Multiplication magic square
Why adding numbers to get the magic sum? You get the magic sum if you multiply the numbers in the multiplication magic square.
3x3 multiplication magic square
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|
|
216 |
216 |
216 |
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|
|
216 |
|
|
|
216 |
|
216 |
|
18 |
1 |
12 |
|
|
216 |
|
4 |
6 |
9 |
|
|
216 |
|
3 |
36 |
2 |
|
Source: Sayles, 1913
4x4 multiplication magic square (with smallest possible digits)
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5040 |
5040 |
5040 |
5040 |
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|
5040 |
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|
|
|
5040 |
|
5040 |
|
1 |
15 |
24 |
14 |
|
|
5040 |
|
12 |
28 |
3 |
5 |
|
|
5040 |
|
21 |
6 |
10 |
4 |
|
|
5040 |
|
20 |
2 |
7 |
18 |
|
Source: Sayles
5x5 multiplication magic square
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|
|
362880 |
362880 |
362880 |
362880 |
362880 |
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|
|
362880 |
|
|
|
|
|
362880 |
|
362880 |
|
1 |
15 |
42 |
16 |
36 |
|
|
362880 |
|
14 |
32 |
9 |
3 |
30 |
|
|
362880 |
|
27 |
6 |
10 |
28 |
8 |
|
|
362880 |
|
20 |
7 |
24 |
54 |
2 |
|
|
362880 |
|
48 |
18 |
4 |
5 |
21 |
|
Source: Marián Trenkler, 19 januari 2001
6x6 panmagic and 2x2 & 3x3 compact multplication magic square
|
729 |
16 |
23328 |
1 |
11664 |
32 |
|
576 |
324 |
18 |
5184 |
36 |
162 |
|
3 |
3888 |
96 |
243 |
48 |
7776 |
|
46656 |
4 |
1458 |
64 |
2916 |
2 |
|
9 |
1296 |
288 |
81 |
144 |
2592 |
|
192 |
972 |
6 |
15552 |
12 |
486 |
Source: W.S. Andrews, magic squares and cubes, Dover, publ., 1960, p. 292
8x8 Franklin panmagic multiplication magic square
|
1 |
1080 |
42 |
1260 |
3 |
360 |
14 |
3780 |
|
378 |
140 |
9 |
120 |
126 |
420 |
27 |
40 |
|
180 |
6 |
7560 |
7 |
540 |
2 |
2520 |
21 |
|
840 |
63 |
20 |
54 |
280 |
189 |
60 |
18 |
|
36 |
30 |
1512 |
35 |
108 |
10 |
504 |
105 |
|
168 |
315 |
4 |
270 |
56 |
945 |
12 |
90 |
|
5 |
216 |
210 |
252 |
15 |
72 |
70 |
756 |
|
1890 |
28 |
45 |
24 |
630 |
84 |
135 |
8 |
Source: Christian Boyer, 2006
8x8 Multiplication ánd addition magic square
|
162 |
207 |
51 |
26 |
133 |
120 |
116 |
25 |
|
105 |
152 |
100 |
29 |
138 |
243 |
39 |
34 |
|
92 |
27 |
91 |
136 |
45 |
38 |
150 |
261 |
|
57 |
30 |
174 |
225 |
108 |
23 |
119 |
104 |
|
58 |
75 |
171 |
90 |
17 |
52 |
216 |
161 |
|
13 |
68 |
184 |
189 |
50 |
87 |
135 |
114 |
|
200 |
203 |
15 |
76 |
117 |
102 |
46 |
81 |
|
153 |
78 |
54 |
69 |
232 |
175 |
19 |
60 |
Source: Dénes en Keedwell
