool?" exclaimed the astonished King.

But Sissa's request was far from foolish. How many grains of rice had Sissa asked for?

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PostPosted: Thu Nov 24, 2005 4:56 am
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number9dream
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 		Well I'm no mathematician but i think it could be
Spoiler (Rollover to View):
2 to the power of 63 +1 = 9223372036854775809

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PostPosted: Thu Nov 24, 2005 5:15 am
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sixsidedsquare
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 		I'm no mathmo either but using MATLAB, I get it to be:
Spoiler (Rollover to View):
2080 grains


PostPosted: Thu Nov 24, 2005 6:43 am
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European Chris
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Spoiler (Rollover to View):
"I'm no mathmo either but using MATLAB, I get it to be:2080 grains"

No, that would be an arithmetic progression 1,2,3,4....63,64.

I don't think number9dream's answer is quite right either, I think that would be 1 away from the number of rice grains on the 64th square.

I think, and I might be wrong.

2^0+2^1+2^2.....2^62+2^63=2^64-1=18446744073709600000.


Quote:
But Sissa's request was far from foolish.


Well it was-he asked for rice. It's not very flavoursome is it.

EDIT: to add 1 and to tidy it up and to change it to TAKE one.
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PostPosted: Thu Nov 24, 2005 7:05 am
Last edited by European Chris on Thu Nov 24, 2005 12:09 pm; edited 4 times in total
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number9dream
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European Chris wrote:
I don't think number9dream's answer is quite right either,


Told you i was no mathmo, yours sounds much more like it Embarassed
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PostPosted: Thu Nov 24, 2005 7:33 am
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sixsidedsquare
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 		oops Embarassed pays to read the question right.

Spoiler (Rollover to View):
Making it a bit more accurate it's 18446744073709551616 grains
Still not actually sure if thats rounded or not..


Cheers to snowchyld for the unrounded number

PostPosted: Thu Nov 24, 2005 7:57 am
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European Chris
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 		Durh, I was using a scientifc calculator and didn't even think about it-I'm a spaz.

Also, surely you have to add one as well. The number of grains must be an odd number as 2^x=even (not when x=0) and we also have 2^0=odd. I've just been for a Thursday lunchtime Gins and I'm feeling a bit slow.
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PostPosted: Thu Nov 24, 2005 9:17 am
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sixsidedsquare
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 		Well duh me, it's just like binary

Spoiler (Rollover to View):
The largest number that can be represented by 64 bits is 2^64 -1
being 18446744073709551615, an odd number like you said European Chris.
See what we got for not having the mathmo's around Wink


PostPosted: Thu Nov 24, 2005 9:34 am
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chichiri
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 		Confirmed that!

no da

PostPosted: Thu Nov 24, 2005 10:57 am
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European Chris
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European Chris wrote:
Durh, I was using a scientifc calculator and didn't even think about it-I'm a spaz.

Also, surely you have to add one as well. The number of grains must be an odd number as 2^x=even (not when x=0) and we also have 2^0=odd. I've just been for a Thursday lunchtime Gins and I'm feeling a bit slow.


Take one rather. [note to self] must read and understand the question) [/note to self]
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PostPosted: Thu Nov 24, 2005 12:07 pm
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GasparLewis
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 		Considering all the old doubling games, I do believe the sum total is:

Spoiler (Rollover to View):
2^65 - 1


Whatever that may calculate to.

PostPosted: Thu Nov 24, 2005 2:32 pm
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European Chris
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Spoiler (Rollover to View):
No, in general the sum of all the grains of rice is 2^x-1.

This is derived from 2^0+2^1+....2^64.

And it x=64 due to 8x8=number of squares

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PostPosted: Thu Nov 24, 2005 3:40 pm
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spugmeistress
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 		I stuck 111......1111 (64x 1's, if you get what I mean?) into a binary -> decimal converter, that should've got the answer, right?

Spoiler (Rollover to View):

cept it came out with 18,446,744,073,709,552,000
which is the same as your answer up until the end. guess it could have rounded without me asking it to?


can anyone even start to describe any of these numbers in words?! i'm lost about 9 digits past the decimal point :)

hmm i wonder how much that many grains of rice would weigh...

to be fair, rice might not be flavoursome but i bet he'd get a fair bit out of sticking it on ebay ;)

rach =)

PostPosted: Thu Nov 24, 2005 9:26 pm
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nasixi
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Joined: 25 Nov 2005
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 		After trying a couple of obvious answers using my calculator, I used excel, simply doubling the number each time. Unless I've done something wrong, my answer came out as

Spoiler (Rollover to View):
18446744073709500000


But that didn't work.

Then again, I've had a few drinks, so my typing might have suffered!

PostPosted: Fri Nov 25, 2005 6:42 pm
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Forgery
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 		Is there difinatly a numerical answer to this?? I don't have the card so I cannot see how the answer should be inputted but...

Spoiler (Rollover to View):
I've heard this puzzle many of times and everytime I have heard it, I have also been told 'If you did this (doubling the rice per square) there will not be enough grains of rice in the world to fit onto the chess board.' That's why Siss's request was far from foolish, because it is impossible


Ok from reading the question again this may not be write because the question does state how many, but I may be on to something, I dunno lol

PostPosted: Fri Nov 25, 2005 8:48 pm
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