# Word Meaning Vectors

*English translation by SOTA – AI Community of the Russian original. Organisers who would like this translation removed can email sota.ai.community@gmail.com.*

*Task 4 of the school stage of the All-Russian School Olympiad (VsOSh) 2025/26 in artificial intelligence (region group III), grades 9–11. The official answer and solution are in a separate file.*

To compare the meanings of words, a computer assigns each word three numbers $(x, y, z)$ — a meaning vector. To measure how close two words are, one takes the number

$$S = x_1 x_2 + y_1 y_2 + z_1 z_2,$$

that is, the corresponding coordinates are multiplied and added up. Then:

- if $S > 0$, the words are close in meaning;
- if $S < 0$, the meanings are opposite;
- if $S = 0$, there is no connection in meaning.

Six words with known meaning vectors are given:

| Word | Meaning vector |
|:---:|:---:|
| camel | $(3,\ 4,\ 5)$ |
| fish | $(-3,\ -4,\ 0)$ |
| snowman | $(-4,\ 3,\ -5)$ |
| tea | $(-7,\ 1,\ 5)$ |
| glacier | $(3,\ 4,\ -5)$ |
| pond | $(-7,\ 1,\ 0)$ |

Determine the meaning vectors for the words iceberg, whale, mouse and kettle.

*[Translator's note: the original file does not list the vectors to choose from. The official solution calls them A, B, C and D; as a set, they are $(-4, 3, 0)$, $(-4, 3, 5)$, $(4, -3, 0)$ and $(4, -3, -5)$.]*

**Scoring criterion:** 3 points for each correct answer. Total — 12 points

**Maximum score for the task — 12**