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The problem consists of six triangles, and the numbers in each triangle follow a specific pattern. The task is to identify this pattern and use it to find the missing values \( A \), \( B \), and \( C \).

Let's analyze the pattern in the triangles:

1. **First Triangle**: 
   - Top: \(-4\)
   - Bottom Left: \(-15\)
   - Bottom Right: \(-7\)

   Here, the difference between the bottom left (\(-15\)) and bottom right (\(-7\)) is \(-15 - (-7) = -8\), which matches the number at the top (\(-4\)) when doubled: \(-4 \times 2 = -8\).

2. **Second Triangle**: 
   - Top: \(3\)
   - Bottom Left: \(2\)
   - Bottom Right: \(-8\)

   The difference between the bottom left and bottom right is \(2 - (-8) = 10\). Doubling the top number gives \(3 \times 2 = 6\), which does not immediately match the difference. We may need to adjust our assumptions or find a different rule here.

3. **Third Triangle**: 
   - Top: \(7\)
   - Bottom Left: \(3\)
   - Bottom Right: \(5\)

   The difference between the bottom left and bottom right is \(3 - 5 = -2\), but doubling the top value gives \(7 \times 2 = 14\), again not matching. This suggests the rule may not rely simply on doubling the top number.

Given the discrepancies, we need to examine other relationships or symmetries in these triangles. Let's explore a few hypotheses or patterns, like summing opposite corners or deriving geometric progressions. I'll process this further and solve the remaining triangles to find the missing values.Upon analyzing the differences between the left and right numbers for each triangle, we observe the following:

- For the first triangle: top = \(-4\), difference = \(-15 - (-7) = -8\)
- For the second triangle: top = \(3\), difference = \(2 - (-8) = 10\)
- For the third triangle: top = \(7\), difference = \(3 - 5 = -2\)
- For the fourth triangle: top = \(6\), difference = \(-2 - (-13) = 11\)

It seems that there is no straightforward arithmetic relationship such as multiplying or doubling the top value to match the difference between the left and right numbers. Instead, we might explore more complex relationships or attempt solving the missing values using a different approach.

Let’s try predicting the missing values for \( A \), \( B \), and \( C \) based on potential symmetry or arithmetic balance in the triangles. We'll calculate plausible candidates for these values by analyzing their adjacent values.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like to continue analyzing this problem step by step, or would you like help in a different way? Feel free to ask questions.

Here are some related questions you might find useful:
1. Can I identify other potential patterns in the numbers?
2. How do number puzzles use arithmetic or geometric sequences?
3. What strategies can help solve pattern recognition problems in reasoning puzzles?
4. Could the position of the numbers within the triangles be important?
5. How can symmetry be used to identify missing values in mathematical patterns?

**Tip:** When solving puzzles like this, sometimes the position or relative distance of the numbers matters as much as their values!

These 6 triangles follow the same rules. Find the values of A, B, and C based on the given triangles.

Explore how to solve a reasoning problem with six triangles by identifying the pattern governing the numbers. Learn how to find the missing values of A, B, and C. Suitable for Grades 6-8.

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