1. The problem asks to find the rule for how the minimum number of vertices with match heads increases as the number of house figures increases. 2. From the description, the first figure (1 house) has 6 vertices with match heads. 3. The second figure (2 houses joined side by side) has 8 vertices with match heads. 4. The third figure (3 houses joined side by side) has 10 vertices with match heads. 5. Observing the pattern: for 1 house, vertices = 6; for 2 houses, vertices = 8; for 3 houses, vertices = 10. 6. The number of vertices with match heads increases by 2 for each additional house after the first. 7. We can express this as a linear function of the number of houses $n$: $$\text{vertices} = 6 + 2(n - 1)$$ 8. Simplifying: $$\text{vertices} = 2n + 4$$ 9. This means for each new house added, 2 more vertices with match heads are needed, starting from 6 for one house. 10. This rule matches the given data: - For $n=1$, vertices $= 2(1) + 4 = 6$ - For $n=2$, vertices $= 2(2) + 4 = 8$ - For $n=3$, vertices $= 2(3) + 4 = 10$ Final answer: The minimum number of vertices with match heads increases by 2 for each additional house, following the formula $$\text{vertices} = 2n + 4$$ where $n$ is the number of houses.