(17) Not Every Date Cooperates!
Pankaj Khanna
9424810575
Previous/Next Blog Posts:
(1) Beauty Squarely Introduction & Kuber Yantra
(2) Murphy Radio!? अले वाह!! 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) Dürer Square
(11) Tona Lisa as a Rock Star!
(17) Not Every Date Cooperates!
No! I am not going to discuss your attractive and intelligent 'date'—the one who wisely ran away from you just in time to settle peacefully in the heart of someone else!
This post is about dates of a very different temperament—birth dates that stubbornly refuse to squeeze themselves into the little cells of Ramanujan’s Birthdate Square. These are the rebels of the calendar, the dates that politely decline mathematical accommodation. In short, we are about to explore the limitations of Ramanujan’s Yantras.
Any magic square produced using this method will never be a beautiful pandiagonal or a charming associated magic square. The reason is simple: Ramanujan’s Birthdate Square itself is a normal magic square—and by its very nature, it is neither pandiagonal nor associated.
This is not a flaw, of course. Just a structural truth. Expecting pandiagonal elegance from Ramanujan’s Square is a bit like expecting a classical raga to suddenly break into jazz improvisation.
We have already examined these richer species of magic squares while discussing Khajuraho Magic and the celebrated Dürer Square. Still, a quick recap never hurts. So before we proceed further, let us briefly revisit the comparison of the major types of magic squares, summarized neatly in the table below.
And this clearly explains why Ramanujan’s Birthdate Square is so charming: it chooses personal creativity over classical perfection despite being just a normal Square.
When the four inputs—A (Date), B (Month), C (first two digits of the year), and D (last two digits of the year)—are well-spaced, with no repetitions, all values at least 4, and mutual differences comfortably greater than 3, the Ramanujan Yantra assembles itself impeccably.
Before blaming fate—or Ramanujan—remember his Yantras are generous, but not universal.
Based on the above observations, let us formulate a few rules for the construction of magic squares for your birth date through Ramanujan's Yantras.
There are Five Rules that decide construction of Magic Squares from Ramanujan's Yantras.
Rule 1: The Magic-Sum Rule
Every magic square lives and dies by its magic sum.
If the magic sum is less than 34, a magic square using positive integers is impossible to construct by any Yantra.
Minimum number of a magic square is 1. Minimum sum of all numbers of a magic square is equal to = 1+2+3+...+16 = n(n+1)/2 = (16x17)/2= 136
Sum of four rows= 136
Hence sum of of one row or Magic Sum= 136/4=34.
If the magic sum is less than 30, even non-negative integers (including zero) won’t save you.
If zero is considered as a part of a birthdate square, the minimum sum of sixteen numbers will be equal to (15x16)/2= 120
Hence magic sum= 120/4 = 30
Rule 2: The Distinctness Rule
(The Cardinal Rule)
If any two among A, B, C, D are equal, then obviously magic square with distinct digits can not be constructed by any Yantra. Duplicates here are not a bug. They are the destiny.
Rule 3: The Distance Rule
(The ±3 Trap)
For every pair (X, Y) among {A, B, C, D} ; |X − Y| ≥ 4
Break this rule more than once and duplicate numbers are guaranteed.
And once duplicates arrive, the magic square quietly collapses.
Rule 4: The Small-Number Rule
(Negative Hell)
If two or more of {A, B, C, D} ≤ 2 , the square will inevitably slip into negative numbers.
No amount of optimism can prevent this descent.
Rule 5: The Tiny-D Rule
(Year Trouble Ahead)
The value of D (last two digits of the year) matters more than it looks.
If D = 00, no magic square with positive numbers can be formed.
If D = 01, a square can be made—but zero will sneak in.
When Ramanujan’s Yantra refuses a birth date, it is not a failure of mathematics.
It is an invitation to invent.
So what should one change—the yantra or the birthday!?
We shall journey through many more Yantras and uncover several clever escape routes in the coming blog posts. Though I must confess, there will never be a universal guarantee. Some dates are simply born rebellious.
Next blog post? Something festive and slightly competitive! We shall deploy the magic squares of Khajuraho, Dürer, and Ramanujan to create Happy New Year 2026 magic squares, proudly featuring the adjacent numbers 20 and 26.
Let the numbers line up—and let us see which magic square tradition emerges as the ultimate winner!
Pankaj Khanna
9424810575
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मेरे कुछ अन्य ब्लॉग:
हिन्दी में:
तवा संगीत : ग्रामोफोन का संगीत और कुछ किस्सागोई।
रेल संगीत: रेल और रेल पर बने हिंदी गानों के बारे में।
साइकल संगीत: साइकल पर आधारित हिंदी गाने।
कुछ भी: विभिन्न विषयों पर लेख।
तवा भाजी: वन्य भाजियों को बनाने की विधियां!
मालवा का ठिलवा बैंड: पिंचिस का आर्केस्टा!
ईक्षक इंदौरी: इंदौर के पर्यटक स्थल। (लेखन जारी है।)
अंग्रेजी में:
Love Thy Numbers : गणित में रुचि रखने वालों के लिए।
Epeolatry: अंग्रेजी भाषा में रुचि रखने वालों के लिए।
CAT-a-LOG: CAT-IIM कोचिंग।छात्र और पालक सभी पढ़ें।
Corruption in Oil Companies: HPCL के बारे में जहां 1984 से 2007 तक काम किया।
