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Topic: can pennies equal nickels? (Read 311 times) |
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gkwal
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can pennies equal nickels?
« on: Jul 16th, 2007, 9:30pm » |
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A machine gives out five pennies for each nickel inserted into it. The machine also gives out five nickels for each penny. Can Peter, who starts out with one penny, use the machine in such a way as to end up with an equal number of nickels and pennies?
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towr
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Re: can pennies equal nickels?
« Reply #1 on: Jul 17th, 2007, 1:39am » |
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Let the number of time you exchange a nickel for 5 pennies be N and the number of times you exchange a penny for 5 nickels be P
then the number of pennies is 5N - P + 1
and the number of nickels is 5P - N
6N + 1 can't be 6P for integer P and N, so it can't be done.
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Wikipedia, Google, Mathworld, Integer sequence DB
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rmsgrey
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Re: can pennies equal nickels?
« Reply #2 on: Jul 17th, 2007, 9:42am » |
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A simpler proof:
| hidden: | | Every transaction loses one coin and gains 5, for a net gain of 4 coins. To end up with an equal number of each type, you need an even total number of coins. The actual total will always be 4k+1 (where k is the number of transactions) so will never be even. |
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| « Last Edit: Jul 17th, 2007, 9:44am by rmsgrey » |
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