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none occurs in Danish or in Latin, but there are 6 in Dutch, 13 in
Finnish, and an incredible 221 in German. Yet to be determined is whether a 3 × 3 square exists from which a magic square can be derived that, in turn, yields a third magic square—a magic triplet. Also unknown is the number of 4 × 4 and 5 × 5 language-dependent alphamagic squares.
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A surprisingly large number of 3 × 3 alphamagic squares exist—in
English and in other languages. French allows just one 3 × 3 alphamagic square involving numbers up to 200, but a further 255 squares if the size of the entries is increased to 300. For entries less than 100,
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that remains magic when its numbers are replaced by the number of letters occurring in the name of each number. Hence 3 would be replaced by 5, the number of letters in "three". Since different languages will have a different number of letters for the spelling of the same number, alphamagic squares
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and alphamagic. In the square shown in Figure 1, any three shapes in a straight line—including the diagonals—tile the cross; thus the square is geomagic. The number of letters in the number names printed on any three shapes in a straight line sum to forty five; thus the square is
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If the generated array is also a magic square, the original square is alphamagic. In 2017 British computer scientist Chris
Patuzzo discovered several doubly alphamagic squares in which the generated square is in turn an alphamagic square.
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In 2018, the first 3 × 3 Russian alphamagic square was found by Jamal
Senjaya. Following that, another 158 3 × 3 Russian alphamagic squares were found (by the same person) where the entries do not exceed 300.
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The example below is alphamagic. To find out if a magic square is also an alphamagic square, convert it into the array of corresponding number words. For example,
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Gardner, Martin (1968), A Gardner's
Workout: Training the Mind and Entertaining the Spirit, p. 161, A K Peters/CRC Press, Natick, Mass., July 2001,
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The above example enjoys another special property: the nine numbers in the lower square are consecutive. This prompted
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Counting the letters in each number word generates the following square which turns out to also be magic:
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Sallows has produced a still more magical version—a square which is both
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to describe it as "Surely the most fantastic magic square ever discovered."
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The
Universal Book of Mathematics: From Abracadabra to Zeno's Paradoxes
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329:"Encyclopedia of Science, Games & Puzzles: Alphamagic Squares"
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provides the following information about
Alphamagic Squares:
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are language-dependent. The term alphamagic was coined by
309:, by David Darling, p. 12, Hoboken, NJ: Wiley, 2004
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264:ACM Digital Library, Volume 4 Issue 1, Fall 1986
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357:Science Frontiers Online: Alphamagic Squares
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244:Mathematical Recreations: Alphamagic Square
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184:A geomagic square that is also alphamagic
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233:Wolfram MathWorld: Alphamagic Squares
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16:Magic square with extra constraints
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203:The Universal Book of Mathematics
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482:Prime reciprocal magic square
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172:A geometric alphamagic square
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254:, January 1997, pp. 106-110
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496:Higher dimensional shapes
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487:Most-perfect magic square
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275:Double Alphamagic Squares
541:Pandiagonal magic square
536:Associative magic square
477:Pandiagonal magic square
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577:Eight queens puzzle
280:, November 16, 2015
252:Scientific American
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546:Multimagic square
457:Alphamagic square
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21:alphamagic square
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555:Related concepts
462:Antimagic square
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331:. Archived from
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166:Martin Gardner
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592:Magic series
562:Latin square
472:Heterosquare
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422:Magic square
407:Magic circle
337:. Retrieved
333:the original
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193:alphamagic.
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114:twenty-five
97:twenty-eight
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25:magic square
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587:Magic graph
567:Word square
248:Ian Stewart
30:Lee Sallows
503:Magic cube
427:Magic star
339:2012-07-25
317:0471270474
295:1568811209
220:References
180:Figure 1:
89:twenty-two
92:eighteen
32:in 1986.
607:Category
190:geomagic
508:classes
100:fifteen
36:Example
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108:twelve
400:Types
111:eight
23:is a
313:ISBN
291:ISBN
103:two
86:five
246:by
154:10
74:25
52:18
19:An
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
