NACLO 2026 - Problem HA Tale of Three Scripts
Open round | 15 points | N/A | Problem statement | Official solution | Tags: Writing system
It's relatively easy to tell the three scripts apart. From H3, we know that "ππππππ" is Elbasan. From H4, we know that "πππππ’" is Todhri1. Just look for similar letters, especially "π" and "π".
| Latin | 1. mbasi 3. njeriu 10. Γ«shtΓ« 13. gΓ«zojnΓ« 14. kohΓ«n 15. pΓ«rsa | A. njohja C. lindur D. kundΓ«r E. shtetet I. burrave L. gjithΓ« |
|---|---|---|
| Elbasan | 2. πππππ π 4. πππ ππ 8. πππππππ | B. ππ‘ππππ F. πππππ G. πππ£ππππ M. ππππππ π O. ππππ |
| Todhri | 5. πππππ₯π 6. ππ€πππ 7. πππ£π 9. ππππ 11. π§ππ’ππ’ 12. π‘ππ’ππ’ | H. πππ J. ππππππ K. πππππ N. πππππ |
The scripts look more or less all alphabetic, although they probably don't correspond glyph-to-glyph, because we have H. πππ but no word on the left hand side has only 3 glyphs. However this still means we can match letter by letter. (Remember Armenian?)
First notice 10. Γ«shtΓ« and O. ππππ. These are the only two words that start and end with the same glyph, so they must match. So in Elbasan: π = Γ«, π = sh, π = t (I'm assuming left-to-right; it will be justified very soon). Therefore, 13. gΓ«zojnΓ« = G. πππ£ππππ, giving us π = g, π£ = z, π = o, π = j, π = n. It's reassuring seeing how many of these glyphs look similarβthis means we are on the right track. No other Latin-Elbasan correspondences are apparent.
In the left column we have two other Latin words containing "Γ«": 14. kohΓ«n and 15. pΓ«rsa, but no other Elbasan words in the right column contain π, so these two words have to match to Todhri. One has "Γ«" in the penultimate place, the other in the second place. We quickly locate K. πππππ and N. πππππ. Therefore, in Todhri, π = p, π = Γ«, π = r, π = s, π = a, π = k, π = o, π = h, π = n (again, assuming left-to-right).
In the right column we have two other Latin words containing "Γ«": D. kundΓ«r and L. gjithΓ«, but again no other Elbasan words in the left column contain π, so again look in Todhri for π. We find 6. ππ€πππ and 7. πππ£πβone with π in the penultimate position and the other in the last position, and with 6 beginning with "k" and ending with "r"; everything is very nicely consistent. This tells us that in Todhri, π€ = un, π = d, π = gj, π = i, π£ = th.
Now we've exploited all the "Γ«" correspondences. We go back to finding similar glyph sequences. Notice we have three words that end with "ABA" on both sides: 5. πππππ₯π, 11. π§ππ’ππ’, 12. π‘ππ’ππ’; E. shtetet, B. ππ‘ππππ, M. ππππππ π. Because in B "πππ" and M "ππ π", we have "π" occurring either as "A" or "B", they must correspond to "ππ₯π" and "π’ππ’" in some other order. This leaves E "tet" to correspond to "π’ππ’" (one of 11 or 12). Therefore in Todhri, π’ = t, π = e.
In J. ππππππ, we have a word ending in "n". We know that "n" is "π" in Elbasan, and no other Latin word on the left ends in "n", so 8. πππππππ = J. ππππππ. We already know that πππππ = "rohen" by all the work above, so in Elbasan, π = r, π = h, π = e.
Now go back to the three "ABA" words. They have now become: 5. koπeπ₯e, 11. π§itet, 12. π‘etet; E. shtetet, B. nπ‘πtet, M. πoππeπ e. Therefore 5 = M, 11 = B, 12 = E. In Elbasan, π = i, π = k. In Todhri, π‘ = sht. (We try not to make Elbasan-Todhri correspondences to avoid complicating things.)
In 4. πππ ππ, the word ends in "r". The only word on the right ending in "r" is C. lindur. So in Elbasan, π = l, π = nd, π = u.
Now we don't have many words left and most of the vowels figured out, so we can match them based on vowel sequences.
- 9. ππππ = A. njohja because we recognize "o" and "a". In Todhri, π = nj, π = hj.
- 3. njeriu = F. πππππ because we recognize "eriu". In Elbasan, π = nj.
- 2. πππππ π = I. burrave because of "u" and "e". In Elbasan, π = b, π = rr, π = a, π = v.
- 1. mbasi = H. πππ as the only word ending with "i". In Todhri, π = mb, π = as.
- 5. πππππ₯π = M. ππππππ π. In Todhri, π₯ = v.
- 8. πππππππ = J. ππππππ.
- 11. π§ππ’ππ’ = B. ππ‘ππππ. In Todhri, π§ = ππ‘, but we don't know what the Elbasan π‘ is.
Let's list out the alphabet we have so far:
| Latin | Elbasan | Todhri | Latin | Elbasan | Todhri |
|---|---|---|---|---|---|
| a | π | π | as | π | |
| b | π | gj | π | ||
| e | π | π | hj | π | |
| Γ« | π | π | mb | π | |
| g | π | nd | π | π | |
| h | π | nj | π | π | |
| i | π | π | n? | ππ‘ | π§ |
| j | π | rr | π | ||
| k | π | π | sh | π | |
| l | π | sht | π‘ | ||
| n | π | π | th | π£ | |
| o | π | π | |||
| p | π | ||||
| r | π | π | |||
| s | π | ||||
| t | π | π’ | |||
| u | π | π€ | |||
| v | π | π₯ | |||
| z | π£ |
(I've reanalyzed "ππ€πππ" as "k-u-nd-Γ«-r" instead of "k-un-d-Γ«-r". Although both are compatible with the data since "π€" and "π" only appeared once, we have Elbasan for "nd" but not "un", so the "nd" bigram seems more justified.)
E2, E3, E4 are just table lookup. Note that "πππππ’" contains the "π" character which I've revised to be "nd" instead of just "d". I don't know if treating it as just "d" is allowed, since it's also compatible with the input data.
Footnotes
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The Todhri script was added to Unicode in Unicode 16 (2024), so at the time of writing, very few fonts support it. I had to use Noto Serif's Todhri font. β©