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        riddles >> medium >> can pennies equal nickels?
        
(Message started by: gkwal on Jul 16^th, 2007, 9:30pm)

Title: can pennies equal nickels?
Post by gkwal on Jul 16^th, 2007, 9:30pm

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?

Title: Re: can pennies equal nickels?
Post by towr on Jul 17^th, 2007, 1:39am

[hide]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.[/hide]

Title: Re: can pennies equal nickels?
Post by rmsgrey on Jul 17^th, 2007, 9:42am

A simpler proof:

[hideb]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.[/hideb]