There is only a single country in the world that uses a $7 banknote: Fiji. There's a mathematical reason for why we don't see more unusual sized notes and coins that goes back to a French balloon engineer, and how it took an Olympic gold medal to change this system.
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This is a $7 banknote. In fact, it's the world's only $7 note. It's from Fiji and was released in 2017, and before this, there wasn't a country in the entire world that used a $7 note or coin. And seven's a cool number, so why is it so rare?
In this video, I dive into that story as well as answering the bigger question about why we don't see more unusual size currencies.
Firstly, I don't know where in the world you're watching this, or what type of money you use, but I want you to think of a note or coin in your own currency. Now, here's my bet. I bet what you're thinking of starts with one, two or five.
So why is that? Well, the world loves the metric system, and every country has now moved to a decimal currency. That is where the major unit can get broken down into 100, or sometimes 1000, minor units. So $1 is 100 cents. There were a couple of outliers, Madagascar and Mauritania, but their minor units have become worth so little that they're essentially not used.
Now, this wasn't always the case. Historically, different currencies had different sub-units. This included India, the UK, the Spanish Empire. And in the Harry Potter universe, one Galleon equals 17 Sickles, equals 493 Knuts. But all around the muggle world, we use units of 100. That's 'cause we have a base 10 number system, likely because we have 10 of these.
You know when you travel and you leave the country, and you might have a few extra bank notes. Often too small for a money exchanger to turn into a different currency. Well, I travel a bunch, and I've been collecting these. Part souvenir, part money that can't be exchanged, and part cash that I can take back next time I go back to the country. I'm gonna do a test. So the plan is to divide them into one, two, five, and all other numbers.
So let's do that now. Okay, let's dive into it. Here are two things I love, vertical bank notes and animals on currency. Well done, Venezuela. This far through, nothing yet on this pile at all. Here's the sister currency to the seven Fijian note, that's the five. And the final note is a very beat up Myanmar Kyat, 200 goes right here. So look, that's it, that's the entire money set broken up into one, two, five and the rest. As you can see, nothing other than our Fijian $7 note would fit right here. And I think that shows just how rare this is. Of the entire stack of money, this was the only note that wasn't a one, two, or five.
This is known as a preferred number series, and this is pretty cool. One particular type of preferred number series is the Renard series. Now, this goes back to the 1870s when Colonel Charles Renard, his job was a balloon wrangler. That is, he looked after captive balloons that were used in defence, in spying. And when he turned up, he realised that there were over 400 different sizes of cables. Now, he thought this was crazy from a logistics, and cost, and management perspective. So what he did is he redesigned the system and got it down so he only needed 17 different size cables.
So what it does, is rather than have them as fixed width, is that you increase them by the same multiplier. This means there's more precision at the smaller end, and a fixed amount at the bigger end. Here's why that's cool. If you've ever worked in retail, and had to give someone change, you've had to make a decision about what coins to give someone to kind of minimize the amount of change they get.
So let's pretend that this is your coin set. It's the same as the Euro coins and the Australian coins before we got rid of our one and two cent pieces. If you had to give someone 63 cents, which coins would you give them? Now, I'm sure you got that right, but how did you do it? Working out which coins to choose for change isn't a simple process for every type of theoretical coin set. But, if your currency uses the one, two, five system, there is a simple way to do this, and it's called the greedy algorithm. The way the greedy algorithm works, is at each step you just choose the largest value you can. You don't look ahead, you don't optimise, you just go big at every stage.
So for our coin example, you just simply choose the largest amount you can, and that will give you the optimal solution. Researchers have looked into this, and they call any coin system where the greedy algorithm works canonical. And it's basically every currency system in the world. So back to our $7 note. When I got this, I was in Fiji and getting change for a coffee. Now, as I said, these are incredibly rare. So when I got it, I kind of looked at it, and I didn't say anything, 'cause I didn't wanna cause a fuss. I just quietly went back to my table and Googled it to see if it was real. So the story behind the banknote is less about maths and more about sport.
In 2016, Fiji won the gold medal at the Olympic Games in the rugby sevens. This was a huge deal, the country's first ever Olympic medal, and to celebrate they printed two million of these. They also printed a 50 cent coin, both of which feature the winning team and their UK coach Ben Ryan, who I only mention because there's not a lot of redhead people with glasses in Fiji, it's a bit of a rarity. And the number of Fijians that say that I look like him is enormous.
So now that it has a $7 note, the Fijian currency is no longer greedy algorithm optimised. Although, with their huge pride for their national team, I really don't think they care one bit. And around the world, generally the only currencies that don't work are the ones that have printed commemorative notes. The greedy algorithm is an optimal way to give change to reduce the number of coins, but what if your goal was to create a currency system that would on average give you the fewest number of coins for change?
Well, a mathematician from Canada looked into this, and what they found that if you only had four coins, so comparing it to the current U.S. system. If you had a one, five, 18 and 25 cent coin, that would on average give you 17% less coins per change transaction.
So farewell dime, and say hello to the octadeca coin. So how do we get more interesting values of currency? Well, maybe we need to start winning more gold medals in weird and wonderful sports.
I'm Julian O'Shea, and thanks for watching. If you enjoyed that, I'd love to invite you to subscribe. I've got a lot more cool videos coming up soon, including one about the largest value bank note ever.