Chance News 56
I can calculate the motion of heavenly
bodies but not the madness of people
After losing a fortune in the
South Sea Company bubble of 1720
This forsooth is from the October 2009 RSS Forsooth.
Of course in those days we worked on the assumption that
everything was normally distributed and we have seen in the
last few months that there is no such thing as a normal distribution.
Scientific Computing World
You can see the context of this comment here.
Minimizing the number of coins jingling in your pocket
Do We Need a 37-Cent Coin? Steven d. Levitt, October 6, 2009, Freakonomics Blog, The New York Times.
The current system of coins in the United States is inefficient. Patrick DeJarnette studied this problem and his work was highlighted in the Freakonomics blog. Dr. DeJarnette makes two assumptions.
1. Some combination of coins must reach every integer value in [0,99].
2. Probability of a transaction resulting in value v is uniform from [0,99].
Under this system, the average number of coins that you would receive in change during a random transaction would be 4.7. The system that would work better is rather bizzarre.
The most efficient systems? The penny, 3-cent piece, 11-cent piece, 37-cent piece, and (1,3,11,38) are tied at 4.10 coins per transaction.
Such a set of coins would be evocative of the monetary system in the Harry Potter books.
The article goes on to discuss systems where the coins are more conveniently priced and which single change in coins would lead to the greatest savings.
Submitted by Steve Simon
1. Minimizing the number of coins received in change is not the only criteria for a set of coin denominations. What other criteria make sense.
2. Is it logical to assume a uniform distribution in this problem?
3. What coin could be added to the current mix of coins to minimize the number of coins given in change.