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**Understanding the Math Puzzle: A Deceptively Simple Challenge**

Mathematical puzzles are an excellent way to challenge the mind, often appearing simple at first glance but requiring deeper thought to solve. One such puzzle that has recently circulated on social media asks participants to determine the value associated with the number 3 based on a given pattern. The puzzle is presented as follows:

- 9 = 90
- 8 = 72
- 7 = 56
- 6 = 42
- 3 = ?

At first glance, the numbers on the right side appear to be unrelated to those on the left, leading to some confusion. However, there is a logic behind the pattern, and recognizing it is the key to solving the puzzle.

### Step-by-Step Breakdown

To solve this puzzle, let’s analyze the pattern:

**Examine the Differences:**- Subtract each number on the left from its corresponding number on the right.
- $90−9=81$
- $72−8=64$
- $56−7=49$
- $42−6=36$

These differences—81, 64, 49, and 36—are all perfect squares:

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- $81=_{2}$
- $64=_{2}$
- $49=_{2}$
- $36=_{2}$

- Subtract each number on the left from its corresponding number on the right.
**Identify the Pattern:**- Notice that the right-hand number is the sum of the left-hand number and the square of the left-hand number. This can be written as: $Right-hand number=Left-hand number+(Left-hand number_{2}$

**Apply the Pattern to the Missing Value:**- To find the value corresponding to the number 3, apply the same logic: $Right-hand number=3+_{2}=3+9=12$

Thus, the correct answer for the value associated with 3 in this puzzle is **12**.

### The Power of Mathematical Puzzles

This puzzle is a great example of how mathematics can be both challenging and fun. It forces us to think beyond simple arithmetic and explore patterns that aren’t immediately obvious. These kinds of puzzles are not just about finding the correct answer but also about developing problem-solving skills and learning to recognize patterns and sequences.

**Why Such Puzzles Matter**

Mathematical puzzles like this one have several benefits:

**Improving Analytical Skills:**They encourage you to think critically and analyze information before jumping to conclusions.**Boosting Creativity:**Often, the solution to a puzzle requires creative thinking or an unconventional approach.**Enhancing Patience and Perseverance:**Puzzles can be challenging and require time to solve, teaching patience and perseverance.**Developing Mathematical Understanding:**They provide an opportunity to deepen your understanding of mathematical concepts and their applications.

In conclusion, while the math puzzle involving the numbers 9, 8, 7, 6, and 3 may seem simple at first, it demonstrates the importance of pattern recognition and mathematical reasoning. The correct answer, 12, is a testament to the power of logical thinking and the beauty of mathematics.

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So, next time you encounter a puzzle like this, take your time, look for patterns, and enjoy the process of discovery. You might be surprised at how much fun math can be!

This article explains the logic behind the puzzle and highlights the value of such exercises in improving problem-solving skills.