In 2000, a new 2,000-yen denomination was introduced in Japan. The coincidence of these two numbers followed legislation a year earlier that was based on a whim of then prime minister. Hearing the news, I felt that the new banknote was unnecessary and should have difficulty in circulating, because the Japanese were strange to such a 2's denomination. Later my intuition turned out to be true: 2,000-yen note became rare and in effect changed into a commemorative in a decade. The new face has lost face.
However, some nations in the world have such 2's denominations. For instance, the euro currency has the denominations of 1,2,5C (Combination of 1, 2, and 5). On the other hand, the yen currency has 1,5C (Combination of 1 and 5). Why currencies differ as to the combination of denominations? There must be something wrong, and be an ideal combination common to whatever currency on the earth! This belief led me to study the efficiencies of denominational combinations.
Having studied the theme with all my insight, I was convinced that the answer is an unknown 1,4C, whether in coins' places or in banknotes' places. Incidentally, the page title "1¤4" means a currency with 1,4C in all places. For example, if the yen currency turns into 1¤4, its denominations will be: 1-yen, 4-yen, 10-yen, 40-yen, 100-yen, 400-yen, 1,000-yen, 4,000-yen, and 10,000-yen. This new set of denominations does help people treat cash by largely reducing, the number of coins and banknotes from 1¤5, and the number of denominations from 1¤2¤5. The whole story of my work can be reached through a paper "An Efficient Combination of the Denominations of a Currency".
You can also learn here the basics of my study. Two tables below give a comparison between 1,5C and 1,4C. The first table shows minimum numbers of coins to make Y1 (the amount of 1 yen) to Y9 without change, using 1-yen coins and 5-yen coins. And the second table is a similar test with 1-yen coins and 4-yen coins.
| To make | How | Number of coins | ||
|---|---|---|---|---|
| 5-yen | 1-yen | Total | ||
| Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 |
1 1+1 1+1+1 1+1+1+1 5 5+1 5+1+1 5+1+1+1 5+1+1+1+1 |
0 0 0 0 1 1 1 1 1 |
1 2 3 4 0 1 2 3 4 |
1 2 3 4 1 2 3 4 5 |
| Total | 5 | 20 | 25 | |
| To make | How | Number of coins | ||
|---|---|---|---|---|
| 4-yen | 1-yen | Total | ||
| Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 |
1 1+1 1+1+1 4 4+1 4+1+1 4+1+1+1 4+4 4+4+1 |
0 0 0 1 1 1 1 2 2 |
1 2 3 0 1 2 3 0 1 |
1 2 3 1 2 3 4 2 3 |
| Total | 8 | 13 | 21 | |
Although these tests are so simple and limited, the results suggest that 1,4C needs smaller number of coins than the current 1,5C. Indeed, in my paper, I conducted detailed tests on 1,2C to 1,9C, and reached the conclusion that 1,4C is the best combination. People in Japan can enjoy lighter and more compact wallets if 5-yen coins are replaced by 4-yen coins. 10-yen's place, 100-yen's place, and 1,000-yen's place follow suit.
1¤4 is the best option not only for the conventional 1¤5 countries, but for 1¤2¤5 communities as well. Euro nations, for example, have as many as 15 denominations (0.01-euro, 0.02-euro, 0.05-euro, 0.1-euro, 0.2-euro, 0.5-euro, 1-euro, 2-euro, 5-euro, 10-euro, 20-euro, 50-euro, 100-euro, 200-euro, and 500-euro). But if they transfer to 1¤4, the number of denominations reduces to 10 (0.01-euro, 0.04-euro, 0.1-euro, 0.4-euro, 1-euro, 4-euro, 10-euro, 40-euro, 100-euro, and 400-euro). This implies that in daily cash transactions, people can differentiate coins and banknotes in their wallets more easily than ever, taking less time or having fewer miscalculations. For 1¤2¤5 nations, there can be other choices including 1¤5 to cut their wide variety of denominations. But 1¤4 is the best among them in terms of efficiency.
1¤4 could have appeared whenever and wherever the monetary system based on the decimal system exists. Nevertheless, there has not been such a precedent in human history. Why? It would be because terrestrial humans in general have been simple enough to be gripped by the notion that the currency denominations must be the devisors of 10 (1, 2, or 5). However, that is just a prejudice, and other denominations have the right to circulation.
Now, you are free to choose whatever denominations you like. According to the author, the best option is 1¤4, and 1¤3 might deserve consideration for another alternative. Remember, though, not to continue your traditions whether 1¤5 or 1¤2¤5, both of which are too primitive to survive civilization on the planet.