Happy New Year 2023 – A Magic Square of Order Four

Mathematics is on the artistic side a creation of new rhythms, orders, designs, harmonies, and on the knowledge side, is a systematic study of various rhythms, orders, designs and harmonies.

William L. Schaaf

Welcome to the blog Math1089 – Mathematics for All.

2022 is about to pass, and 2023 is coming. This is the moment to leave the old and welcome the new. Let’s hope that 2023 will

add the joys;

subtract the sorrows;

multiply the happiness; and

divide the love

among your loved ones. Happy New Year!

2023

A square matrix can tell us so many things and even show us some magic. Consider the following magic square, which uses the first day of the New Year 2023 (January 1, 2023) to fill the cells in the top row. The first number 1 represents the date, the second number 1 is the month, and the third and fourth numbers together 2023 is the year. Clearly, the

The first number 1 represents the date, the second number 1 is the month, and the third and fourth numbers together 2023 is the year. Clearly, this is a magic square of additive type. Our next blog post will be about a multiplicative magic square.

Few Notable Properties

(a) The sum of the row elements in each row is equal to 45. For example,

1 + 1 + 20 + 23 = 45

27 + 16 + 2 + 0 = 45

12 + 15 + 12 + 6 = 45

5 + 13 + 11 + 16 = 45

(b) The sum of the column elements in each column is equal to 45. For example,

1 + 27 + 12 + 5 = 45

1 + 16 + 15 + 13 = 45

20 + 2 + 12 + 11 = 45

23 + 0 + 6 + 16 = 45

(c) The sum of the diagonal elements is also equal to 139. For example,

1 + 16 + 12 + 16 = 45 (green)

23 + 15 + 2 + 23 = 45 (light blue)

(d) The sum of the corner elements is also equal to 45. For example,

1 + 23 + 16 + 5 = 45

(e) The sums of the numbers in the two sets of like coloured cells are again the same number 139. For example,

1 + 20 + 11 + 13 = 45 (yellow)

27 + 0 + 6 + 12 = 45 (purple)

(f) The sums of the numbers in the two sets of like coloured cells are again the same number 139. For example,

1 + 27 + 11 + 6 = 45 (yellow)

20 + 0 + 13 + 12 = 45 (blue)

(g) The sum of the numbers in the four central cells is again 45. For example,

16 + 2 + 12 + 15 = 45

(h) The sums of the numbers in the like-coloured 2 × 2 blocks are all 45. For example,

1 + 1 + 16 + 27 = 45 (light blue)

20 + 23 + 0 + 2 = 45 (orange)

12 + 6 + 16 + 11 = 45 (olive green)

12 + 15 + 13 + 5 = 45 (green)

During your explorations, if you find something not listed here, feel free to mail us or add yours using the comments. Your suggestions are eagerly and respectfully welcome! See you soon with a new mathematics blog that you and I call Math1089 – Mathematics for All!“.

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