An alphamagic square is a magic square 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 are language-dependent.[1] Alphamagic squares were invented by Lee Sallows in 1986.[2][3]
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,
5
22
18
28
15
2
12
8
25
converts to ...
five
twenty-two
eighteen
twenty-eight
fifteen
two
twelve
eight
twenty-five
Counting the letters in each number word generates the following square which turns out to also be magic:
4
9
8
11
7
3
6
5
10
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.[4]
The above example enjoys another special property: the nine numbers in the lower square are consecutive. This prompted Martin Gardner to describe it as "Surely the most fantastic magic square ever discovered."[5]
A geometric alphamagic squareedit
Figure 1: A geomagic square that is also alphamagic
Sallows has produced a still more magical version—a square which is both geomagic 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 alphamagic.
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, 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.
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.
^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, ISBN1568811209
^The Universal Book of Mathematics: From Abracadabra to Zeno's Paradoxes, by David Darling, p. 12, Hoboken, NJ: Wiley, 2004, ISBN0471270474
^. Archived from the original on 2017-10-10. Retrieved 2012-07-25.
External linksedit
Science Frontiers Online: Alphamagic Squares
April 10, 2024
alphamagic, square, alphamagic, square, magic, square, that, remains, magic, when, numbers, replaced, number, letters, occurring, name, each, number, hence, would, replaced, number, letters, three, since, different, languages, will, have, different, number, le. An alphamagic square is a magic square 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 are language dependent 1 Alphamagic squares were invented by Lee Sallows in 1986 2 3 Contents 1 Example 2 A geometric alphamagic square 3 Other languages 4 References 5 External linksExample editThe 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 5 22 1828 15 212 8 25converts to five twenty two eighteentwenty eight fifteen twotwelve eight twenty fiveCounting the letters in each number word generates the following square which turns out to also be magic 4 9 811 7 36 5 10If 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 4 The above example enjoys another special property the nine numbers in the lower square are consecutive This prompted Martin Gardner to describe it as Surely the most fantastic magic square ever discovered 5 A geometric alphamagic square edit nbsp Figure 1 A geomagic square that is also alphamagicSallows has produced a still more magical version a square which is both geomagic 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 alphamagic Other languages editThe Universal Book of Mathematics provides the following information about Alphamagic Squares 6 7 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 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 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 References edit Wolfram MathWorld Alphamagic Squares Mathematical Recreations Alphamagic Square by Ian Stewart Scientific American January 1997 pp 106 110 ACM Digital Library Volume 4 Issue 1 Fall 1986 Double Alphamagic Squares Futility Closet November 16 2015 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 ISBN 1568811209 The Universal Book of Mathematics From Abracadabra to Zeno s Paradoxes by David Darling p 12 Hoboken NJ Wiley 2004 ISBN 0471270474 Encyclopedia of Science Games amp Puzzles Alphamagic Squares Archived from the original on 2017 10 10 Retrieved 2012 07 25 External links editScience Frontiers Online Alphamagic Squares Retrieved from https en wikipedia org w index php title Alphamagic square amp oldid 1217036142, wikipedia, wiki, book, books, library,
