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 |
|