From 1 to 9, which number should be put in the middle of a magic square( 3 by 3 magic square), so that no matter how you add three numbers in a straight line .... up, down, sideways or diagonally .... you will get the same answer.
I believe 5
To find the number that should be put in the middle of a 3 by 3 magic square, we can use the following steps:
Step 1: Calculate the average
Sum all the numbers from 1 to 9: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45. Then, divide this sum by 9 (the number of cells in the magic square): 45 / 9 = 5.
Step 2: Determine the complementary number
Since there are three possible lines to form an equal sum (rows, columns, and diagonals), the sum for each line should be 15 (45 divided by 3). So, subtract the average (5) from 15 to get the complementary number: 15 - 5 = 10.
Step 3: Find the middle number
Now, from the given numbers (1 to 9), check which number is equal to the complementary number (10). In this case, there is no such number.
Step 4: Adjust the middle number
Since there is no number equal to the complementary number, we need to adjust it. In a magic square, the diagonals contribute to the central sum twice, whereas rows and columns contribute only once. Therefore, let's divide the complementary number by 2: 10 / 2 = 5.
Therefore, the number that should be put in the middle of the magic square is 5.