Russian Alphamagic and Alphapanmagic Square Work

[Lee Croft]

Colleague Slavovedy,

   The work reflected below can be investigated further at www.russianaz.org/news/2009/Not_to_Perish.html


33
Тридцать
три
(11)    85
Восемьдесят
пять
(15)    38
Тридцать
восемь
(14)    86
Восемьдесят
шесть
(16)
58
Пятьдесят
восемь
(15)    66
Шестьдесят
шесть
(15)    53
Пятьдесят
три
(12)    65
Шестьдесят
пять
(14)
83
Восемьдесят
три
(14)    35
Тридцать
пять
(12)    88
Восемьдесят
восемь
(17)    36
Тридцать
шесть
(13)
68
Шестьдесят
восемь
(16)    56
Пятьдесят
шесть
(14)    63
Шестьдесят
три
(13)    55
Пятьдесят
пять
(13)



The above array is a fourth order (i.e. 4 X 4) Russian Cyrillic-alphabet ALPHAPANMAGIC SQUARE, the first one known.  It was generated by a Java computer program authored by Math/Russian major Samuel J. Comi in his Arizona State University Barrett Honors College undergraduate thesis, entitled “Magic Numerical Structures as They Apply to Russian,” defended on Thursday, October 28, 2010.  I have suggested that, in accordance with scholarly tradition in the study of such arrays, Sam call it the “SAM PAN.”  This astonishing array is mathematically “magical” because the primary numbers in each of its cells sum to a constant value of 242 on any full row, column, or main diagonal.  It is linguistically “alphamagical” because the number of Cyrillic alphabet letters in the Russian name of these primary numbers also sums to a constant value of 56 on any full row, column, or main diagonal.  But this array is not only “magical,” but “panmagical,” in that its primary numbers sum to the same constant value of 242 on the “broken diagonals” (e.g. the 1-3 diagonals like 33 with 56, 88, 65, or 55 with 83, 66, 38…or the 2-2 diagonals like 38, 65, 83, 56, or 58, 85 36, 63…) as well as on any of its four constituent outer quadrants (e.g. 33, 85, 58, 66 or 88, 36, 63, 55…), on its four corners (33, 86, 68, 55) or its center quadrant (66, 53, 35, 88).  And this array is “alphapanmagical”  because the sums of the number of Cyrillic letters in the Russian names of these numbers sum to a constant value of 56 on any of the broken diagonals, the outer quadrants, the corners, or the center quadrant.  Still, this is not all.  If the numbers of this amazing array are all digitally reversed—that is, if the 33 becomes a 33, the 85 becomes 58, the 38 becomes 83, the 86 becomes 68 and so on, then the array remains alphapanmagical to the same constant sum of 242, and the numbers of letters to spell each Russian digitally reversed number’s name still sums equivalently to 56.
                    Lee B. Croft, Prof. of Russian, Arizona State University