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How to create a two-digit magic square from non-repeating numbers without zeros

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    How to create a two-digit magic square from non-repeating numbers without zeros
    Using two-digit numbers to create magic squares improves concentration and logical thinking.

    This article explains the method for creating magic squares from two-digit numbers. The method increases concentration and promotes logical thinking in children and adults. You don't have to be a mathematician to create a two-digit magic square. Read the previous article "The Magic Square Luo Shu Reveals its Secrets" to learn more about the requirements for creating magic squares.

    Forming the Base Table

    A magic square starts from the base table. The first column consists of three numbers with different digits. Vertical rows of digits in the columns must show the keys. Let's create a magic square using the main keys: 7-1-4 and 2-5-8.

    The first column of a magic square Write the keys 7-4-1 and 2-5-8 vertically in the first column. The second column is derived from the digits of the first column in the following order:
    • First digit from the middle row (1) and second digit from the bottom row (8) → 18.
    • First digit of the bottom row (4) and second digit of the top row (2).
    • First digit of the top row (7) and second digit of the middle row (5).
    		 The second column of a magic square

    Derive the third column from the second column using the same procedure to get the base table.

    72 18 45 = 135
    15 42 78 = 135
    48 75 12 = 135
    = 135 = 135 = 135
    • The same sum in horizontal and vertical rows.
    • Nine numbers with unique sets of digits.

    Converting the Base Table into a Magic Square

    First, decide which number of the base table will be in the middle. Follow these steps:

    Step 1

    Add each lower number in the base table to two other numbers in different horizontal and vertical rows. Each lower number gives two combinations.

    Step 1

    Step 2

    Among six combinations, find two where the sums are equal (sum = 135). The common number is 45, the center of the magic square.

    Step 2

    Step 3

    Rearrange rows and columns so that 45 is in the middle. There are three possible variants.

    Magic square

    Complete Section of Three Subsections

    Complete section of three subsections

    The Digital Values of the Numbers of the Subsections

    Digital values of the numbers of the subsections

    A recommended video:



    Exercise

    1. Convert the second and third subsection into a magic square.
    2. Create your own magic square using different combinations of keys: 1-4-7, 2-5-8, 3-6-9.