The Magic Encyclopedia ™ DataBase

All Magic Squares to Tesseracts of order 3
(by Aale de Winkel)

With thanks to <John R Hendricks>, who provided the normalized positioned order 3 tesseracts, with the square and 4 cubes it provides a complete reference to all order 3 squares cubes and tesseracts.

General solution (from given data):
1. place the given numbers on their positions
2. use 1-agonal rules to obtain missing 1-agonal number
3. use n-agonal rules to obtain missing hypercube corners
4. use 1-agonal rules to solve the rest of the missing numbers
The above solution is used by the downloadable spreadsheet and is seen to be "summation stable" (ie: changing the sum, will result in a hypercube with this sum) henche the spreadsheet might be used using pe prime numbers also (of course one needs to check used numbers, and might need to specify the central number)

The order 3
normalized magic square
#1 (2 7)

2 7 6
9 5 1
4 3 8


Complete list of order 3 normalized magic cubes
There are only 4 cubes in normalized position
## .C .X .Y .Z
1: 1 15 17 23
2: 2 15 18 24
3: 4 17 18 26
4: 6 16 17 26
Actual listing of cubes
#1

01 15 26 | 23 07 12 | 18 20 04
17 19 06 | 03 14 25 | 22 09 11
24 08 10 | 16 21 05 | 02 13 27
#2

02 15 25 | 24 07 11 | 16 20 06
18 19 05 | 01 14 27 | 23 09 10
22 08 12 | 17 21 04 | 03 13 26
#3

04 17 21 | 26 03 13 | 12 22 08
18 19 05 | 01 14 27 | 23 09 10
20 06 16 | 15 25 02 | 07 11 24
#4

06 16 20 | 26 03 13 | 10 23 09
17 21 04 | 01 14 27 | 24 07 11
19 05 18 | 15 25 02 | 08 12 22


Complete list of order 3 normalized magic tesseracts
The 58 order 3 tesseracts here presented in normalized position
## No. .C .X .Y .Z .W XY YZ XZ s
01 38: 01 45 51 53 54 56 58 64: 3
02 46: 01 45 69 71 72 20 22 46: 3
03 54: 01 51 69 77 78 08 16 34: 3
04 34: 01 53 71 77 80 06 12 30: 3
05 01: 01 54 72 78 80 05 11 29: 1
## No. .C .X .Y .Z .W XY YZ XZ s
06 12: 02 43 51 52 54 56 60 65: 2
07 11: 02 43 69 70 72 20 24 47: 2
08 26: 02 45 49 52 54 56 59 66: 2
09 16: 02 45 67 70 72 20 23 48: 2
10 15: 02 49 69 76 78 08 18 35: 2
11 25: 02 51 67 76 78 08 17 36: 2
12 35: 02 52 70 78 81 06 11 29: 3
13 36: 02 52 72 76 81 05 12 29: 3
14 31: 02 52 72 78 79 05 11 28: 3
15 37: 02 54 70 76 81 05 11 30: 3
16 32: 02 54 70 78 79 05 10 29: 3
17 33: 02 54 72 76 79 04 11 29: 3
## No. .C .X .Y .Z .W XY YZ XZ s
18 44: 03 43 49 52 53 56 59 65: 3
19 50: 03 43 67 70 71 20 23 47: 3
20 56: 03 49 67 76 77 08 17 35: 3
21 04: 03 52 70 76 80 05 11 29: 1
22 03: 03 53 71 77 80 04 10 28: 3
## No. .C .X .Y .Z .W XY YZ XZ s
23 13: 04 45 47 48 54 58 59 70: 2
24 23: 04 45 65 66 72 22 23 52: 2
25 24: 04 47 71 74 80 06 18 33: 2
26 58: 04 48 72 74 81 05 16 31: 3
27 52: 04 48 72 75 80 05 17 32: 3
28 14: 04 53 65 74 80 06 15 36: 2
29 57: 04 54 66 74 81 05 13 34: 3
30 53: 04 54 66 75 80 05 14 35: 3
31 55: 04 54 72 74 75 02 13 31: 3
## No. .C .X .Y .Z .W XY YZ XZ s
32 51: 05 43 46 48 54 60 59 71: 3
33 43: 05 43 64 66 72 24 23 53: 3
34 45: 05 45 46 48 52 59 58 71: 3
35 39: 05 45 64 66 70 23 22 53: 3
36 19: 05 48 72 73 79 04 17 32: 2
37 21: 05 52 72 73 75 02 15 32: 2
38 20: 05 54 66 73 79 04 14 35: 2
39 06: 05 54 70 73 75 02 14 33: 2
## No. .C .X .Y .Z .W XY YZ XZ s
40 28: 06 43 46 47 52 59 60 72: 2
41 29: 06 43 64 65 70 23 24 54: 2
42 10: 06 52 70 73 74 02 14 32: 3
## No. .C .X .Y .Z .W XY YZ XZ s
43 30: 10 51 59 60 78 16 17 52: 2
44 27: 10 53 59 62 80 12 15 48: 2
45 49: 10 54 60 62 81 11 13 46: 3
46 47: 10 54 60 63 80 11 14 47: 3
47 48: 10 54 62 63 78 13 14 49: 3
## No. .C .X .Y .Z .W XY YZ XZ s
48 42: 11 49 58 60 78 18 17 53: 3
49 40: 11 51 58 60 76 17 16 53: 3
50 05: 11 52 61 63 78 15 14 50: 2
51 07: 11 54 60 61 79 10 14 47: 2
52 17: 11 54 61 63 76 14 13 50: 2
## No. .C .X .Y .Z .W XY YZ XZ s
53 22: 12 49 58 59 76 17 18 54: 2
54 09: 12 52 61 62 76 14 15 51: 3
## No. .C .X .Y .Z .W XY YZ XZ s
55 41: 13 53 56 62 74 15 12 51: 3
56 02: 13 54 57 62 75 14 10 49: 2
57 18: 13 54 57 63 74 14 11 50: 2
## No. .C .X .Y .Z .W XY YZ XZ s
58 08: 14 54 57 61 73 13 11 50: 3
Actual listing of tesseracts
#01

