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]
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.
The Universal Book of Mathematics provides the following information about Alphamagic Squares: [6] [7]
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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