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Topic: Arthur's Round Table (Read 498 times) |
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ThudnBlunder
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Arthur's Round Table
« on: Jun 10th, 2003, 9:48am » |
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Arthur sits around his table with his knights. He has one pound more than the knight on his left, and this knight in turn has one pound more than the knight on his left, and so on. Arthur decides to give one pound to the knight on his left, and he in turn gives two pounds to the knight on his left, and this knight gives three pounds to the knight on his left, and so on. This process continues until one knight has no money left. At this point Arthur has four times as much money as the person to his left.
How many knights does Arthur have, and how much money did his poorest knight begin with?
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| « Last Edit: Jun 10th, 2003, 10:44am by ThudnBlunder » |
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THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
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towr
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Re: Arthur's Round Table
« Reply #1 on: Jun 10th, 2003, 11:48am » |
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does it go round the table once, or multiple times? Or are we supposed to find out ourselves..
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Wikipedia, Google, Mathworld, Integer sequence DB
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ThudnBlunder
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Re: Arthur's Round Table
« Reply #2 on: Jun 10th, 2003, 11:56am » |
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Quote:| are we supposed to find out ourselves.. |
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Yes.
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THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
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harpanet
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Re: Arthur's Round Table
« Reply #3 on: Jun 10th, 2003, 12:02pm » |
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6 Knights (+ Arthur) and the poorest had 2 pounds
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ThudnBlunder
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Re: Arthur's Round Table
« Reply #4 on: Jun 10th, 2003, 12:25pm » |
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harpanet, why should anyone believe you?
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THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
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harpanet
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Re: Arthur's Round Table
« Reply #6 on: Jun 10th, 2003, 1:25pm » |
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THUDandBLUNDER said Quote:| harpanet, why should anyone believe you? |
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Towr said Quote:| because he has a good reputation |
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I choose to take that literally  . Is this all because of the professor with his matches? 
T&B, I would infer that you are commenting on posting an answer without some sort of explanation. After my original post I set to work on a 'workings' post, but got totally confused with all the markup used in my algebra and gave up after 15 minutes (well that's my excuse, and I'm sticking to it).
OK. First of all I made the reasonable assumption that the pattern of each knight having one more than the knight on his left ends with the poorest knight, who has Arthur on his left.
I then realised that what was happening was that each knight passed to his left what he got from his right, and added a pound of his own. I likened this to each knight simply putting 1 pound into a central pot until the poorest knight was tapped out.
As the poorest knight is to Arthur's right there will always be a a whole number of 'contribution' rounds and in the end Arthur ends up with the pot.
So I calculated the before and after state of Arthur's and his lefthand companion's wealth relative to the poorest knight and made an equation out of it.
I ended up with:
P = 3 - 7/K, where P is the amount of money held by the poorest knight at the start and K is the number of knights (including Arthur). As both P and K must be integers, the only value for K (assuming Arthur has at least 1 knight with him and isn't some lonely old man with delusions of grandeur) was 7 (6 knights plus Arthur), which means the poorest knight must have started with 2 pounds.
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