01 45 77 | 53 58 12 | 69 20 34
51 56 16 | 64 27 32 | 08 40 75
71 22 30 | 06 38 79 | 46 63 14

54 59 10 | 67 21 35 | 02 43 78
65 25 33 | 09 41 73 | 49 57 17
04 39 80 | 47 61 15 | 72 23 28

68 19 36 | 03 44 76 | 52 60 11
07 42 74 | 50 55 18 | 66 26 31
48 62 13 | 70 24 29 | 05 37 81
#02

01 45 77 | 71 22 30 | 51 56 16
69 20 34 | 46 63 14 | 08 40 75
53 58 12 | 06 38 79 | 64 27 32

72 23 28 | 49 57 17 | 02 43 78
47 61 15 | 09 41 73 | 67 21 35
04 39 80 | 65 25 33 | 54 59 10

50 55 18 | 03 44 76 | 70 24 29
07 42 74 | 68 19 36 | 48 62 13
66 26 31 | 52 60 11 | 05 37 81
#03

01 51 71 | 77 16 30 | 45 56 22
69 08 46 | 34 75 14 | 20 40 63
53 64 06 | 12 32 79 | 58 27 38

78 17 28 | 43 57 23 | 02 49 72
35 73 15 | 21 41 61 | 67 09 47
10 33 80 | 59 25 39 | 54 65 04

44 55 24 | 03 50 70 | 76 18 29
19 42 62 | 68 07 48 | 36 74 13
60 26 37 | 52 66 05 | 11 31 81
#04

01 53 69 | 77 12 34 | 45 58 20
71 06 46 | 30 79 14 | 22 38 63
51 64 08 | 16 32 75 | 56 27 40

80 15 28 | 39 61 23 | 04 47 72
33 73 17 | 25 41 57 | 65 09 49
10 35 78 | 59 21 43 | 54 67 02

42 55 26 | 07 50 66 | 74 18 31
19 44 60 | 68 03 52 | 36 76 11
62 24 37 | 48 70 05 | 13 29 81
#05

01 54 68 | 78 11 34 | 44 58 21
72 05 46 | 29 79 15 | 22 39 62
50 64 09 | 16 33 74 | 57 26 40

80 13 30 | 37 63 23 | 06 47 70
31 75 17 | 27 41 55 | 65 07 51
12 35 76 | 59 19 45 | 52 69 02

42 56 25 | 08 49 66 | 73 18 32
20 43 60 | 67 03 53 | 36 77 10
61 24 38 | 48 71 04 | 14 28 81
#06

02 43 78 | 52 60 11 | 69 20 34
51 56 16 | 65 25 33 | 07 42 74
70 24 29 | 06 38 79 | 47 61 15

