1. The problem presents two pentagons with vertex numbers, where the left pentagon is known and the right pentagon has one missing vertex number at the top. 2. Looking at the left pentagon, the vertices are: top = 3, upper left = 6, upper right = 9, bottom left = 9, bottom right = 27. 3. Observe the pattern for the left pentagon vertices: each vertex seems related by a factor: - 3 to 6 is multiplication by 2 - 6 to 9 is multiplication by 1.5 - 9 to 9 is multiplication by 1 - 9 to 27 is multiplication by 3 4. Another approach is to check for powers or consistent factor relations: - The bottom right vertex 27 is $3^3$. - The top vertex 3 is $3^1$. - The upper left 6 and upper right 9 also relate to 3. 5. Now for the right pentagon, known vertices are: - upper left = 8 - upper right = 12 - bottom left = 16 - bottom right = 64 6. Notice some of these are powers of 2: 8 = $2^3$, 16 = $2^4$, 64 = $2^6$ (though 64 is $2^6$ instead of $2^5$). 7. Observe the pattern from the right pentagon’s vertices and how they might relate to the missing top vertex: - Left pentagon top vertex was 3 (base number), right pentagon’s likely base is 4, since 8 = 4*2, 12 = 4*3, 16 = 4*4, 64 = 4^3. 8. With this, the left pentagon uses base 3, the right pentagon probably uses base 4. 9. The missing top vertex corresponds to the base number for the right pentagon, which is likely 4. 10. Therefore, the missing number is $\boxed{4}$.