Of all trinkets to bring back on a business trip, shot glasses make a lot of sense, and they were collected by previous generations of the men in my family. They're small and contain no liquid, so getting them home in a carry-on bag is generally possible no matter how full it already is. They're inexpensive, and you almost never see two alike. Finally, even when you're in a hurry, I've never seen an airport which didn't have a souvenir shop with some shot glasses. ...that is, until my trip to Mumbai.
* * * * *
I scoured the shops along the entire length of the small airport. I had arrived well before the flight was even scheduled to board, as recommended by my local colleagues. While there was some traffic, even at 10:30pm, I had made it to the airport and proceeded through the somewhat cumbersome security measures far faster than likely expected. With over two hours to kill, I could literally check every shelf for shot glasses. "Maybe they'll be ornately painted," I thought, "maybe they won't even be made of glass." But after a thorough look, weary from the overall trip, I gave up and waited out the rest of the time hanging my head over a drink in one of the airport's bars.
I also hadn't managed to find the other item I usually bring back from foreign trips: foreign money. Upon returning from a distant journey, I empty my pockets, my wallet, and my suitcase of the interesting cash and stuff it into a plastic zip-lock bag. I now have several of these bags in my collection. They're cool to have, and if ever I'm sent back to a place where the money's good, the trip feels jump-started by the pocketful of spendable. Of course, the easiest way to get some local currency is to withdraw it from an ATM — another common sight at an airport. However, I didn't immediately see one, and after my search for a shot glass didn't turn anything up, I lost my motivation and was simply ready to go home.
As the trip was to India, however, I did miss out on a unique feature of owning some Indian Rupees, besides each bill having a picture of Gandhi on it. Their value relative to most other common currencies is quite small, leading to bills of large magnitude. (As of now, a single US Dollar is worth about 62 Rupees.) British Pounds, Swiss Francs, Euros: all of these are well within a factor of two of the US Dollar. In addition, as the place was somewhat poor, a few hundred bucks converted to Indian Rupees would be an substantial sum.
Like most currencies, the Indian Rupee is subdivided into a unit 100 times smaller. Called a "paisa", this value is too small to be of much use to anybody, and by now the smallest officially-backed coin has a value of 50 paise, or half a Rupee. The decision to remove the smallest denominations of a local currency from circulation is not easy. It indicates a clear recognition of inflation, and it affects both the prices set by retailers, and our purchasing experience. The 'States have held out on dropping the penny for longer than I expected they would. Even Canada has recently discontinued production of their one-cent piece, at a time when the Canadian Dollar was at parity with the US'. In Switzerland, their one-cent coin called a "Rappen" was removed right before my first visit in 2007. In fact, the 5-Rappen coin is now nearing a point of dis-use, with few machines recognizing it, and a sort of melancholy creeping over me whenever I receive one as change.
I do believe the structure of the Swiss denominations to be superior to those of the US Dollar, though, and should we progress to a point where both 1- and 5-cent pieces must be removed, this will be even more clear. The following is an analysis I performed on the two sets of money. To begin, we'll define the two currencies.
The common coins of the United States have the following values (in cents): 1, 5, 10, and 25. While half-Dollar (50-cent) and 1-Dollar (100-cent) coins technically exist, these are not nearly so common, and a person typically never expects to receive them as change from anybody except a bank. However, we'll include them in our comparison of the two systems.
The common coins of Switzerland have the following values (in Rappen): 5, 10, 20, 50, 100, 200, and 500. Strictly speaking, beginning with 50-Rappen, the coins are labeled as Francs. i.e. they have values of half-Franc, 1-Franc, 2-Francs, and 5-Francs. The distribution of these coins is much more balanced than the US coins, in that none are noticeably less common or available than the others.
One measure of the effectiveness of a set of denominations is how change is made. For example: how many coins would you need to use in order to make change for certain values up to 10 bucks? The following chart shows the number of coins required against the change being made. (Note, this does not tell you how many coins you'd need in order to be able to cover any of these transactions. Rather, the plot shows the number of coins particular to that specific total monetary amount.
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| Number of Coins Required to Make Change for Values up to 10 Bucks |
It is already apparent that the US system requires many more coins, due to a lack of anything larger than one Dollar. (If the 1-Dollar and half-Dollar coins are neglected, the comparison looks much worse, with up to 45 coins needed to make as much as $9.94!) The emerging patterns show the repeated sequence of coins needed to create certain values, supplemented with a few larger coins as the total value increases. Below is another chart of the same data, only it is shown as a histogram, as if all data points of the above graph were forced to move left and be stacked against the vertical axis before swapping axes.