54 59 10 | 68 19 36 | 01 45 77
64 27 32 | 09 41 73 | 50 55 18
05 37 81 | 46 63 14 | 72 23 28

67 21 35 | 03 44 76 | 53 58 12
08 40 75 | 49 57 17 | 66 26 31
48 62 13 | 71 22 30 | 04 39 80
#07

02 43 78 | 70 24 29 | 51 56 16
69 20 34 | 47 61 15 | 07 42 74
52 60 11 | 06 38 79 | 65 25 33

72 23 28 | 50 55 18 | 01 45 77
46 63 14 | 09 41 73 | 68 19 36
05 37 81 | 64 27 32 | 54 59 10

49 57 17 | 03 44 76 | 71 22 30
08 40 75 | 67 21 35 | 48 62 13
66 26 31 | 53 58 12 | 04 39 80
#08

02 45 76 | 52 59 12 | 69 19 35
49 56 18 | 66 25 32 | 08 42 73
72 22 29 | 05 39 79 | 46 62 15

54 58 11 | 68 21 34 | 01 44 78
65 27 31 | 07 41 75 | 51 55 17
04 38 81 | 48 61 14 | 71 24 28

67 20 36 | 03 43 77 | 53 60 10
09 40 74 | 50 57 16 | 64 26 33
47 63 13 | 70 23 30 | 06 37 80
#09

02 45 76 | 70 23 30 | 51 55 17
67 20 36 | 48 61 14 | 08 42 73
54 58 11 | 05 39 79 | 64 26 33

72 22 29 | 50 57 16 | 01 44 78
47 63 13 | 07 41 75 | 69 19 35
04 38 81 | 66 25 32 | 53 60 10

49 56 18 | 03 43 77 | 71 24 28
09 40 74 | 68 21 34 | 46 62 15
65 27 31 | 52 59 12 | 06 37 80
#10

02 49 72 | 76 18 29 | 45 56 22
69 08 46 | 35 73 15 | 19 42 62
52 66 05 | 12 32 79 | 59 25 39

78 17 28 | 44 55 24 | 01 51 71
34 75 14 | 21 41 61 | 68 07 48
11 31 81 | 58 27 38 | 54 65 04

43 57 23 | 03 50 70 | 77 16 30
20 40 63 | 67 09 47 | 36 74 13
60 26 37 | 53 64 06 | 10 33 80
#11

02 51 70 | 76 17 30 | 45 55 23
67 08 48 | 36 73 14 | 20 42 61
54 64 05 | 11 33 79 | 58 26 39

78 16 29 | 44 57 22 | 01 50 72
35 75 13 | 19 41 63 | 69 07 47
10 32 81 | 60 25 38 | 53 66 04

43 56 24 | 03 49 71 | 77 18 28
21 40 62 | 68 09 46 | 34 74 15
59 27 37 | 52 65 06 | 12 31 80
#12

02 52 69 | 78 11 34 | 43 60 20
70 06 47 | 29 79 15 | 24 38 61
51 65 07 | 16 33 74 | 56 25 42

81 14 28 | 37 63 23 | 05 46 72
32 73 18 | 27 41 55 | 64 09 50
10 36 77 | 59 19 45 | 54 68 01

40 57 26 | 08 49 66 | 75 17 31
21 44 58 | 67 03 53 | 35 76 12
62 22 39 | 48 71 04 | 13 30 80
#13

02 52 69 | 76 12 35 | 45 59 19
72 05 46 | 29 79 15 | 22 39 62
49 66 08 | 18 32 73 | 56 25 42

81 14 28 | 38 61 24 | 04 48 71
31 75 17 | 27 41 55 | 65 07 51
11 34 78 | 58 21 44 | 54 68 01

40 57 26 | 09 50 64 | 74 16 33
20 43 60 | 67 03 53 | 36 77 10
63 23 37 | 47 70 06 | 13 30 80
#14

02 52 69 | 78 11 34 | 43 60 20
72 05 46 | 28 81 14 | 23 37 63
49 66 08 | 17 31 75 | 57 26 40

79 15 29 | 38 61 24 | 06 47 70
32 73 18 | 27 41 55 | 64 09 50
12 35 76 | 58 21 44 | 53 67 03

42 56 25 | 07 51 65 | 74 16 33
19 45 59 | 68 01 54 | 36 77 10
62 22 39 | 48 71 04 | 13 30 80
#15

