Let's solve the problem step by step to determine the missing number in the table:
We are given the following table:
[tex]\[
\begin{array}{|c|c|c|}
\hline
11 & 3 & 2 \\
\hline
7 & 12 & 6 \\
\hline
14 & 12 & ? \\
\hline
\end{array}
\][/tex]
Our task is to find the missing value represented by `?`.
### Step 1: Analyze the Given Data
First, let's calculate the sum of the numbers in each of the given rows:
- For the first row: [tex]\( 11 + 3 + 2 = 16 \)[/tex]
- For the second row: [tex]\( 7 + 12 + 6 = 25 \)[/tex]
### Step 2: Identify a Possible Pattern
When we observe the sums calculated above:
- First row sum: [tex]\( 16 \)[/tex]
- Second row sum: [tex]\( 25 \)[/tex]
### Step 3: Apply the Pattern to the Third Row
Now, let's check the sum of the first two numbers in the third row and use the pattern to find the missing value.
- The sum of the first and second numbers in the third row: [tex]\( 14 + 12 = 26 \)[/tex]
### Step 4: Calculate the Missing Number
To balance the sum similar to previous rows, we need to find a number that makes the row sum consistent.
From the sums calculated in the first and second rows, we observed the pattern that third value in the row balances out the previous sums.
To determine the missing value for the third row, we set the sum of the numbers in this row to match a logical sum increment pattern:
[tex]\[
\text{sum of the third row} = 26 - 16 + 25 - 16 = 10 \quad (\text{To maintain consistent difference metric})
\][/tex]
Therefore, the missing number in the third row is [tex]\( 10 \)[/tex].
### Conclusion:
The missing number in the table is [tex]\( 10 \)[/tex].
Thus, the answer is:
[tex]\[
\boxed{10}
\][/tex]
