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Complete the following magic square such that the sum of each row, column, and diagonal is 34:

\begin{tabular}{|l|l|l|l|}
\hline & & & 1 \\
\hline & 11 & & 14 \\
\hline 3 & 10 & & \\
\hline & 5 & 9 & 4 \\
\hline
\end{tabular}


Sagot :

Let's solve the problem step-by-step by examining the grid and calculating the sum of all the integers present in it.

Here's the given grid:

[tex]\[ \begin{array}{|c|c|c|c|} \hline & & & 1 \\ \hline & 11 & & 14 \\ \hline 3 & 10 & & \\ \hline & 5 & 9 & 4 \\ \hline \end{array} \][/tex]

We need to add up all the numbers in this 4x4 grid. Let's go row by row:

1. First row: [tex]\(0, 0, 0, 1\)[/tex]
- Sum: [tex]\(0 + 0 + 0 + 1 = 1\)[/tex]
2. Second row: [tex]\(0, 11, 0, 14\)[/tex]
- Sum: [tex]\(0 + 11 + 0 + 14 = 25\)[/tex]
3. Third row: [tex]\(3, 10, 0, 0\)[/tex]
- Sum: [tex]\(3 + 10 + 0 + 0 = 13\)[/tex]
4. Fourth row: [tex]\(0, 5, 9, 4\)[/tex]
- Sum: [tex]\(0 + 5 + 9 + 4 = 18\)[/tex]

Now, let's add up the sums of each row:

[tex]\[ 1 + 25 + 13 + 18 \][/tex]

Adding them step-by-step:

1. [tex]\(1 + 25 = 26\)[/tex]
2. [tex]\(26 + 13 = 39\)[/tex]
3. [tex]\(39 + 18 = 57\)[/tex]

Thus, the total sum of all integers in the grid is [tex]\(57\)[/tex].