02 54 67 | 76 11 36 | 45 58 20
70 05 48 | 30 79 14 | 23 39 61
51 64 08 | 17 33 73 | 55 26 42

81 13 29 | 38 63 22 | 04 47 72
32 75 16 | 25 41 57 | 66 07 50
10 35 78 | 60 19 44 | 53 69 01

40 56 27 | 09 49 65 | 74 18 31
21 43 59 | 68 03 52 | 34 77 12
62 24 37 | 46 71 06 | 15 28 80
#16

02 54 67 | 78 10 35 | 43 59 21
70 05 48 | 29 81 13 | 24 37 62
51 64 08 | 16 32 75 | 56 27 40

79 14 30 | 38 63 22 | 06 46 71
33 73 17 | 25 41 57 | 65 09 49
11 36 76 | 60 19 44 | 52 68 03

42 55 26 | 07 50 66 | 74 18 31
20 45 58 | 69 01 53 | 34 77 12
61 23 39 | 47 72 04 | 15 28 80
#17

02 54 67 | 76 11 36 | 45 58 20
72 04 47 | 29 81 13 | 22 38 63
49 65 09 | 18 31 74 | 56 27 40

79 14 30 | 39 61 23 | 05 48 70
32 75 16 | 25 41 57 | 66 07 50
12 34 77 | 59 21 43 | 52 68 03

42 55 26 | 08 51 64 | 73 17 33
19 44 60 | 69 01 53 | 35 78 10
62 24 37 | 46 71 06 | 15 28 80
#18

03 43 77 | 52 59 12 | 68 21 34
49 56 18 | 65 27 31 | 09 40 74
71 24 28 | 06 37 80 | 46 62 15

53 60 10 | 69 19 35 | 01 44 78
66 25 32 | 07 41 75 | 50 57 16
04 38 81 | 47 63 13 | 72 22 29

67 20 36 | 02 45 76 | 54 58 11
08 42 73 | 51 55 17 | 64 26 33
48 61 14 | 70 23 30 | 05 39 79
#19

03 43 77 | 70 23 30 | 50 57 16
67 20 36 | 47 63 13 | 09 40 74
53 60 10 | 06 37 80 | 64 26 33

71 24 28 | 51 55 17 | 01 44 78
48 61 14 | 07 41 75 | 68 21 34
04 38 81 | 65 27 31 | 54 58 11

49 56 18 | 02 45 76 | 72 22 29
08 42 73 | 69 19 35 | 46 62 15
66 25 32 | 52 59 12 | 05 39 79
#20

03 49 71 | 76 17 30 | 44 57 22
67 08 48 | 35 75 13 | 21 40 62
53 66 04 | 12 31 80 | 58 26 39

77 18 28 | 45 55 23 | 01 50 72
36 73 14 | 19 41 63 | 68 09 46
10 32 81 | 59 27 37 | 54 64 05

43 56 24 | 02 51 70 | 78 16 29
20 42 61 | 69 07 47 | 34 74 15
60 25 38 | 52 65 06 | 11 33 79
#21

03 52 68 | 76 11 36 | 44 60 19
70 05 48 | 29 81 13 | 24 37 62
50 66 07 | 18 31 74 | 55 26 42

80 15 28 | 39 61 23 | 04 47 72
33 73 17 | 25 41 57 | 65 09 49
10 35 78 | 59 21 43 | 54 67 02

40 56 27 | 08 51 64 | 75 16 32
20 45 58 | 69 01 53 | 34 77 12
63 22 38 | 46 71 06 | 14 30 79
#22

03 53 67 | 77 10 36 | 43 60 20
71 04 48 | 28 81 14 | 24 38 61
49 66 08 | 18 32 73 | 56 25 42

80 13 30 | 37 63 23 | 06 47 70
31 75 17 | 27 41 55 | 65 07 51
12 35 76 | 59 19 45 | 52 69 02

40 57 26 | 09 50 64 | 74 16 33
21 44 58 | 68 01 54 | 34 78 11
62 22 39 | 46 72 05 | 15 29 79
#23

04 45 74 | 48 59 16 | 71 19 33
47 58 18 | 70 21 32 | 06 44 73
72 20 31 | 05 43 75 | 46 60 17

54 56 13 | 68 25 30 | 01 42 80
67 27 29 | 03 41 79 | 53 55 15
02 40 81 | 52 57 14 | 69 26 28

65 22 36 | 07 39 77 | 51 62 10
09 38 76 | 50 61 12 | 64 24 35
49 63 11 | 66 23 34 | 08 37 78
#24

