Invitational round | 10 points | 83.02% | Problem statement | Official solution | Tags: SyntaxPuzzle
The sentences all have the following form:
Tá [1] [2] ag [3] [4].
| [1] | [2] | [3] | [4] |
|---|---|---|---|
| garmhac | santach | deartháir | cliste |
| iníon | chineálta | nia | cúthail |
| deirfiúr | chliste | garmhac | cineálta |
| deartháir | cineálta | deirfiúr | bheag |
| iníon | shantach | deirfiúr | chúthail |
The English translations given are of the form:
A [A] [B] has a [C] [D].
| [A] | [B] | [C] | [D] |
|---|---|---|---|
| short | sister | kind | brother |
| smart | brother | greedy | grandson |
| shy | nephew | kind | daughter |
There are five distinct lexical items in each of [1][3], [2][4], [A][C], and [B][D]. Obviously, [1][3] either map to [A][C] or [B][D]. It's relatively easy to tell that [1][3] map to [B][D] (that is, they are nouns), because words in [2][4] obviously underwent inflection (insertion of "h"), which is presumably gender agreement. This also tells us the gender groups of the Irish words: { garmhac, deartháir, nia } co-occur with adjectives without "h", and { deirfiúr, iníon } have adjectives with "h". There are 3 masculine nouns (brother, nephew, grandson) and 2 feminine nouns (sister, daughter) in the English translations, so we can deduce that the former group are masculine and the latter are feminine, where adjectives agree with feminine nouns by inserting "h".
This still leaves two possibilities for the word for "brother": garmhac or deartháir. Suppose "brother" is "garmhac". "Brother" co-occurs with "kind", which appears twice in the same position, so "kind" must be "santach" because "cineálta" only appears once in position [4]. This means that the word co-occurring with "shantach", "iníon", must be "daughter". But the sentence that "daughter" appears in involves a masculine and a feminine noun, while the sentence that "iníon" appears in involves two feminine nouns, so this is a contradiction. Therefore, "brother" must be "deartháir", and "cineálta" means "kind". This also tells us that position [1] maps to position [D], i.e. the full mapping is [1234] = [DCBA]. Once this is determined, the three sentences can be easily paired up, which gives all mappings:
The remaining two sentences are: (deirfiúr, chliste, garmhac, cineálta) and (iníon, shantach, deirfiúr, chúthail), which map to (sister, smart, grandson, kind) and (daughter, greedy, sister, shy), so the final translations are (again, the order of the words are the exact opposite or the Irish ones):
Similarly, given the sentences (daughter, shy, grandson, smart) and (nephew, short, sister, greedy) (order reversed from their appearance in the English translations), we can translate word by word to (iníon, chúthail, garmhac, cliste) and (nia, beag, deirfiúr, shantach), giving the final translations: