Pennies, Dimes, and Quarters (Posted on 2009-02-17)

In my left pocket I have a mix of pennies (1 cent) and quarters (25 cents). In my right pocket I have a bunch of dimes (10 cents). The number of coins in each pocket is the same, so is the cash value. What is the smallest (nonzero) number of coins I can have?

What if I had coins of x cents and z cents in my left pocket and coins of y cents in my right pocket - is there some quantitiy of coins I can have so that each pocket has the same number of coins and same cash value? (The value of the coins are positive integers x > y > z.)

16 coins: 8 coins and 80 cents in each pocket. Three quarters and five pennies in my left pocket and and eight dimes in my right pocket.

y-z of x cent coins and x-y of z cent coins in my left pocket. x-z of y cent coins in my right pocket. The number of coins in each pocket is x-z and the value is x*y-y*z.

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