René Chrétien created a 3x3x3 magic rectangle to contruct a 27x27 panmagic square with extra special magic features.
Matrix 3x3x3 |
||||
7 |
9 |
23 |
39 |
|
4 |
11 |
24 |
39 |
|
26 |
1 |
12 |
39 |
|
15 |
22 |
2 |
39 |
|
19 |
17 |
3 |
39 |
|
14 |
0 |
25 |
39 |
|
6 |
20 |
13 |
39 |
|
18 |
16 |
5 |
39 |
|
8 |
21 |
10 |
39 |
|
117 |
117 |
117 |
Take 1x number from first grid +1 (shift 2 to the left)
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
+ 27x number from second grid (shift 2 to the right)
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
26 |
14 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
19 |
18 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
20 |
11 |
20 |
11 |
19 |
18 |
26 |
14 |
21 |
23 |
2 |
13 |
24 |
3 |
5 |
12 |
0 |
8 |
7 |
15 |
6 |
4 |
17 |
16 |
1 |
25 |
10 |
9 |
22 |
= 27x27 panmagic square
253 |
617 |
561 |
309 |
533 |
505 |
729 |
393 |
589 |
645 |
57 |
365 |
673 |
85 |
141 |
337 |
1 |
225 |
197 |
421 |
169 |
113 |
477 |
449 |
29 |
701 |
281 |
696 |
282 |
263 |
613 |
567 |
312 |
535 |
510 |
705 |
392 |
592 |
625 |
60 |
364 |
649 |
90 |
143 |
340 |
7 |
221 |
207 |
422 |
164 |
134 |
|