Problem Breakdown and Solutions:

4. Triangle Puzzle:

We need to figure out the missing number ? in the triangle.

• Bottom row: $1, 81, 64, 49$
• Second row: $4, ?, 36$
• Top row: $9, 25$

Analysis: Each element in the second row is the mean of two numbers beneath it: $\text{Middle number} = \frac{\text{left number} + \text{right number}}{2}.$

• For $4$: $\frac{1 + 81}{2} = 41$, but this seems inconsistent. Let’s re-check:
• The missing value in the pyramid passes matches almost any geometric###