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give a method of construction and enumeration of all most-perfect magic squares. They also show that there is a
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Apart from the trivial case of the first order square, most-perfect magic squares are all of order 4
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Number of essentially different most-perfect pandiagonal magic squares of order 4n from The
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Two 12 × 12 most-perfect magic squares can be obtained adding 1 to each element of:
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Most-perfect
Pandiagonal Magic Squares: Their Construction and Enumeration
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Construction of a fourth-order most-perfect magic square from a
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112 5 122 23 111 13 139 30 129 12 140 22
371:
103 66 93 48 104 58 76 41 86 59 75 49
359:
136 33 126 15 137 25 109 8 119 26 108 16
337:
115 15 98 13 131 30 112 44 129 46 96 29
386:
115 2 125 20 114 10 142 27 132 9 143 19
383:
106 63 96 45 107 55 79 38 89 56 78 46
377:
34 135 24 117 35 127 7 110 17 128 6 118
365:
64 105 54 87 65 97 37 80 47 98 36 88
362:
73 44 83 62 72 52 100 69 90 51 101 61
346:
124 32 141 34 108 17 127 3 110 1 143 18
343:
123 7 106 5 139 22 120 36 137 38 104 21
340:
116 40 133 42 100 25 119 11 102 9 135 26
334:
76 80 93 82 60 65 79 51 62 49 95 66
331:
75 55 58 53 91 70 72 84 89 86 56 69
328:
16 140 33 142 0 125 19 111 2 109 35 126
325:
23 107 6 105 39 122 20 136 37 138 4 121
322:
24 132 41 134 8 117 27 103 10 101 43 118
319:
31 99 14 97 47 114 28 128 45 130 12 113
316:
64 92 81 94 48 77 67 63 50 61 83 78
18:
389:
67 102 57 84 68 94 40 77 50 95 39 85
380:
43 74 53 92 42 82 70 99 60 81 71 91
368:
1 116 11 134 0 124 28 141 18 123 29 133
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4 113 14 131 3 121 31 138 21 120 32 130
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71 59 54 57 87 74 68 88 85 90 52 73
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431: = 36, there are about 2.7 × 10
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49:. Unsourced material may be challenged and removed.
466:, India, 2008, 128 pages, ISBN 978-81-8449-321-4
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281:as a most-perfect magic square given in the
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477:STRONGLY MAGIC SQUARES by T. V. Padmakumar
492:On-Line Encyclopedia of Integer Sequences
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109:Learn how and when to remove this message
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444:Kathleen Ollerenshaw, David S. Brée:
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301:with distinct diagonals, M, and its
47:adding citations to reliable sources
397:All most-perfect magic squares are
260:/2 along a (major) diagonal sum to
125:Most-perfect magic square from the
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424:and most-perfect magic squares.
237:with two additional properties:
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453:Number Theory and Magic Squares
34:needs additional citations for
256:All pairs of integers distant
241:Each 2 × 2 subsquare sums to 2
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617:Prime reciprocal magic square
435:most-perfect magic squares.
233:containing the numbers 1 to
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58:"Most-perfect magic square"
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622:Most-perfect magic square
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418:one-to-one correspondence
223:most-perfect magic square
676:Pandiagonal magic square
671:Associative magic square
612:Pandiagonal magic square
287:Sringeri Sharada Peetham
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433:essentially different
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410:Kathleen Ollerenshaw
43:improve this article
712:Eight queens puzzle
462:2010-02-25 at the
422:reversible squares
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681:Multimagic square
592:Alphamagic square
408:. In their book,
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399:panmagic squares
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650:Magic hypercube
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208:transcription
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60: –
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54:Find sources:
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32:This article
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727:Magic series
697:Latin square
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607:Heterosquare
557:Magic square
542:Magic circle
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41:Please help
36:verification
33:
722:Magic graph
702:Word square
127:Parshvanath
638:Magic cube
562:Magic star
457:Sura books
439:References
393:Properties
283:Panchangam
132:temple in
69:newspapers
303:transpose
277:Image of
225:of order
134:Khajuraho
99:July 2021
742:Category
460:Archived
420:between
269:Examples
245:, where
643:classes
487:A051235
485::
136:, India
83:scholar
85:
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535:Types
229:is a
90:JSTOR
76:books
483:OEIS
427:For
412:and
305:, M.
212:the
130:Jain
62:news
16:Data
195:15
181:10
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156:14
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45:by
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221:A
210:of
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506:v
429:n
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262:s
258:n
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