The problem gives 7 numbers and 7 unmatched word forms in random order. 15, 1,16,2,10,11,14 and aina-bumfit, para-dig,bumfit,aina-dig,aina,dig,peina The question is to figure out the number peina-bumfit represents. If it makes a different, the problem states that this counting was used to count sheep in Millom,Cumbria in Northern England.

I assumed that when dashes were involved then it meant there were two digits. That would mean there are a minimum of 4 single-digit numbers since there are 4 un-dashed phrases. So the base has to be greater than 11 since it's 1,2,10,11... in order. But you have "para" and "aina"(assuming powers increase from right to left) and "bumfit and "dig"(is powers increase left to right). Then one of the leading digits would be at minimum 1 and the other at minimum 2. But then the value represented by the 2 digit would need to be at least (11 + 1)*2 = 24, which is greater than any of the listed numbers

Could someone please help me with this? Thank you. If there is anything wrong with this question please tell me, this is my first question on Linguistics Stack Exchange.

  • 3
    An interesting homework question! You have a false assumption in your thinking, though: the base doesn’t necessarily have to be bigger than 11 – it could be base-5, for example, with simplex terms for 5, 10, 15 and 20, similar to how Welsh works. (You can easily Google the answer, but it’s more fun to work it out yourself. I will let you know, though, that Welsh is a hint here – if you know anything about Celtic languages, that will help you recognise some of the sheep-counting numbers.) Commented Jun 30, 2022 at 22:37
  • 3
    I went to check my answer on omniglot.com/language/numbers/celtic2.htm, and if the list there is correct, the numerals you have been given don’t include 14. The correct number, 13, makes a slightly different solution less likely.
    – Keelan
    Commented Jul 1, 2022 at 6:32
  • Perhaps the website where I found the problem had a typo. Thank you Commented Jul 1, 2022 at 15:39
  • My mistake was in assuming that the words followed a base system, where aina-peina would mean 1(base) + 2. Commented Jul 1, 2022 at 16:33

2 Answers 2


Although there is already an accepted answer, I will give some more clues on how to decode this kind of riddle.

Decoding without resorting to linguistic background information

There are single morphemes (aina, bumfit, dig, paina, and para) and compounds. There are several possibilities in decoding the compounds:

  • small + big (like in English four-teen)
  • big + small (like in English twenty-one)
  • times (like in French quatre-vingt "80", or English four-ty "40")
  • -small + big (like in Latin un-de-viginti "19")

Since the aina occurs three times (once single, two times as prefix) we can guess that aina means "one", and that we have the small+big pattern. Since both 2 and 12 are in the number set, we indentify paina-dig as "12", solving two more words. Next we can see that bumfit and aina-bumfit are 15 and 16 respectively, leaving para-dig for "14" (in the formulation of the riddle as given by the original post).

Using linguistic background information

Given that the numbers come from a part of England, their linguistic provenance is restricted to Germanic (including Anglo-Saxon and Nordic), Celtic (including dead Celtic languages like Brythonic and living ones like Welsh), and Romance (Norman French). Knowing the numbers in those languages quickly identifies aina as "one", dig as "ten", and bumfit as "something with five, either fifteen or fifty" and the given set of possible solutions narrows it down to "fifteen". paina and para are more distorted but can now be assigned using the other clues of the riddle.

P.S. A friend of mine (German native speaker) used to count dice steps in a board game (German orthographic transcription) ein, pei, dei, fie, fum

EDIT: The numbers used in the problem are known under the name sheep-counting numbers and there is a Wikipedia article titled Yan tan tethera about them.

  • +1 for actually showing the process! However, with the question as given and using no background info, I think another solution would assign 15 to dig and 10 to bumfit, taking para as 'one before' so that para-dig becomes 15-1=14. Then peina-bumfit would be 12. But as I wrote in another comment, I'm not sure the question has it right; I think 14 should be replaced by 13. This makes the "-small + big" pattern, as you call it, less likely.
    – Keelan
    Commented Jul 4, 2022 at 12:38

Peina-bumfit is 17 - These are all corruptions of older Brythonic languages once spoken throughout England.

Peina is "2", Bumfit is "15", so essentially, '15 and 2'.

The older Celtic counting/numbers are not as in other European languages. They are vigesimal systems (based on 20)

In Welsh, for example, dau ar bymtheg ar ddeugain is 57 (two upon fifteen upon twoscore). 30 is "two 15s". It's a very different way of looking at numbers and counting!


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