(18) Welcoming 2026, Square by Square.๐๐๐ท๐ผ
Pankaj Khanna
9424810575
List of previous articles on the subject of Magic Squares:
(1) Beauty Squarely Introduction & Kuber Yantra
(2) Murphy Radio!? เค
เคฒे เคตाเคน!! My first Experience of Magic Square.
(3) Decoding the Quadratum Mirabile! How to solve 3x3 Magic Squares.
(4) Lo Shu Square History of Chinese Magic Square.
(5) The Unhurried Odyssey of a Turtle!! History of Magic Squares in short.
Brief Introduction.
(7) Khajuraho Magic: Introduction.
(8) Chautisa Yantra: Mytho-math Spice.
(9) Dรผrer Square : Introduction.
(10) European Chautisa and Tona Lisa. Properties of Durer's Square.
(11) Tona Lisa as a Rock Star! More prperties of Durer Square
(12) Why no Books or Research Papers ? To save environment and much more...
(13) Ramanujan: The Man Who Treated Numbers Like Pets. About Famous Mathematician Ramanujan.
(14) When Mathematics Met Ramanujan. About Ramanujan's Main work of Mathematics.
(15) Ramanujan's Date with numbers. About Ramanujan's Square.
(16) The Surrogate Ramanujan Yantra More about Ramanujan's Square.
(17) Not Every Date Cooperates! Limitations of Ramanujan's Square.
(18) Welcoming 2026, Square by Square.
Over the past journey, we have explored the elegance of the Khajuraho Magic Square, admired the timeless brilliance of the Dรผrer Square, and played with the delightful ingenuity of Ramanujan’s Square. More importantly, we have not merely admired them—we have learned how to construct them, number by number, square by square.
Today, let us put our knowledge to the test.The challenge is simple yet delightful: Can we welcome 2026 into a 4×4 Magic Square by placing 20 and 26 side-by-side in any row? There are many options available, luckily.
To do so, we shall construct four different Magic Squares—one inspired by the Khajuraho Magic Square, one guided by the timeless Dรผrer Square, one crafted using Ramanujan’s Yantra and one freestyle: Sort of 'numerical biography'.
(1) Crafting the Magic Square using Ramanujan’s Yantra.
The first row here is proudly assembled from New Year 2026 and Ramanujan’s birth year 1887. However, the original Ramanujan Yantra, in a moment of numerical mischief, insisted on producing repeated numbers. To restore harmony, I politely summoned the Surrogate Ramanujan Yantra, which promptly sorted out the trouble.
And thus, a magic square with all distinct numbers gracefully emerges—almost as if Ramanujan Srinivas himself were approving from the background.
All the properties of Ramanujan's Square are intact in this square too. Sum of each row, each column, two diagonals, four corners, seven small 2x2 squares is the same and equal to 151.
For more details, please see the previous blog posts written on Ramanujan and his Birthdate Square:
(2) Magic Square guided by the timeless brilliance of Durer Square.
The magic sum of this Associated Magic Square has been chosen very deliberately: 90. Every row, every column, and both diagonals march obediently to this number. Even five of the smaller 2×2 squares can’t resist joining the party—each summing to 90 as well. And all the magnificent properties of an Associated Magic square can be found here in this magic square too.
And just when you think the numbers are done celebrating; 2026 makes a cheerful appearance in the third row to wish you a Happy and Prosperous New Year.
May the New Year be as balanced, harmonious, and delightful to all the readers as the above Associated Magic Square.
But beware—this well-meaning 90 also comes with a friendly advisory: please don’t exceed 90 ml on New Year’s Eve!
Mathematics may forgive many things, but excess is not one of them!
All the properties of Durer Square have been discussed in details in the following Blog posts.
(3) New year Magic Square inspired by the Khajuraho Magic.
Writing about the Khajuraho Square on New Year’s Eve? That’s a risky move.I might be disowned, if not ceremonially eliminated, by my childhood and college friends. We grew up on Khajuraho beer. For us, Khajuraho meant beer. And beer alone. In those halcyon days, that was the only “sculpture” we knew. And happily studied it in depth at bars, terraces, parks, fields and culverts.
It was only much later, after graduation and the slow sobering that adulthood brings, that Khajuraho revealed its other avatar: The Erotic Poetry Carved in Stone.
(Khajuraho Trio: The Sculptures, The Magic Square and The beer.)
Very bad indeed! The effects of strong Khajuraho beer have managed to alter everything at once in the above image of the famous trio—the numbers in the magic square, the sculpture of Khajuraho, and even the label on the beer bottle itself!
Ok! Ok!! Let me correct it.
Now Khajuraho Trio is restored and it wishes you a very Happy New Year, a bit soberly now!
