Open round | 15 points | 39.27% | Problem statement | Official solution | Tags: Number systemHistorical
For number systems, first figure out the base. Since we are only dealing with 1–9 here, an obvious base is 5. Indeed, we have 4 words that start with "atz-az-", which are probably 6–9, which gives "atz-az-" meaning "plus 5".
The problem also gives berr-eri = another finger, which obviously means 2. That also gives atz-az-berr-eri = 7. B also contains "berr-eri", so we need another number that has something to do with 2—and that is 3, which is 5 － 3 (subtracting from a base is also common, such as Roman numerals). So "-ahur" means "5 minus". So "eri-ahur" is 5 － 1 = 4. The remaining word that contains "eri", "bada-eri", is therefore 1. The other word, "be-oro-atz", must be 5 because it contains "atz". The remaining derivations just involve prepending "atz-az-" to the previous numbers, so we get:
| Word | Number |
|---|---|
| A. *bada-eri | 1 |
| E. *berr-eri | 2 |
| B. *berr-eri-ahur | 3 |
| I. *eri-ahur | 4 |
| D. *be-oro-atz | 5 |
| H. *atz-az-eri | 6 |
| C. *atz-az-berr-eri | 7 |
| G. *atz-az-berr-eri-ahur-itzi | 8 |
| F. *atz-az-bada-eri-ahur-itzi | 9 |
The interesting question is how each morpheme maps to a body part. Since 1, 2, 3 all have "eri", "eri" must mean "finger" instead of "another", leaving "berr" as "another". "ahur" is "5 minus", which, when looking at the diagram, is "(in) palm (of hand)" (in other words, "2 fingers in palm" means "3 fingers"). 5–9 all have "atz", so it is "hand". Therefore "az" is "with". "oro" only occurs in 5, so it's "whole". This leaves "bada" as "there is".
H3 is a quite unhinged problem in my opinion. 8 and 9 end with "-itzi", so they match to the two modern Basque words that end with "-tzi". "bederatzi" also contains the "B-D" sequence, so it is 9, leaving "zortzi" as 8. "bortz", as the only one ending with "-tz", naturally maps to 5. We have "zazpi", "hamar", and "sei" left for 6, 7, and 10. 7 "atz-az-berr-eri" looks convincingly able to simplify to "zazpi" (the only one that contains a plosive "b"), so 7 is "zazpi". 6 "atz-az-eri" has nothing that could become "h" or "m", so it is "sei", leaving 10 as "hamar".