04 45 74 | 66 23 34 | 53 55 15
65 22 36 | 52 57 14 | 06 44 73
54 56 13 | 05 43 75 | 64 24 35

72 20 31 | 50 61 12 | 01 42 80
49 63 11 | 03 41 79 | 71 19 33
02 40 81 | 70 21 32 | 51 62 10

47 58 18 | 07 39 77 | 69 26 28
09 38 76 | 68 25 30 | 46 60 17
67 27 29 | 48 59 16 | 08 37 78
#25

04 47 72 | 74 18 31 | 45 58 20
71 06 46 | 33 73 17 | 19 44 60
48 70 05 | 16 32 75 | 59 21 43

80 15 28 | 42 55 26 | 01 53 69
30 79 14 | 25 41 57 | 68 03 52
13 29 81 | 56 27 40 | 54 67 02

39 61 23 | 07 50 66 | 77 12 34
22 38 63 | 65 09 49 | 36 76 11
62 24 37 | 51 64 08 | 10 35 78
#26

04 48 71 | 74 16 33 | 45 59 19
72 05 46 | 31 75 17 | 20 43 60
47 70 06 | 18 32 73 | 58 21 44

81 14 28 | 40 57 26 | 02 52 69
29 79 15 | 27 41 55 | 67 03 53
13 30 80 | 56 25 42 | 54 68 01

38 61 24 | 09 50 64 | 76 12 35
22 39 62 | 65 07 51 | 36 77 10
63 23 37 | 49 66 08 | 11 34 78
#27

04 48 71 | 75 17 31 | 44 58 21
72 05 46 | 32 73 18 | 19 45 59
47 70 06 | 16 33 74 | 60 20 43

80 13 30 | 40 57 26 | 03 53 67
28 81 14 | 27 41 55 | 68 01 54
15 29 79 | 56 25 42 | 52 69 02

39 62 22 | 08 49 66 | 76 12 35
23 37 63 | 64 09 50 | 36 77 10
61 24 38 | 51 65 07 | 11 34 78
#28

04 53 66 | 74 15 34 | 45 55 23
65 06 52 | 36 73 14 | 22 44 57
54 64 05 | 13 35 75 | 56 24 43

80 12 31 | 42 61 20 | 01 50 72
33 79 11 | 19 41 63 | 71 03 49
10 32 81 | 62 21 40 | 51 70 02

39 58 26 | 07 47 69 | 77 18 28
25 38 60 | 68 09 46 | 30 76 17
59 27 37 | 48 67 08 | 16 29 78
#29

04 54 65 | 74 13 36 | 45 56 22
66 05 52 | 34 75 14 | 23 43 57
53 64 06 | 15 35 73 | 55 24 44

81 11 31 | 40 63 20 | 02 49 72
32 79 12 | 21 41 61 | 70 03 50
10 33 80 | 62 19 42 | 51 71 01

38 58 27 | 09 47 67 | 76 18 29
25 39 59 | 68 07 48 | 30 77 16
60 26 37 | 46 69 08 | 17 28 78
#30

04 54 65 | 75 14 34 | 44 55 24
66 05 52 | 35 73 15 | 22 45 56
53 64 06 | 13 36 74 | 57 23 43

80 10 33 | 40 63 20 | 03 50 70
31 81 11 | 21 41 61 | 71 01 51
12 32 79 | 62 19 42 | 49 72 02

39 59 25 | 08 46 69 | 76 18 29
26 37 60 | 67 09 47 | 30 77 16
58 27 38 | 48 68 07 | 17 28 78
#31

04 54 65 | 74 13 36 | 45 56 22
72 02 49 | 31 81 11 | 20 40 63
47 67 09 | 18 29 76 | 58 27 38

75 14 34 | 43 57 23 | 05 52 66
32 79 12 | 21 41 61 | 70 03 50
16 30 77 | 59 25 39 | 48 68 07

44 55 24 | 06 53 64 | 73 15 35
19 42 62 | 71 01 51 | 33 80 10
60 26 37 | 46 69 08 | 17 28 78
#32

05 43 75 | 48 59 16 | 70 21 32
46 60 17 | 71 19 33 | 06 44 73
72 20 31 | 04 45 74 | 47 58 18

54 56 13 | 67 27 29 | 02 40 81
68 25 30 | 03 41 79 | 52 57 14
01 42 80 | 53 55 15 | 69 26 28

