coin rolls  aha:!

every night, i dump all the change in my pocket into a big bucket.

when I buy things, i never hand over coins. always bills. so i accumulate a lot of coins. even if the purchase price is $1.01, and i have lots of coins in my pocket, i pay $2 and take the 99c in change. all the more coins to dump in my change bucket!

after about 10 years of this, i decide to roll all the coins into rolls. remember that a quarter roll is $10, a dime roll is $5, nickels $2, pennies 50 cents. so I go to the Banking Supply Store and buy empty paper rolls.

the Banking supply store, conveniently, sells assortment packs of coin rolls. each assortment pack contains W quarter rolls, X dime rolls, Y nickel rolls, and Z penny rolls.

the question: what is the optimum ratio of W to X to Y to Z to maximize the probability that I will use up the assortment packs at the same rate, e.g. without lots of leftover nickel tubes and stuff.

p.s. this problem should ideally be solved using Excel (but if you really like doing these things by hand, be my guest).

submitted by joel

paul brinkley makes these assumptions which are all good assumptions to make:
Assumption 1: The price of purchases made, modulo $1, is an even distribution from 0 cents to 99 cents.
Assumption 2: The cashier will always give you the least number of coins mathematically possible, and will always have enough of each type of coin to do this. So you'll never get 99 pennies as change for a $1.01 purchase, for example.
Assumption 3: Half dollars don't exist.