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Math and Science / Re: Least amount of change
« on: June 26, 2012, 01:44:30 am »
The answer is finding the least amount of change that allows you to match most combinations possible.
You'll need 4 pennies so you can fill the gap between nickels.
Adding in 2 nickels and 1 dime lets you cover all values from 1-24.
It follows that adding in 3 quarters would then cover all values from 1-99
So the following combination is the least amount of change you should carry:
4 pennies
2 nickels
1 dime
3 quarters
Since the distribution of purchase costs are random in this scenario, it follows that on average, half of your coins will be used (or at least close to that).
Actually, this would be the solution if you wanted to minimize the amount of change you received. But this isn't the solution to this particular problem. Using the solution presented above coupled with the fact that the cashier will always present the least amount of change, that means you will receive on average 5 coins. Knowing this means that you also know the probability of receiving a particular coin.
pennies: 40%
nickels: 20%
dime: 10%
quarters: 30%
So you want to select 5 coins with the highest probability.
In that case, you would select 4 pennies and 1 quarter.
You'll need 4 pennies so you can fill the gap between nickels.
Adding in 2 nickels and 1 dime lets you cover all values from 1-24.
It follows that adding in 3 quarters would then cover all values from 1-99
So the following combination is the least amount of change you should carry:
4 pennies
2 nickels
1 dime
3 quarters
Since the distribution of purchase costs are random in this scenario, it follows that on average, half of your coins will be used (or at least close to that).
Actually, this would be the solution if you wanted to minimize the amount of change you received. But this isn't the solution to this particular problem. Using the solution presented above coupled with the fact that the cashier will always present the least amount of change, that means you will receive on average 5 coins. Knowing this means that you also know the probability of receiving a particular coin.
pennies: 40%
nickels: 20%
dime: 10%
quarters: 30%
So you want to select 5 coins with the highest probability.
In that case, you would select 4 pennies and 1 quarter.