64 24 35 | 08 37 78 | 51 62 10
09 38 76 | 49 63 11 | 65 22 36
50 61 12 | 66 23 34 | 07 39 77
#33

05 43 75 | 66 23 34 | 52 57 14
64 24 35 | 53 55 15 | 06 44 73
54 56 13 | 04 45 74 | 65 22 36

72 20 31 | 49 63 11 | 02 40 81
50 61 12 | 03 41 79 | 70 21 32
01 42 80 | 71 19 33 | 51 62 10

46 60 17 | 08 37 78 | 69 26 28
09 38 76 | 67 27 29 | 47 58 18
68 25 30 | 48 59 16 | 07 39 77
#34

05 45 73 | 48 58 17 | 70 20 33
46 59 18 | 71 21 31 | 06 43 74
72 19 32 | 04 44 75 | 47 60 16

52 56 15 | 68 27 28 | 03 40 80
69 25 29 | 01 41 81 | 53 57 13
02 42 79 | 54 55 14 | 67 26 30

66 22 35 | 07 38 78 | 50 63 10
08 39 76 | 51 61 11 | 64 23 36
49 62 12 | 65 24 34 | 09 37 77
#35

05 45 73 | 66 22 35 | 52 56 15
64 23 36 | 53 57 13 | 06 43 74
54 55 14 | 04 44 75 | 65 24 34

70 20 33 | 50 63 10 | 03 40 80
51 61 11 | 01 41 81 | 71 21 31
02 42 79 | 72 19 32 | 49 62 12

48 58 17 | 07 38 78 | 68 27 28
08 39 76 | 69 25 29 | 46 59 18
67 26 30 | 47 60 16 | 09 37 77
#36

05 48 70 | 73 17 33 | 45 58 20
72 04 47 | 32 75 16 | 19 44 60
46 71 06 | 18 31 74 | 59 21 43

79 14 30 | 42 55 26 | 02 54 67
29 81 13 | 25 41 57 | 69 01 53
15 28 80 | 56 27 40 | 52 68 03

39 61 23 | 08 51 64 | 76 11 36
22 38 63 | 66 07 50 | 35 78 10
62 24 37 | 49 65 09 | 12 34 77
#37

05 52 66 | 73 15 35 | 45 56 22
72 02 49 | 32 79 12 | 19 42 62
46 69 08 | 18 29 76 | 59 25 39

75 14 34 | 44 55 24 | 04 54 65
31 81 11 | 21 41 61 | 71 01 51
17 28 78 | 58 27 38 | 48 68 07

43 57 23 | 06 53 64 | 74 13 36
20 40 63 | 70 03 50 | 33 80 10
60 26 37 | 47 67 09 | 16 30 77
#38

05 54 64 | 73 14 36 | 45 55 23
66 04 53 | 35 75 13 | 22 44 57
52 65 06 | 15 34 74 | 56 24 43

79 11 33 | 42 61 20 | 02 51 70
32 81 10 | 19 41 63 | 72 01 50
12 31 80 | 62 21 40 | 49 71 03

39 58 26 | 08 48 67 | 76 17 30
25 38 60 | 69 07 47 | 29 78 16
59 27 37 | 46 68 09 | 18 28 77
#39

05 54 64 | 73 14 36 | 45 55 23
70 02 51 | 33 79 11 | 20 42 61
48 67 08 | 17 30 76 | 58 26 39

75 13 35 | 44 57 22 | 04 53 66
32 81 10 | 19 41 63 | 72 01 50
16 29 78 | 60 25 38 | 47 69 07

43 56 24 | 06 52 65 | 74 15 34
21 40 62 | 71 03 49 | 31 80 12
59 27 37 | 46 68 09 | 18 28 77
#40

06 43 74 | 47 60 16 | 70 20 33
46 59 18 | 72 19 32 | 05 45 73
71 21 31 | 04 44 75 | 48 58 17

52 56 15 | 69 25 29 | 02 42 79
68 27 28 | 01 41 81 | 54 55 14
03 40 80 | 53 57 13 | 67 26 30

65 24 34 | 07 38 78 | 51 61 11
09 37 77 | 50 63 10 | 64 23 36
49 62 12 | 66 22 35 | 08 39 76
#41

06 43 74 | 65 24 34 | 52 56 15
64 23 36 | 54 55 14 | 05 45 73
53 57 13 | 04 44 75 | 66 22 35

