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Let's go through each question one by one.

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### Problem 1
In the \(4 \times 4\) table, the product of numbers in each row, column, and diagonal is the same. We need to find the value of \(4H\).

#### Table:

\[
\begin{array}{|c|c|c|c|}
\hline
\frac{1}{2} & 32 & A & B \\
\hline
C & 8 & D & 2 \\
\hline
4 & 1 & E & 16 \\
\hline
F & G & H & 16 \\
\hline
\end{array}
\]

By setting up equations based on the product condition, we can solve for \(H\) and find \(4H\).

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### Problem 2
The average score of \(A\), \(B\), \(C\), \(D\), and \(E\) is 80. Also:
- The average score of \(A\), \(B\), and \(C\) is 85.
- The average score of \(C\), \(D\), and \(E\) is 75.

We are asked to find the score of \(C\).

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### Problem 3
In a competition, the average score of participants is 77. One-eighth of the participants pass to the next round with an average score of 83. We are to determine the average score of participants who did not pass.

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### Problem 4
A spider moves around a hexagon with side lengths as shown (9 cm, 18 cm, etc.). The spider keeps a constant distance of 3.5 cm from the hexagon. We need to find the distance traveled by the spider after 3 full rotations.

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I’ll start solving each question step-by-step. Shall I proceed with all of them or a specific one?

Solve the following:
1. In a 4 x 4 table, the product of numbers in each row, column, and diagonal is the same. Find the correct value for 4H.
2. The average test scores of A, B, C, D, and E is 80. The average score of A, B, and C is 85, while the average score of C, D, and E is 75. What is the test score of C?
3. In a math competition with an average score of 77, 1/8 of the participants advanced with an average score of 83. Find the average score of those who did not advance.
4. A spider moves around a hexagon with side lengths as shown, maintaining a distance of 3.5 cm from the hexagon. Find the total distance traveled by the spider after 3 full rotations.

Explore solutions to math problems involving averages, geometric properties of hexagons, and finding values based on multiplicative patterns in a table. Perfect for students in Grades 9-11, these problems cover algebraic and geometric concepts in depth.

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