What happens if you put loads of coins on a chessboard?

daz said:
If you're squaring the last number to get the next, 1 times itself is 1. So square 2 would be 1. And square 3 would be 1. And square 4...
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Yes OK, including 1 may be wrong then. georges has the right idea though.
 
georges said:
Nah, the pattern uses n^2 x 20p, not the previous value^2
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Historically the pattern is an excercise in exponentials, i.e. 2^(n-1).
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i remember a similar thing being told when i was at school, except it was with grains of rice, and that by the final square you would have enough rice to fill a swimming pool.
 
Dist said:
i remember a similar thing being told when i was at school, except it was with grains of rice, and that by the final square you would have enough rice to fill a swimming pool.
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Way more than that! If you read that Wiki article posted above then on the 2nd half of the board alone the rice would weigh in at around 460 billion tonnes
 
Dist said:
i remember a similar thing being told when i was at school, except it was with grains of rice, and that by the final square you would have enough rice to fill a swimming pool.
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It would be a bit more than that!
Assuming (conservatively) that a grain of rice is 1mm^3, you would end up with a 2km x 2km x 2km cube!

EDIT. And if you used 20p pieces stacked up (assuming 1mm high for each) you would end up with a stack that is over 61,000 the distance from the Earth to the Sun.
 
Rotty said:
we did this at school many years ago( about 9 yrs old at the time I think ), starting with one grain of rice on first square etc etc , at the end it was proved that there wasn't enough rice in the world to complete it ( or so the teacher said :p )
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Yep same here, some sort of dodgy story behind it about a king rewarding some guy for a good deed, guy asked for the rice thing, king laughed, then realised how much he actually needed to give him etc etc...
 
elfy said:
50p says you can't prove there's not enough rice in the world :)
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From here http://r0.unctad.org/infocomm/anglais/rice/market.htm annual rice production is around 400 million tons.

And from here http://www.daniweb.com/forums/thread29895.html a grain of rice weighs around 28mg

Now, that means that annually we produce around 1.4 x 10^16 grains of rice per year.

On the last square there would be 2^63 = 9.2 x 10^18 grains

Thus you would need the total rice production for 640 years at the current rate to equal the amount for the last square.
I think we can safely say that we don't currently have 640 years of rice in storage, so where's my 50p? ;)

(Yes, I'm bored before anyone asks)
 
Haircut said:
From here http://r0.unctad.org/infocomm/anglais/rice/market.htm annual rice production is around 400 million tons.

And from here http://www.daniweb.com/forums/thread29895.html a grain of rice weighs around 28mg

Now, that means that annually we produce around 1.4 x 10^16 grains of rice per year.

On the last square there would be 2^63 = 9.2 x 10^18 grains

Thus you would need the total rice production for 640 years at the current rate to equal the amount for the last square.
I think we can safely say that we don't currently have 640 years of rice in storage, so where's my 50p? ;)

(Yes, I'm bored before anyone asks)
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I think you have a mistake, I would imagine it takes much more than 640 years. The total amount of rice grains is a lot larger mass than that of the earth.
 
D.P. said:
I think you have a mistake, I would imagine it takes much more than 640 years. The total amount of rice grains is a lot larger mass than that of the earth.
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I don't think that's right.

Assuming 2^0 = 1 grain on the first square there would be 2^63 grains on the 64th square.
2^63 = 9.2 x 10^18 as I said above.
From memory the Earth weighs around 6 x 10^24kg so that doesn't add up.
 
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