70 20 33 | 51 61 11 | 02 42 79
50 63 10 | 01 41 81 | 72 19 32
03 40 80 | 71 21 31 | 49 62 12

47 60 16 | 07 38 78 | 69 25 29
09 37 77 | 68 27 28 | 46 59 18
67 26 30 | 48 58 17 | 08 39 76
#42

06 52 65 | 73 14 36 | 44 57 22
70 02 51 | 32 81 10 | 21 40 62
47 69 07 | 18 28 77 | 58 26 39

74 15 34 | 45 55 23 | 04 53 66
33 79 11 | 19 41 63 | 71 03 49
16 29 78 | 59 27 37 | 48 67 08

43 56 24 | 05 54 64 | 75 13 35
20 42 61 | 72 01 50 | 31 80 12
60 25 38 | 46 68 09 | 17 30 76
#43

10 51 62 | 60 17 46 | 53 55 15
59 16 48 | 52 57 14 | 12 50 61
54 56 13 | 11 49 63 | 58 18 47

78 08 37 | 44 73 06 | 01 42 80
43 75 05 | 03 41 79 | 77 07 39
02 40 81 | 76 09 38 | 45 74 04

35 64 24 | 19 33 71 | 69 26 28
21 32 70 | 68 25 30 | 34 66 23
67 27 29 | 36 65 22 | 20 31 72
#44

10 53 60 | 62 15 46 | 51 55 17
59 12 52 | 48 61 14 | 16 50 57
54 58 11 | 13 47 63 | 56 18 49

80 06 37 | 42 73 08 | 01 44 78
39 79 05 | 07 41 75 | 77 03 43
04 38 81 | 74 09 40 | 45 76 02

33 64 26 | 19 35 69 | 71 24 28
25 32 66 | 68 21 34 | 30 70 23
65 27 31 | 36 67 20 | 22 29 72
#45

10 54 59 | 62 13 48 | 51 56 16
60 11 52 | 46 63 14 | 17 49 57
53 58 12 | 15 47 61 | 55 18 50

81 05 37 | 40 75 08 | 02 43 78
38 79 06 | 09 41 73 | 76 03 44
04 39 80 | 74 07 42 | 45 77 01

32 64 27 | 21 35 67 | 70 24 29
25 33 65 | 68 19 36 | 30 71 22
66 26 31 | 34 69 20 | 23 28 72
#46

10 54 59 | 63 14 46 | 50 55 18
60 11 52 | 47 61 15 | 16 51 56
53 58 12 | 13 48 62 | 57 17 49

80 04 39 | 40 75 08 | 03 44 76
37 81 05 | 09 41 73 | 77 01 45
06 38 79 | 74 07 42 | 43 78 02

33 65 25 | 20 34 69 | 70 24 29
26 31 66 | 67 21 35 | 30 71 22
64 27 32 | 36 68 19 | 23 28 72
#47

10 54 59 | 63 14 46 | 50 55 18
62 13 48 | 49 57 17 | 12 53 58
51 56 16 | 11 52 60 | 61 15 47

78 02 43 | 38 79 06 | 07 42 74
37 81 05 | 09 41 73 | 77 01 45
08 40 75 | 76 03 44 | 39 80 04

35 67 21 | 22 30 71 | 66 26 31
24 29 70 | 65 25 33 | 34 69 20
64 27 32 | 36 68 19 | 23 28 72
#48

11 49 63 | 60 17 46 | 52 57 14
58 18 47 | 53 55 15 | 12 50 61
54 56 13 | 10 51 62 | 59 16 48

78 08 37 | 43 75 05 | 02 40 81
44 73 06 | 03 41 79 | 76 09 38
01 42 80 | 77 07 39 | 45 74 04

34 66 23 | 20 31 72 | 69 26 28
21 32 70 | 67 27 29 | 35 64 24
68 25 30 | 36 65 22 | 19 33 71
#49

11 51 61 | 60 16 47 | 52 56 15
58 17 48 | 53 57 13 | 12 49 62
54 55 14 | 10 50 63 | 59 18 46

76 08 39 | 44 75 04 | 03 40 80
45 73 05 | 01 41 81 | 77 09 37
02 42 79 | 78 07 38 | 43 74 06

36 64 23 | 19 32 72 | 68 27 28
20 33 70 | 69 25 29 | 34 65 24
67 26 30 | 35 66 22 | 21 31 71
#50

11 52 60 | 63 14 46 | 49 57 17
61 15 47 | 50 55 18 | 12 53 58
51 56 16 | 10 54 59 | 62 13 48

