# Word Meaning Vectors: Solution

*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. Answer and official solution.*

**Answer:**

- Kettle – $(-4, 3, 5)$
- Iceberg – $(4, -3, -5)$
- Whale – $(-4, 3, 0)$
- Mouse – $(4, -3, 0)$

**Solution.**

**1) Kettle.** We want a strong connection with “tea” and a zero connection with “snowman”.

$$\langle A, \text{tea} \rangle = (-4) \cdot (-7) + 3 \cdot 1 + 5 \cdot 5 = 56 > 0, \qquad \langle A, \text{snowman} \rangle = 16 + 9 - 25 = 0.$$

$A$ fits. Hence, *kettle* $\to (-4, 3, 5)$.

**2) Iceberg.** It should be “cold”: close to “glacier” and opposite to “camel”.

$$\langle B, \text{glacier} \rangle = 4 \cdot 3 + (-3) \cdot 4 + (-5) \cdot (-5) = 25 > 0, \quad \langle B, \text{camel} \rangle = 4 \cdot 3 + (-3) \cdot 4 + (-5) \cdot 5 = -25 < 0.$$

$B$ fits. Hence, *iceberg* $\to (4, -3, -5)$.

**3) Whale.** A connection with water without “up/down” along $z$: close to “pond” and orthogonal to “fish”.

$$\langle C, \text{pond} \rangle = (-4) \cdot (-7) + 3 \cdot 1 + 0 \cdot 0 = 31 > 0, \qquad \langle C, \text{fish} \rangle = 12 - 12 + 0 = 0.$$

$C$ fits. Hence, *whale* $\to (-4, 3, 0)$.

**4) Mouse.** The last vector $D = (4, -3, 0)$ remains. As a check: $\langle D, \text{fish} \rangle = -12 + 12 + 0 = 0$, $\langle D, \text{camel} \rangle = 12 - 12 + 0 = 0$; neutral connections are acceptable.

**Answer.**

$$
\begin{array}{lcl}
\text{kettle} & \to & (-4,\ 3,\ 5),\\
\text{iceberg} & \to & (4,\ -3,\ -5),\\
\text{whale} & \to & (-4,\ 3,\ 0),\\
\text{mouse} & \to & (4,\ -3,\ 0).
\end{array}
$$