Time for us to sober up as well! Let us now return, clear-headed and number-minded, to the New Year Magic Square inspired by the Khajuraho Magic Square:
This, too, is a pandiagonal square, true to the spirit of the original. Among the entire royal family of magic squares, the Khajuraho Square remains my undisputed favourite—and not without reason. Look at its awesome Properties:
Every row, every column, both main diagonals, all four corners, all nine small 2×2 squares, and even the four elusive broken diagonals march in flawless harmony to the same sum. Ninety four in this case. No tantrums, no exceptions—just pure numerical discipline. Khajuraho Square can claim righteously : "Since tenth Century, no branches anywhere!"
We have already explored the many delightful and almost unbelievable properties of the Khajuraho Square in detail in the following blog posts:
(7) Khajuraho Magic: Introduction.
(8) Chautisa Yantra: Mytho-math Spice.
(9) Dรผrer Square : Comparision with Khajuraho Square.
(4) Biographical Magic Square: (Numerical Biography from birth year to the current year.)
I have created a magic square for myself as well and named it Biographical Magic Square. It begins with my birth year, 1962, placed in the first two cells of the top row, and concludes with the New Year 2026, written in the last two cells of the bottom row. ( And have written titles of my various Blogs under the auspicious numbers in a random order.)
Fixing four numbers in such an arbitrary manner greatly restricts the freedom to construct a magic square. Unsurprisingly, for this particular choice of fixed dates, the classical Khajuraho, Dรผrer, and Ramanujan models all politely decline the challenge.
We shall shortly unveil a few freshly devised models crafted especially for constructing biographical—and other delightfully personal—magic squares. Consider this blog post merely the opening act.
More patterns, more properties, and many more magic squares are already lining up backstage, eager to welcome 2026 in grand numerical style.
As we step into 2026, these magic squares remind us that numbers are never merely numbers.
With a little imagination, they begin to mark time, celebrate moments, and even wish us well. Whether shaped by the stone-carved discipline of Khajuraho, the Renaissance precision of Dรผrer, or the playful ingenuity of Ramanujan’s yantra, each square offers the same quiet invitation: to explore, to invent, and to enjoy the magic hidden in order itself.
May 2026 add up beautifully like a Khajuraho/ Dรผrer/ Ramanujan Square for you all.
(Numbers are smiling. Curtains half-open. The next four-plus fun-filled blog posts will dissect, decode, and gently demystify how these New Year magic squares came into existence.)
Pankaj Khanna
9424810575
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เคฎेเคฐे เคुเค เค
เคจ्เคฏ เคฌ्เคฒॉเค:
เคนिเคจ्เคฆी เคฎें:
เคคเคตा เคธंเคीเคค : เค्เคฐाเคฎोเคซोเคจ เคा เคธंเคीเคค เคเคฐ เคुเค เคिเคธ्เคธाเคोเค।
เคฐेเคฒ เคธंเคीเคค: เคฐेเคฒ เคเคฐ เคฐेเคฒ เคชเคฐ เคฌเคจे เคนिंเคฆी เคाเคจों เคे เคฌाเคฐे เคฎें।
เคธाเคเคเคฒ เคธंเคीเคค: เคธाเคเคเคฒ เคชเคฐ เคเคงाเคฐिเคค เคนिंเคฆी เคाเคจे।
เคुเค เคญी: เคตिเคญिเคจ्เคจ เคตिเคทเคฏों เคชเคฐ เคฒेเค।
เคคเคตा เคญाเคी: เคตเคจ्เคฏ เคญाเคिเคฏों เคो เคฌเคจाเคจे เคी เคตिเคงिเคฏां!
เคฎाเคฒเคตा เคा เค िเคฒเคตा เคฌैंเคก: เคชिंเคिเคธ เคा เคเคฐ्เคेเคธ्เคा!
เคเค्เคทเค เคंเคฆौเคฐी: เคंเคฆौเคฐ เคे เคชเคฐ्เคฏเคเค เคธ्เคฅเคฒ। (เคฒेเคเคจ เคाเคฐी เคนै।)
เค
ंเค्เคฐेเคी เคฎें:
Love Thy Numbers : เคเคฃिเคค เคฎें เคฐुเคि เคฐเคเคจे เคตाเคฒों เคे เคฒिเค।
Epeolatry: เค
ंเค्เคฐेเคी เคญाเคทा เคฎें เคฐुเคि เคฐเคเคจे เคตाเคฒों เคे เคฒिเค।
CAT-a-LOG: CAT-IIM เคोเคिंเค।เคाเคค्เคฐ เคเคฐ เคชाเคฒเค เคธเคญी เคชเคข़ें।
Corruption in Oil Companies: HPCL เคे เคฌाเคฐे เคฎें เคเคนां 1984 เคธे 2007 เคคเค เคाเคฎ เคिเคฏा।
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