78 02 43 | 37 81 05 | 08 40 75
38 79 06 | 09 41 73 | 76 03 44
07 42 74 | 77 01 45 | 39 80 04

34 69 20 | 23 28 72 | 66 26 31
24 29 70 | 64 27 32 | 35 67 21
65 25 33 | 36 68 19 | 22 30 71
#51

11 54 58 | 61 14 48 | 51 55 17
60 10 53 | 47 63 13 | 16 50 57
52 59 12 | 15 46 62 | 56 18 49

79 05 39 | 42 73 08 | 02 45 76
38 81 04 | 07 41 75 | 78 01 44
06 37 80 | 74 09 40 | 43 77 03

33 64 26 | 20 36 67 | 70 23 30
25 32 66 | 69 19 35 | 29 72 22
65 27 31 | 34 68 21 | 24 28 71
#52

11 54 58 | 63 13 47 | 49 56 18
61 14 48 | 50 57 16 | 12 52 59
51 55 17 | 10 53 60 | 62 15 46

76 02 45 | 38 81 04 | 09 40 74
39 79 05 | 07 41 75 | 77 03 43
08 42 73 | 78 01 44 | 37 80 06

36 67 20 | 22 29 72 | 65 27 31
23 30 70 | 66 25 32 | 34 68 21
64 26 33 | 35 69 19 | 24 28 71
#53

12 49 62 | 59 18 46 | 52 56 15
58 17 48 | 54 55 14 | 11 51 61
53 57 13 | 10 50 63 | 60 16 47

76 08 39 | 45 73 05 | 02 42 79
44 75 04 | 01 41 81 | 78 07 38
03 40 80 | 77 09 37 | 43 74 06

35 66 22 | 19 32 72 | 69 25 29
21 31 71 | 68 27 28 | 34 65 24
67 26 30 | 36 64 23 | 20 33 70
#54

12 52 59 | 62 15 46 | 49 56 18
61 14 48 | 51 55 17 | 11 54 58
50 57 16 | 10 53 60 | 63 13 47

76 02 45 | 39 79 05 | 08 42 73
38 81 04 | 07 41 75 | 78 01 44
09 40 74 | 77 03 43 | 37 80 06

35 69 19 | 22 29 72 | 66 25 32
24 28 71 | 65 27 31 | 34 68 21
64 26 33 | 36 67 20 | 23 30 70
#55

13 53 57 | 62 12 49 | 48 58 17
56 15 52 | 51 61 11 | 16 47 60
54 55 14 | 10 50 63 | 59 18 46

74 06 43 | 42 79 02 | 07 38 78
45 73 05 | 01 41 81 | 77 09 37
04 44 75 | 80 03 40 | 39 76 08

36 64 23 | 19 32 72 | 68 27 28
22 35 66 | 71 21 31 | 30 67 26
65 24 34 | 33 70 20 | 25 29 69
#56

13 54 56 | 62 10 51 | 48 59 16
57 14 52 | 49 63 11 | 17 46 60
53 55 15 | 12 50 61 | 58 18 47

75 05 43 | 40 81 02 | 08 37 78
44 73 06 | 03 41 79 | 76 09 38
04 45 74 | 80 01 42 | 39 77 07

35 64 24 | 21 32 70 | 67 27 29
22 36 65 | 71 19 33 | 30 68 25
66 23 34 | 31 72 20 | 26 28 69
#57

13 54 56 | 63 11 49 | 47 58 18
57 14 52 | 50 61 12 | 16 48 59
53 55 15 | 10 51 62 | 60 17 46

74 04 45 | 40 81 02 | 09 38 76
43 75 05 | 03 41 79 | 77 07 39
06 44 73 | 80 01 42 | 37 78 08

36 65 22 | 20 31 72 | 67 27 29
23 34 66 | 70 21 32 | 30 68 25
64 24 35 | 33 71 19 | 26 28 69
#58

14 54 55 | 61 11 51 | 48 58 17
57 13 53 | 50 63 10 | 16 47 60
52 56 15 | 12 49 62 | 59 18 46

73 05 45 | 42 79 02 | 08 39 76
44 75 04 | 01 41 81 | 78 07 38
06 43 74 | 80 03 40 | 37 77 09

36 64 23 | 20 33 70 | 67 26 30
22 35 66 | 72 19 32 | 29 69 25
65 24 34 | 31 71 21 | 27 28 68