Question

Complete the following multiplication grid:

6	1
7	5	3
2		4

Answer 1

Hint: We have given the multiplication grid and we are asked to fill in the blanks of the grid. There is a pattern that we have to recognize to solve this grid. As you can see that, the sum of the numbers written in the first column is 15. Also, the sum of the numbers written in the second row and in the diagonal is also 15 so we have to fill the blanks in such a way so that the sum of the elements in any row or column or diagonal should be 15.

Complete step-by-step solution:
The multiplication $3\times 3$ grid which is given in the above problem is as follows:

6	1
7	5	3
2		4

If we add the numbers written in the first column of the above $3\times 3$ grid we get,
$\begin{align}
  & 6+7+2 \\
 & =15 \\
\end{align}$
Now, if we add the numbers written in the second row of the above grid we get,
$\begin{align}
  & 7+5+3 \\
 & =15 \\
\end{align}$
Also, adding the numbers written in the main diagonal of a $3\times 3$ grid we get,
$\begin{align}
  & 6+5+4 \\
 & =15 \\
\end{align}$
From the above, if you analyze carefully the above additions you will find that when we add numbers written in any row or column or the diagonal we are getting 15 so we are going to use this pattern to find the numbers which can be written in the blank spaces.
Let us assume the numbers that could be possible in the blank space which lies in the first row is x and the number that could be possible in the blank space in the third row is y. This assumption we have shown in by putting x and y in the said blanks.

6	1	x
7	5	3
2	y	4

Now, applying the pattern in finding the values of x and y we get,
Adding the numbers in the first row and equating them to 15 we get,
$\begin{align}
  & 6+1+x=15 \\
 & \Rightarrow 7+x=15 \\
 & \Rightarrow x=15-7=8 \\
\end{align}$
Adding the numbers in the third row and equating the result of addition to 15 we get,
$\begin{align}
  & 2+y+4=15 \\
 & \Rightarrow y+6=15 \\
 & \Rightarrow y=15-6=9 \\
\end{align}$
Hence, we got the values of x and y as 8 and 9 respectively.
In the below table, we have substituted the values of x and y as 8 and 9.

6	1	8
7	5	3
2	9	4

Note: You can check if the values that you filled in blank spaces are correct or not by checking that in any row or column or diagonal the sum of numbers should be 15.
Checking the addition of numbers in the third column we get,
$\begin{align}
  & 8+3+4 \\
 & =15 \\
\end{align}$
We are getting the sum as 15. It means that the number “8” that we filled is correct.
Similarly, we are adding the numbers written in the third row we get,
$\begin{align}
  & 2+9+4 \\
 & =15 \\
\end{align}$
Again, we are getting the sum as 15 so this means that the number “9” that we filled is correct.