The Fibonacci Mystery: Can You Solve This Unique Math Puzzle?

Mathematics is full of intriguing patterns, and today, we bring you a puzzle that will challenge your number sense! This puzzle is based on a well-known sequence, but can you spot the pattern and find the missing number?

The Puzzle:

Below is a 4×4 grid of numbers. However, one number is missing. Your task is to figure out what it should be!

2	3	5	8
3	5	8	13
5	8	13	21
8	13	?	55

What number should replace the question mark (?) in the grid?

Hint: Look closely at the relationships between the numbers in each row and column.

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Solution & Explanation:

The pattern in the grid follows the Fibonacci sequence, where each number is the sum of the two preceding numbers.

Let’s analyze the rows:

• Row 1: 2, 3, (2+3=5), (3+5=8)
• Row 2: 3, 5, (3+5=8), (5+8=13)
• Row 3: 5, 8, (5+8=13), (8+13=21)
• Row 4: 8, 13, (8+13=21), (13+21=34)

Thus, the missing number (?) is 21.

Final Answer:

The missing number is 21.

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Question:2

The Secret Code of the Squares

You are given a 4×4 grid of numbers, but one number is missing. The pattern follows a hidden mathematical rule. Can you find the missing number?

1	4	9	16
2	8	18	32
3	12	?	48
4	16	36	64

Your Challenge:

Find the missing number (?) in the grid.

Hint: The numbers follow a squared pattern combined with multiplication. Look carefully at how the numbers in each row relate to the row number.

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Solution & Explanation:

The numbers in the grid follow this pattern:

Each number in the table is calculated as:

$$\text{Row Number} \times \text{Column Number}^2$$

Let's verify this with some examples:

• Row 1: 1×1² = 1, 1×2² = 4, 1×3² = 9, 1×4² = 16
• Row 2: 2×1² = 2, 2×2² = 8, 2×3² = 18, 2×4² = 32
• Row 3: 3×1² = 3, 3×2² = 12, 3×3² = 27, 3×4² = 48
• Row 4: 4×1² = 4, 4×2² = 16, 4×3² = 36, 4×4² = 64

Thus, the missing number (?) is 27.

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Final Answer:

The missing number is 27.

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Why is This Puzzle Interesting?

This puzzle is not just about numbers; it demonstrates the beauty of mathematical patterns. The Fibonacci sequence appears in nature, from sunflower spirals to galaxies, making it one of the most fascinating sequences in mathematics.

Did you solve it correctly? Share your thoughts in the comments!