Math puzzle worksheet with a geometric pattern and numerical values for solving.

Problem Analysis:

The image shows a geometric pattern with numbers placed in various positions. The task appears to involve identifying a pattern or rule governing the placement and values of these numbers. The numbers are distributed across different shapes (circles, triangles, squares) within a larger geometric figure.

Observations:

1. Numbers in Circles:
- There are several circles containing numbers such as \(29\), \(12\), \(-14\), \(-12\), etc.
- These numbers seem to be strategically placed around the perimeter of the figure.

2. Numbers in Triangles and Squares:
- Numbers like \(200\), \(-55\), \(10\), \(-8\), etc., are placed inside triangles and squares.
- Some numbers appear repeatedly, such as \(-55\) and \(200\).

3. Symmetry:
- The figure exhibits rotational symmetry. The arrangement of numbers seems consistent when rotated by certain angles.

4. Repetition:
- Certain numbers (\(200\), \(-55\), \(10\), \(-8\)) repeat in specific patterns within the triangles and squares.
- The numbers in circles also show a repeating pattern around the perimeter.

Hypothesis:

The task likely involves identifying a mathematical or logical relationship between the numbers in the circles, triangles, and squares. Given the symmetry and repetition, it is possible that:
- The numbers in the circles follow a specific sequence or pattern.
- The numbers in the triangles and squares are related to the numbers in the circles through some arithmetic operation (e.g., addition, subtraction, multiplication).

Step-by-Step Solution:

#### Step 1: Analyze the Numbers in Circles
The numbers in the circles are:
\[ 29, 12, -14, -12, -14, -12, 12, 29 \]

These numbers form a repeating sequence:
\[ 29, 12, -14, -12 \]
This sequence repeats twice around the perimeter.

#### Step 2: Analyze the Numbers in Triangles and Squares
The numbers in the triangles and squares include:
- \(200\)
- \(-55\)
- \(10\)
- \(-8\)
- \(-14\)
- \(-15\)

These numbers appear to be related to the numbers in the circles. Let us investigate possible relationships:

1. Relationship Between Circles and Triangles/Squares:
- Consider the number \(200\). It appears in the center of some squares. This might be a constant value or a result of an operation involving the numbers in the circles.
- The number \(-55\) appears frequently in triangles. This could be a result of subtracting a specific value from the numbers in the circles.

2. Arithmetic Operations:
- Let us test simple operations:
- Adding or subtracting the numbers in the circles.
- Multiplying or dividing the numbers in the circles.

#### Step 3: Test a Hypothesis
Suppose the numbers in the triangles and squares are derived from the numbers in the circles using a specific operation. For example:
- The number \(200\) might be a constant added to or subtracted from the numbers in the circles.
- The number \(-55\) might be the result of subtracting a specific value from the numbers in the circles.

Let us test this hypothesis by focusing on one section of the figure:

- In one section, the circle contains \(29\), and the adjacent triangle contains \(-55\).
- Another section has a circle with \(-14\) and a triangle with \(-55\).

If we assume a consistent operation:
\[ \text{Triangle value} = \text{Circle value} + \text{Constant} \]

For the first pair:
\[ -55 = 29 + \text{Constant} \]
\[ \text{Constant} = -55 - 29 = -84 \]

For the second pair:
\[ -55 = -14 + \text{Constant} \]
\[ \text{Constant} = -55 + 14 = -41 \]

The constants do not match, so this simple addition/subtraction hypothesis does not hold. Let us try another approach.

#### Step 4: Consider Patterns in Repetition
The numbers \(-55\) and \(200\) appear frequently. These might be results of specific operations or constants in the pattern. Given the symmetry, it is likely that the numbers in the triangles and squares are derived from the numbers in the circles through a consistent rule.

#### Step 5: Conclusion
The problem likely requires identifying the repeating sequence in the circles and understanding how the numbers in the triangles and squares are derived from them. The exact rule might involve a combination of arithmetic operations and positional relationships.

Final Answer:

The solution involves recognizing the repeating sequence in the circles (\(29, 12, -14, -12\)) and understanding the relationship between the numbers in the circles and those in the triangles and squares. The exact rule might require further exploration of arithmetic operations and positional patterns.

\[
\boxed{29, 12, -14, -12}
\]