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.)
Part I
16 coins:
3 quarters + 5 pennies = 8 dimes
Part II
(
Assuming coins involved are limited to those in current circulation of U.S. currency...) only multiples of 6, 8, 22, 38, and 98 coins can result in a quantity of coins in each pocket with the same cash value.
6 coins:1 dollar + 2 quarters = 3 halfdollars
8 coins:1 quarter + 3 nickles = 4 dimes
12 coins:
[6 coins] x 2
1 quarter + 5 dimes = 6 nickles
1 dollar + 5 dimes = 6 quarters
16 coins:[8 coins] x 2
3 quarters + 5 pennies = 8 dimes
3 halfdollars + 5 dimes = 8 quarters
18 coins:[6 coins] x 3
4 dimes + 5 pennies = 9 nickles
1 halfdollar + 8 nickles = 9 dimes
4 halfdollars + 5 nickles = 9 quarters
4 dollars + 5 dimes = 9 halfdollars
22 coins:1 dollar + 10 pennies = 11 dimes
38 coins:1 dollar + 18 nickles = 19 dimes
4 dollars + 15 nickles = 19 quarters
9 dollars + 10 nickles = 19 halfdollars
66 coins:[22 coins] x 3
8 dollars + 25 pennies = 33 quarters
98 coins:4 halfdollars + 45 pennies = 49 nickles
9 halfdollars + 40 pennies = 49 dimes
24 halfdollars + 25 pennies = 49 quarters
198 coins:[6 coins] x 33
[18 coins] x 11
[22 coins] x 9
[66 coins] x 3
4 dollars + 95 pennies = 99 nickles
49 dollars + 50 pennies = 99 halfdollars
Edited on February 17, 2009, 2:25 pm

Posted by Dej Mar
on 20090217 14:15:11 