To begin with I apologise for the typo in my original question title - I meant ‘18’ when i wrote 8!! (And have now included the no. 19)

Thanks so much for replies I received to this question from a few people.

I think I need to expand on my question and give a little more context – here goes and I’ll try not to ramble too much!

**My question is specifically about the apparent outlier nature of the numbers 16, 17 and 18 (and 19 I’ve just realised)** in the traditional Vigesimal Welsh number system – but specifically I’m talking about the number words rather than the numbers.(E.G. 16 eggs are always 16 eggs numerically – but how you say this in words varies immensely (10+6, 1 over 15, 10 plus 5 and 1 over, 20-4 and so on).

**So question 1** is simply re. the number 18 – why/how did this become worded as 2 x 9 (‘ *Deunaw* ’) and so completely out of step with the other Welsh teen numbers?

**Question 2** requires a longer preamble (apologies!!) and follows below.

(First thing - as I understand it the Welsh number words system (not the numbers – the words for the numbers) has been modernised to make the teen numbers more uniform and standard. My question is about the older traditional system). I could be wrong about this.

So, assuming the above to be correct, with the traditional Welsh Vigesimal (counting by 20) system for teen numbers, it looks like 11-15 follow a standard system of combining the numbers 1-5 with the word for ten (or a variation of the word for ten) – e.g un(1) with *derg* (10) = *Unarddeg* (11) and this rule seems to apply up to no. 15.

**But then,** unlike other Vigesimal number systems there appears a new ‘rule whereby 16 becomes not 6 over 10 but, 1 over 15 ( *Un ar bymtheg* ). It’s the same method for no. 17 and no. 19 – from what I can see.

**That is the crux of the 2nd question – why is this so? How did this originate? What is the etymology?**

**Background musings**

The rule creation using no.15 does not seem to specifically be a component of other Indo-European number word systems.

For example Scottish Gaelic uses or used to use a Vigesimal numbering system (see the numbers 20,30.40 etc) but has the teen number words consistently using the ‘1 over 10, 2 over 10 method) ….I think.

I suspect that like Welsh, Scottish Gaelic may have had different ‘rules’ for forming some of the teen number words to the modern consistent ‘number over 10 system)….but so far cannot find anything attesting to that.

**Does anyone know if an older Gaelic number word system did have different (non-uniform) number words system for the teen numbers?**

**A brief comparison with other Indo-European languages.**

**FRENCH**

French, probably from shared Celtic/Gaul links has parts of the Vigesimal system (esp. numbers 80 (quatre vingt/4 x20) and 90 (quatre-vingt-dix (4 x 20 plus 10).

However French does not, with teen number words, have any significance with the number 15.

**Although** French teen number words do have two rules.

1st rule for French seems to be stemming from the Latin source for numbers 11-16 whereby the numbers for 1-6 are combined with a form of the number 10.(It’s hard to spot but I think time has just blurred the link with ten ( *dix* ) for numbers 11-16 e.g. *onze, douze treize* etc

Then French teen number words change rule for numbers 17-19 (becoming *dix-sept* (10 plus 7) *dix-huit (* 10 plus 8) etc…

Interestingly the numbers 17-19 follow a different naming rule in French are almost the same numbers following a different naming rule in Welsh (apart from the number 16) BUT (intriguingly) in a totally different way.

To make the scenario even more etymologically intriguing – the Latin source for Romance languages like French, Italian, Spanish etc also has non uniform number words for the teen numbers.

**LATIN**

The teen number words for 11-17 follow a uniform system e.g. 11 is *undecim* from *unus* (1) and *decem* (10) and the pattern continues up to and inc. 17.

Then 18 and 19 number words are formed by a different system of subtracting from 20.

e.g. 18 is *duedeviginti* which means 2 from 20.

(apologies that I cannot type this with the appropriate diacritical marks)

**INDIAN/HINDI** (as an Indo-European language)

This is pure conjecture - but it strikes me that the Indian/Huindi number word for 16 shows no relation to the number 6 (e.g. so not ‘6 over 10’). Whereas the other numbers 13-19 seem to be comprised of the common 3 over 10, 4 over 10 etc method).

Which is, once again, intriguing…

I’ll end here and wait apprehensively to see what replies I get!!

Slainte Mhath

Colin