Have you ever come across a number puzzle that looks simple at first glance but turns out to be more challenging than expected? Well, today, we have an intriguing one for you! Take a moment to analyze the following pattern:
If:
2 → 6
3 → 12
4 → 20
5 → 30
6 → 42
Then:
9 → ?
At first, this might look like a basic arithmetic or multiplication problem, but there’s a hidden logic that makes it more interesting. Can you crack the pattern and find the missing number? Take a few minutes before scrolling down for the solution!
Common Mistakes People Make When Solving This Puzzle
Before we break down the solution, let’s discuss some common errors people make while attempting puzzles like this. Often, people look for linear patterns, such as simple multiplication or addition. Here are a few misconceptions:
- Thinking It’s a Straight Multiplication Pattern
Some might think each number is simply multiplied by a fixed value. However, there’s no constant multiplier that works for all given numbers. - Looking for a Basic Arithmetic Progression
If you check the differences between outputs (6, 12, 20, 30, 42), they are increasing, but not by a fixed amount. This means a simple addition or subtraction rule won’t apply. - Ignoring the Hidden Mathematical Structure
The biggest mistake is overlooking how both multiplication and addition work together in this sequence. Sometimes, puzzles require thinking beyond basic operations.
Now, let’s walk through the logic step by step!
Breaking Down the Pattern – Step by Step Solution
Instead of relying on guesswork, let’s analyze the given numbers and find the hidden relationship.
- Looking at the outputs:
- 2 → 6
- 3 → 12
- 4 → 20
- 5 → 30
- 6 → 42
- Checking for a pattern: Each number follows a specific formula:
n × (n + 1) = Output
Let’s test this with the given values:
- 2 × (2 + 1) = 2 × 3 = 6
- 3 × (3 + 1) = 3 × 4 = 12
- 4 × (4 + 1) = 4 × 5 = 20
- 5 × (5 + 1) = 5 × 6 = 30
- 6 × (6 + 1) = 6 × 7 = 42
- Applying the same logic to n = 9:
- 9 × (9 + 1) = 9 × 10 = 90
So, the correct answer is 90!
Why Does This Logic Work?
This formula follows a simple quadratic sequence based on multiplying a number with its successor (the next integer). Such patterns frequently appear in number-based puzzles because they combine multiplication and incremental addition.
Many people assume a linear formula (adding the same number each time) instead of checking for multiplicative relationships, which is why they often make mistakes.
Final Thoughts – Keep Training Your Brain!
Puzzles like this aren’t just fun—they help boost your logical thinking and problem-solving skills. The key takeaway? Always look for hidden relationships in numbers instead of relying on basic arithmetic. The more you practice, the better you become at spotting patterns.
Enjoyed this puzzle? Share it with your friends and challenge them to solve it! And if you love brain teasers, stay tuned for more tricky math riddles to sharpen your mind.
