**Counting systems seem like a pretty straightforward thing**, right? You just add a few simple numbers like 60+3 to get 63 or 80+7 to form 87. That’s it, **easy-peasy**.

Weeeeell, if you’re nodding your head after reading that, **perhaps you are a native speaker of one of the big European languages** such as English, Spanish, Italian or maybe even German, even though they turn things around a little, but it’s still pretty much the same. (Notice how I’m leaving a big one out? I’m looking at you, French!).

Actually, it turns out that **there are quite a bunch of ways to express a quantity** and of course not all languages use the same one. Surprisingly enough, **we don’t really need to go very far** to find some examples, **we have them here in Europe**. Which brings us to today’s topic! Here **I’ll be telling you about unusual ways of counting used in 4 European languages**. These languages are **Basque, Welsh, Breton and Danish**, but for the sake of readability I’ll divide it into two parts.

Today’s turn will be **Welsh and Basque**, but before getting into specifics…

**Image: Designed by Vvstudio – Freepik.com**

## A little bit of background

Most of the numerical systems you may be familiar with are **“decimal systems”** which means they are **based around the number 10 and its multiples**. Just like the examples I gave you at the very beginning of this post, you take a word for “60”, you think of it as 6 times 10 and then you add “3” to it.

The interesting thing about the languages I’m going to tell you about is that they barely use that system, but a **“vigesimal”** one (or combinations of it with others), which means **their numbers revolve around groups of 20**.

So now that we know what “decimal” and “vigesimal” is, let’s take a closer look at Basque and Welsh. The first one will be easy, pinky promise 😉 .

## Basque’s counting system

**Image: Daniele Schirmo – Wikipedia Commons**

In spite of its vigesimal nature,** Basque’s counting system is rather easy to grasp** since it doesn’t contain exceptions or mixtures of any other systems, as it’s usually the case.

**Up until the number 29 everything is quite familiar to us**, but from that on, ’20-ness’ kicks in and makes **number 30 turn into “20 and 10”, number 40 into “2 x 20”** and so forth. Let me give you a few examples:

**32**–**hogeita hamabi**–**20 and (10 + 2)****46**–**berrogeita sei**–**(2 × 20) and 6****54**––**berrogeita hamalau****(2 × 20) and (10 + 4)****68**––**hirurogeita zortzi****(3 × 20) and 8****73**––**hirurogeita hamairu****(3 × 20) and (10 + 3)****89**––**laurogeita bederatzi****(4 × 20) and 9****91**––**laurogeita hamaika****(4 × 20) and****11**

However, the **number 100** has its own name * “ehun”* so apparently it’s

**not considered as 5 x 20**.

**Click here for a full 1-100 list of Basque numbers.**

## Welsh’s counting systems

**Image: Tobias Jakobs – Wikipedia Commons**

Since Basque was just not “exotic” enough, I’m bringing Welsh to you just to balance things a little bit. You’ll understand why I say that a few lines below 🙂 .

The first thing I should mention is that **the Welsh language actually has two different systems**. The traditional one, which is the one we’re going to talk about here, and the modern one, a regular decimal system.

Interestingly enough, **both are still used**, although the **younger generations tend to use the modern system** much more than the older ones since that’s what they’re taught at school when their education is done in Welsh. However, **the traditional system is still widely used in certain contexts, such as giving ages**.

And now, without further ado, let’s get into the fun part 😀 .

### How does the traditional Welsh counting system work?

As we’ve already seen with Basque, **Welsh is also a vigesimal system**, but in this case things get a little messier because **it sometimes uses 15 as a reference point** as well as some other exceptions I’ll mention below.

**Everything is pretty normal up until number 15**, but then, as I mentioned before, 15 is used as a reference point and **the following numbers add up on it**.

**16**–**un ar bymtheg**–**1 on (5 + 10)****19**–**pedwar ar bymtheg**–**4 on (5 + 10)**

From there on, **all the tens which are a multiple of 20 (20, 40, 60 and 80)** follow the same logic as Basque,

**24**–**pedwar ar hugain**–**4 on 20****47**–**saith a deugain**–**7 and (2 x 20)****63**–**tri a thrigain**–**6 and (3 x 20)****88**–**wyth a phedwar ugain**–**8 and (4 x 20)**

and **all those which are not multiples of 20 except 50 (30, 70 and 90)** go along the lines of the first examples, mixing base 20 with 15 as a reference point.

**37**–**dau ar bymtheg ar hugain**–**2 on (5 + 10) on 20****79**–**pedwar ar bymtheg a thrigain**–**4 on (5 + 10) and (3 x 20)****96**–**un ar bymtheg a phedwar ugain**–**1 on (5 + 10) and (4 x 20)**

#### Exceptions

You may have noticed there are no -8 numbers on the first and third group of examples. The reason why is because the **number 18 is a special one** since it’s not thought of as 3+15 as you would expect, but as 2*9. And that also affects all the higher tens which use number 15 as shown below.

**18**–**deunaw**–**(2 x 9)****38**–**deunaw ar hugain**–**(2 x 9) on 20****78**–**deunaw a thrigain**–**(2 x 9) and (3 x 20)****98**–**deunaw a pedwar ugain**–**(2 x 9) and (4 x 20)**

Finally, there’s **the 50s ten**, which is not 10 and (2 x 20), but **½ × 100** and number 100, which has its own individual name.

**50**–**hanner cant**–**(½ × 100)****55**–**hanner cant a pump**–**(½ × 100) and 5****100**–**cant**

**Click here for a full 1-100 list of traditional Welsh numbers.**

Phew, that last bit got a bit intense, didn’t it? **On the second post of this series I’ll be taking a look at Danish (get ready for some weird things there) and Breton**. Hope you’ve enjoyed it! 😀 .

## Sources

Most of the information about these two counting systems comes from the lists I’ve already linked in each section. However, I’ve also used the wonderfully endless Omniglot’s website, where I got those links.

This paper on Basque numbers was also useful, “Some Elements for the study of the Basque Numbering System“.

And last but not least, thanks to Gareth Popkins from How to get Fluent for taking the time to reply to my email asking about both Welsh counting systems 🙂 .

**Disclaimer: I’m not a native English speaker, therefore you might find weird-sounding/looking sentences or downright wrong stuff.**

### Bea

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