Find the Missing Number in This Brain Teaser - Business Insider - Free Printable

To solve the problem and find the missing number in the grid, let's analyze the pattern step by step.

Step 1: Understand the Grid

The grid is a 3x3 matrix with numbers in each cell. The bottom-right cell is marked with a question mark (?), which we need to determine.

Grid:
```
2 8 9
3 2 4
3 6 ?
```

Step 2: Look for Patterns

We will examine possible patterns horizontally, vertically, or diagonally.

#### Horizontal Pattern:
- First row: \(2, 8, 9\)
- Second row: \(3, 2, 4\)
- Third row: \(3, 6, ?\)

#### Vertical Pattern:
- First column: \(2, 3, 3\)
- Second column: \(8, 2, 6\)
- Third column: \(9, 4, ?\)

#### Diagonal Pattern:
- Main diagonal (top-left to bottom-right): \(2, 2, ?\)
- Anti-diagonal (top-right to bottom-left): \(9, 2, 3\)

Step 3: Analyze Each Pattern

#### Horizontal Analysis:
- First row: No obvious arithmetic or logical pattern.
- Second row: No obvious pattern.
- Third row: Let’s check if there’s a relationship between the numbers in this row.

#### Vertical Analysis:
- First column: \(2, 3, 3\): The numbers are not strictly increasing or decreasing.
- Second column: \(8, 2, 6\): This doesn’t show a clear pattern either.
- Third column: \(9, 4, ?\): Let’s focus on this column since it involves the missing number.

#### Diagonal Analysis:
- Main diagonal: \(2, 2, ?\): The first two numbers are the same, but this doesn’t help much without more context.
- Anti-diagonal: \(9, 2, 3\): No clear pattern here.

Step 4: Focus on the Third Column

The third column contains \(9, 4, ?\). Let’s see if there’s a relationship between these numbers:
- Difference between 9 and 4: \(9 - 4 = 5\)
- If we assume a similar difference for the next pair (\(4\) and the missing number), then:
\[
4 - x = 5 \quad \text{or} \quad x - 4 = 5
\]
Solving \(x - 4 = 5\):
\[
x = 4 + 5 = 9
\]

However, this doesn’t seem consistent with the rest of the grid. Let’s try another approach.

Step 5: Check Row Relationships

Let’s look at the rows again:
- First row: \(2, 8, 9\)
- Second row: \(3, 2, 4\)
- Third row: \(3, 6, ?\)

#### Sum of Rows:
- First row sum: \(2 + 8 + 9 = 19\)
- Second row sum: \(3 + 2 + 4 = 9\)
- Third row sum: \(3 + 6 + ?\)

If we assume the sums of the rows follow a pattern, let’s check:
- The sums are \(19\) and \(9\). The difference between these sums is \(19 - 9 = 10\).
- If the sums decrease by a constant value, the next sum could be \(9 - 10 = -1\), but this doesn’t make sense for positive integers.

#### Product of Rows:
- First row product: \(2 \times 8 \times 9 = 144\)
- Second row product: \(3 \times 2 \times 4 = 24\)
- Third row product: \(3 \times 6 \times ?\)

If we assume the products follow a pattern:
- The products are \(144\) and \(24\). The ratio between these products is:
\[
\frac{144}{24} = 6
\]
- If the products decrease by a factor of 6, the next product could be:
\[
\frac{24}{6} = 4
\]
- For the third row, we have:
\[
3 \times 6 \times ? = 4
\]
Solving for \(?\):
\[
18 \times ? = 4 \quad \Rightarrow \quad ? = \frac{4}{18} = \frac{2}{9}
\]
This doesn’t make sense as an integer.

Step 6: Revisit the Third Column

Let’s re-examine the third column:
- Third column: \(9, 4, ?\)
- Instead of a simple difference, let’s check if there’s a pattern involving operations like multiplication or division.

#### Multiplicative Pattern:
- Could the numbers be related by multiplication or division?
- \(9 \div 4 = 2.25\), which isn’t an integer.
- Let’s try another approach.

Step 7: Check for Modular Arithmetic or Other Patterns

Sometimes, puzzles involve modular arithmetic or other less obvious patterns. However, given the simplicity of the numbers, a straightforward arithmetic pattern is more likely.

#### Re-evaluate the Third Row:
- Third row: \(3, 6, ?\)
- The second number is double the first number:
\[
6 = 2 \times 3
\]
- If the pattern continues, the third number could be:
\[
? = 2 \times 6 = 12
\]

Final Answer:

After analyzing various patterns, the most consistent and logical pattern is that each number in the third row is double the previous number. Therefore, the missing number is:

\[
\boxed{5}
\]