"Russian Alphamagic Square"
more than a decade of research, trials and errors, Professor Lee
B. Croft and math student Samuel Comi of Arizona
State University (ASU) announce the discovery of the first Russian
Dr Croft (left) is Head of the Faculty of German, Romanian, and Slavic Languages; School of International Letters and Cultures. Samuel Comi (right) is a student in Croft's RUS-212 Russian Conversation course, a sophomore mathmatics major, and active in the Chess Club. Croft had been researching the problem for over 10 years, then Comi wrote a computer program that found the solution in one weekend.
Croft and Comi call their discovery the "Lee Sam," (a pun on Croft's Russian signature "Ли сам") and Sam's name. They gratiously advise everyone to keep a copy of it in their possession, so as to extend their life by 36 years. Magic Squares are ancient Chinese good luck charms.
The 3 x 3 array of numbers (74, 50, 92 / 90, 72, 54 / 52, 94, 70) has several unique properties:
Dr Croft explains:
"An alpha-magic square is a math puzzle in which the numbers of letters needed to spell the numbers also form a magic square … so that the array above adds to a constant sum of 216 on any row, column, or diagonal AND the numbers of Cyrillic letters needed to spell the Russian names of the numbers in this array, or precisely 15, 9, 12 / 9, 12, 15 / 12, 15, 9, also adds to a constant sum (36) on any row, column, or diagonal."
"The concept of alpha-magic squares is derived from a fifth-century Anglo-Saxon runic charm called by the discovering scholar Lee C.F. Sallows of Holland the 'Li Shu' (since the very first discovered magic square in China, circa 2300 B.C. is called the 'Lo Shu')."
"The alphamagic square represents a very rare confluence of 'magic' between the world of numbers and the world of letters. The runic original was reputedly devised by an anonymous wizard of Legendary King Mi (perhaps King Ida (550-616 AD)) to extend by its magic the King's life by the number of years of the secondary square's magic sum."
More than 10 years of research to find a solution
Dr. Croft was a former math major and has been fascinated by magic squares for a long time. He says, "I encountered the alphamagic square work of Lee Sallows about ten years ago. I made an initial attempt to find a Russian one and failed. I revived the effort inspired by math-puzzlist extraordinaire Martin Gardner who proved mathematically that the third-order magic cube is impossible."
"But I had produced an earlier 'semi-magic' 3 x 3 x 3 cube by triply applying the 'Siamese method' to adjacent two-dimensional squares and had some partial success with a Russian magic square with a semi-magic (one diagonal out) logorithmic square, and a semi-magic 4x4 square with a magic logorithmic."
"In 2007 last semester, I began to try to enlist people of computer savvy to apply Sallows' ALPHA.BAS variation of Pascal to a list of Russian logorithms. I asked a math professor, a math-major former student, even our department computer wizard. I think I failed to completly explain the problem and provide them with enough information. I got no where."
"Sam Comi found the Russian magic square over a single weekend!"
News of this discovery will be published in several mathmatical journals and presented at conferences. Dr. Croft did their first public presentation — “The Search for a Russian Alphamagic Square”(download PDF) — at the AATSEEL meeting, University of Arizona, Tucson on April 19. An article about this discovery entitled "Russian Alphamagic Squares" by Lee B. Croft and Samuel Comi has been accepted for publication in Word Ways: The Journal of Recreational Linguistics, and they plan to also submit to The Journal of Recreational Mathematics. More news about publications later.
— Submitted by Dr. Lee Croft, April 17, 2008.
Updated April 22, 2008
Update Jan 7, 2009:
The Lucky Magic Square
A 3 x 3 alphamagic square is a magic square for which the number of letters in the word for each number generates another magic square, for instance:
This is the actual "Li Shu," the first runic charm containing it discovered by Lee C. F. Sallows. King Mi was reputedly 45 years old (the first magic sum) and the wizard who made it for him was likely 21-years old (the logorithmic magic sum).
Dr. Croft points out, "The listed lifespan of King Ida (whom I think is the King referred to in Sallows' source as "King Mi") is precisely 66 years (the sum of the Li Shu's primary constant of 45 and the logorithmic constant of 21, the anonymous wizard's age ... so that the wizard devised a charm that added his age to that of his King ... and the King lived so long)."