**Cracking the Code: Unveiling the Missing Number in a Cryptic Sequence**

Brainteasers and number puzzles have captivated humanity for centuries, offering a delightful mix of challenge and satisfaction. Today, we delve into a seemingly simple yet intriguing puzzle: What number must be added to the sequence 7, 13, and 10 to increase the average to 13?

At first glance, the options provided – 24, 20, 22, and 18 – seem like random numbers thrown into the mix. But fear not, for within this numerical labyrinth lies a logical path to the solution.

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**The Power of the Average:**

The key to unlocking this puzzle lies in understanding the concept of an average. Simply put, the average of a set of numbers is the sum of those numbers divided by the number of numbers in the set. In this case, we’re given three numbers (7, 13, and 10) and a target average of 13.

**Setting Up the Equation:**

Let x be the unknown number we need to add to the sequence. To achieve an average of 13, the sum of all four numbers (including x) must be equal to 4 times the target average (since there are four numbers). Mathematically, this translates to:

(7 + 13 + 10 + x) = 4 * 13

Solving for the Missing Piece:

Simplifying the equation, we get:

30 + x = 52

Subtracting 30 from both sides, we isolate x:

x = 52 – 30

Therefore, the number we need to add to the sequence is:

x = 22

Eureka! The Missing Number Revealed:

Congratulations, you’ve cracked the code! The missing number that must be added to the sequence 7, 13, and 10 to achieve an average of 13 is 22.

**Beyond the Numbers: The Importance of Logical Thinking:**

While this puzzle may seem like a mere mathematical exercise, it underscores the importance of logical thinking and problem-solving skills. By breaking down the problem into smaller steps, applying basic mathematical principles, and analyzing the available information, we were able to navigate through the numerical maze and arrive at the correct solution.

So, the next time you encounter a brain teaser or a puzzling sequence, remember this: with a dash of logic and a sprinkle of mathematical prowess, you can unravel even the most cryptic codes!