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Topic: A flock of ducks (Read 1223 times) |
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Roy42
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A flock of ducks
« on: Aug 26th, 2006, 8:34pm » |
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I think it goes in medium, if not....anyway.
Aman took a flock of ducks to market, and when he got back, his wife asked how he had done. He said:
"Well, first i sold Mr. Smith half of the flock and half a duck; then I sold Mr. Brown a third of what was left and a third of a duck; then I met Mr. Robinson and talked him into taking a fourth of what was left and three fourths of a duck; and on the way home i met old man Jones and sold him a fifth of a duck for good measure. Here are the rest of them, 19 ducks."
How many ducks did the man take to market to begin with? It may be pointed out that no duck was divided.
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TimMann
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Re: A flock of ducks
« Reply #1 on: Aug 26th, 2006, 11:58pm » |
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Jones was sold only a fifth of a duck, which contradicts "no duck was divided". I imagine that was supposed to read "I met old man Jones and sold him a fifth of what was left plus a fifth of a duck for good measure", right?
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Icarus
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Re: A flock of ducks
« Reply #2 on: Aug 27th, 2006, 2:39pm » |
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This might have been a little harder if you hadn't said that there were 19 ducks left over, and asked instead what the minimum number of ducks needed was. As it is, it is a fairly straight-forward (or maybe straight-backward) calculation.
And are you sure the riddle was ducks and not dalmations?
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ThudnBlunder
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Re: A flock of ducks
« Reply #3 on: Aug 27th, 2006, 2:48pm » |
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on Aug 27th, 2006, 2:39pm, Icarus wrote:| And are you sure the riddle was ducks and not dalmations? |
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Icarus, are you in danger of developing a sense of humour? 
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| « Last Edit: Aug 27th, 2006, 2:49pm by ThudnBlunder » |
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Roy42
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Re: A flock of ducks
« Reply #4 on: Aug 28th, 2006, 12:01am » |
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Whoops, yes, it is a fifth of the flock and a fifth of a duck, and yes, it is ducks.
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towr
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Re: A flock of ducks
« Reply #5 on: Aug 28th, 2006, 2:41am » |
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on Aug 28th, 2006, 12:01am, Roy wrote:| Whoops, yes, it is a fifth of the flock and a fifth of a duck, and yes, it is ducks. |
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I think he might have been aluding to the answer, rather than actually suggesting you got the species wrong.. 
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| « Last Edit: Aug 28th, 2006, 2:42am by towr » |
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Mecir
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Re: A flock of ducks
« Reply #6 on: Sep 15th, 2006, 10:35am » |
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My first post. And I'm happy to say I got it.
If 19 was not given would these be the possible choices? 11, 16, 21, 26 etc
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| « Last Edit: Sep 15th, 2006, 10:35am by Mecir » |
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Icarus
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Re: A flock of ducks
« Reply #7 on: Sep 15th, 2006, 8:07pm » |
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I'm afraid not. I'm not sure if you meant quantities of ducks to start with, or quantity to have left over instead of 19, but either way it doesn't work.
The minimum starting quantity is 41 ducks, which corresponds to a minimum finishing quantity of 7 ducks. 19 ducks to finish is actually the 2nd smallest value that works.
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Mecir
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Re: A flock of ducks
« Reply #8 on: Sep 18th, 2006, 12:32pm » |
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| hidden: | | You're right. I did not consider that no duck was divided thing. So I came up with a stupid X=5Y+6. |
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Miles
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Re: A flock of ducks
« Reply #9 on: Sep 19th, 2006, 2:41am » |
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on Sep 18th, 2006, 12:32pm, Mecir wrote:| hidden: | | You're right. I did not consider that no duck was divided thing. So I came up with a stupid X=5Y+6. |
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That's not stupid; using your expression (Y is the number of ducks remaining after all transactions), the first three sales put requirements on Y that (Y-1) is a multiple of 2 and a multiple of 3, and (Y-3) is a multiple of 4, which leads to the conclusion that Y=12n+7. Each integer value of n generates a different Y, and the corresponding values for X (the starting number of ducks) are 41, 101, 161, ...
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Icarus
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Re: A flock of ducks
« Reply #10 on: Sep 19th, 2006, 5:08pm » |
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Indeed, x = 5y + 6 is correct. It just wasn't the entire story.
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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