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

Lysander

Lysander

Lysander

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Well, you'd have a chessboard with coins on it, obviously.

What I mean is this. Lets say that you put one 20p piece on square 1; 2 20p pieces on square 2, then 4 on 3, then 16 on 4 etc. By the time you get to the 64th square, how many 20p pieces would there be on that square?

Furthermore, how far would they reach [assuming you could somehow not get them to fall over]?

I don't know the answer, just wondering.
 
Lysander said:
Well, you'd have a chessboard with coins on it, obviously.

What I mean is this. Lets say that you put one 20p piece on square 1; 2 20p pieces on square 2, then 4 on 3, then 16 on 4 etc. By the time you get to the 64th square, how many 20p pieces would there be on that square?

Furthermore, how far would they reach [assuming you could somehow not get them to fall over]?

I don't know the answer, just wondering.
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Exam questions have really changed since I was at school ;)
 
sgx.saint said:
Exam questions have really changed since I was at school ;)
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Haha.. this is not from an exam. It was something I was asked by someone years ago and I just remembered it.
 
Was going to say its just a fairly simple formula to calculate that isnt it.

How far would they reach where?

Laid side by side?
On top of each other?
Sacrificing themselves in a 20p slot powered car?
 
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 )
 
It would be a massive amount of 20ps.

I remember being told a story about a man you got a king to pay him in coins in the same way as you said. In the end theres looooooooads of em!

EDIT - Actually it was probably more like what Rotty said :o
 
Why would you have 1,2,4 then sixteen? Would you not have 8?

If you meant 8, then it would be 2^63 and it would be 9,223,372,036,854,775,808


Then assuming a 20p piece is 0.2cm high, it would be: 18,446,744,073,709,551metres and 61.6cm tall
 
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there was a fable along this line..... but with rice

chess board

The total number of grains of rice on the first half of the chessboard is 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 ... + 2,147,483,648, for a total of exactly 232 − 1 = 4,294,967,295 grains of rice, or about 100,000 kg of rice, with the mass of one grain of rice being roughly 25 mg[3]. This total amount is about 1/1,000,000th of total rice production in India per annum (in 2005) and was considered economically viable to the emperor of India.

The total number of grains of rice on the second half of the chessboard is 232 + 233 + 234 ... + 263, for a total of 264 − 232 grains of rice. This is about 460 billion tonnes, or 6 times the entire weight of the Earth biomass.

On the 64th square of the chessboard there would be exactly 263 = 9,223,372,036,854,775,808 grains of rice. In total, on the entire chessboard there would be exactly 264 − 1 = 18,446,744,073,709,551,615 grains of rice.
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2^64 x 20p (the sum of all the coins on all 64 squares on the chess board)

= more money than there is in the world
 
There'd be so many 20p coins and they'd weigh that much that they'd collapse in on themselves and create their own black hole which, in time, will suck the entire Universe in too!
 
markyp23 said:
Why would you have 1,2,4 then sixteen? Would you not have 8?

If you meant 8, then it would be 2^63 and it would be 9,223,372,036,854,775,808

I think
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I don't think there would be an 8, because you're multiplying each figure by itself. But you're probably not far off.

Bar said:
Was going to say its just a fairly simple formula to calculate that isnt it.

How far would they reach where?

Laid side by side?
On top of each other?
Sacrificing themselves in a 20p slot powered car?
Click to expand...

I mean on top of each other, stacked.

I think the amount of coins would go something like:

Square 1 - 1
Square 2 - 2
Square 3 - 4
Square 4 - 16
Square 5 - 256
Square 6 - 65536

After that it would go up very high indeed.
 
markyp23 said:
If you meant 8, then it would be 2^63 and it would be 9,223,372,036,854,775,808

I think
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2^63 on the final square, but the sum of all the squares will be 2^64.
 
Lysander said:
I think the amount of coins would go something like:

Square 1 - 1
Square 2 - 2
Square 3 - 4
Square 4 - 16
Square 5 - 256
Square 6 - 65536

After that it would go up very high indeed.
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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...
 
markyp23 said:
Why would you have 1,2,4 then sixteen? Would you not have 8?
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Nah, the pattern uses n^2 x 20p, not the previous value^2

(n = square number)


square 1: 1^2 = 1 = 1x20p

square 2: 2^2 = 4 = 4x20p
square 3: 3^2 = 9 = 9x20p
square 4: 4^2 = 16 = 16x20p
square n: n^2 = n^2 = n^2 x20p

Forgotten C2/3 so can't remember the formula for working out this sequence total.

I'll have a look.

Actually, I cbf :p
 
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