Number of Coins Required to Make Change for Values up to 10 Bucks
Here, it is clear not only that the number of coins generally required to be handled in the US system is larger but also that the number of values available from $0.01 to $10.00 is much larger. (i.e. the area covered by the green bars is more than the red, because of values which require 1-cent coins to reach. These are simply unavailable to the Swiss system.)
While not terribly insightful, the following two graphs also came from the analysis, so I thought I'd include them. They show the mass and volume of the required coin sets. 107 grams [0.235 pound-mass] is a substantial amount to be carrying in your pocket. Of course, it's worth noting that most Americans don't have more than one Dollar in coins in their pocket. Usually, only what is collected as change during the day is there, to be removed and placed in a jar once home.
| Mass of Coins Required to Make Change for Values up to 10 Bucks |
| Volume of Coins Required to Make Change for Values up to 10 Bucks |
Clearly, you'd need a 1-cent coin, to be able to make the smallest amount. Next, to make two cents change, you could get a second 1-cent coin. However, as you need already to add a second coin, it would be better to add a larger denomination, so the 2-cent coin is included. Now, the values of two and three cents are covered, since both coins together add to three cents. At this point, a third coin is needed, and the next largest value (4-cents) is chosen. Since values 1-cent through 3-cents were already possible with the first two coins, they can be superimposed on the 4-cent coin to form values 5 cents through 7 cents, before another coin is required. Again, the largest possible is picked (8-cents) with the knowledge that the process of adding the first three coins will work in the same way. By now, a pattern is becoming clear: the coins are 1-cent, 2-cents, 4-cents, and 8-cents. And the maximum values possible are 1 cent, 3 cents, 7 cents, and 15 cents. Note that the maximum value possible for a certain number of coins is equal to the next coin in the sequence minus 1. Thus, adding a 16-cent coin will make the maximum possible value 31 cents.
Adding a 32-cent coin will make the maximum value 63 cents.
Adding a 64-cent coin will make the maximum value 127 cents.
Adding a 128-cent coin will make the maximum value 255 cents.
Adding a 256-cent coin will make the maximum value 511 cents.
...and adding a 512-cent coin will make the maximum value 1023 cents, which is just over 10 Dollars.
In all, 10 coins are needed, with values of 1, 2, 4, 8, 16, 32, 64, 128, 256, and 512 cents.
This is an impressive solution, since the system of US denominations can require up to 17 coins to produce only certain total values, and these 10 coins are capable of making any value up to 10 Dollars in 1-cent increments. What is the drawback? It's crazy difficult to figure out which coins are needed in a certain situation. Quick! How do you make change in the amount of $3.75?!
One technique of making change is known as the "Greedy Algorithm". It involves subtracting the largest coin from the total, determining how much is still needed, and repeating. Using this process would result in the following:
375 - 256 = 119
119 - 64 = 55
55 - 32 = 23
23 - 16 = 7
7 - 4 = 3
3 - 2 = 1
1 - 1 = 0
Thus, $3.75 could be made by the combination 1 + 2 + 4 + 16 + 32 + 63 + 256. The Greedy Algorithm would help you to use this imaginary money system, but the subtraction would still probably require a calculator to perform reliably well. I know I wouldn't feel comfortable doing it in my head all the time. A system which uses rounded-off values is much simpler, which is why real currencies do.
Interestingly, the greedy algorithm is not perfect. In some instances, it will even fail completely. Consider the made-up situation mentioned earlier, where both the 1-cent and 5-cent American coins were discontinued. Making change for 30 cents could be done by using three dimes (10-cent pieces). However, the Greedy Algorithm would begin by suggesting the 25-cent coin, leaving 5 cents needed, and impossible to be fulfilled.
In the Swiss system, if the 5-Rappen coin were removed, all values which are increments of 10-Rappen would still be capable of being formed using the Greedy Algorithm. This is because the larger coins are divisible not only be smaller coins but particularly by the smallest coin of all, the 10-Rappen.
Having considered the above issues, it becomes clear why the Swiss system of denominations works quite well. Without a 1-Rappen coin, all values are rounded to the nearest 5 Rappen, making figuring easy. Considering the relative size of adjacent coins (10-Rappen is twice 5-Rappen, 20-Rappen is twice 10-Rappen, 50-Rappen is nearly twice 20-Rappen, 1 Franc is twice 50-Rappen, 2-Francs is twice 1-Franc, 5-Francs is nearly twice 2-Francs) we see that the current Swiss system is close to the ideal arrangement discussed above that allows all sorts of values to be made from a minimum number of coins.
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