The Magic Encyclopedia ™ DataBase

Pfeffermann's bimagic squares
{note: historical article}
(by Christian Boyer, november 3rd, 2001)

(Editors Note: <Christian Boyer> sent to me (Aale de Winkel) the below listed squares of Pfeffermann who published them as puzzles before their solutions where given, the notes are from Christian, the table is reformatted by me)

The first bimagic square in the world has been built by G. Pfeffermann in France in 1890.
This 8x8 square was published in a french magazine "Les Tablettes du Chercheur" january 15, 1891, with only the half of the numbers. It was a problem for the readers : find the missing numbers ! The solution, and so the full first bimagic square, was published in the next issue of "Les Tablettes du Chercheur", february 1st 1891.
After that, G. Pfeffermann has published other bimagic squares in "Les Tablettes du Chercheur".
(note: the reader who has access to these is urged to sent them to me (Aale de Winkel) to be added)

Pfeffermann's bimagic squares
The here presented squares have the regular number range except for the second which consist of
numbers in arithmetic progression : 1, 4, 7, 10, ., 190.
These squares where solutions to puzzles Pfeffermann can be found in: Pfeffermann Bimagic Square Puzzels

Puzzle #1 (order 8)
(february 1st, 1891)

56 34 08 57 18 47 09 31
33 20 54 48 07 29 59 10
26 43 13 23 64 38 04 49
19 05 35 30 53 12 46 60
15 25 63 02 41 24 50 40
06 55 17 11 36 58 32 45
61 16 42 52 27 01 39 22
44 62 28 37 14 51 21 03 Puzzle #2 (order 8)
(march 15, 1891)

118 121 004 043 184 151 082 061
034 013 136 103 052 091 166 169
187 148 073 070 109 130 007 040
055 088 157 178 025 022 139 100
037 010 127 112 067 076 145 190
097 142 019 028 175 160 085 058
064 079 154 181 046 001 124 115
172 163 094 049 106 133 016 031 Puzzle #3 (order 8)
(april 15, 1891)

16 61 09 60 23 38 18 35
42 27 47 30 49 04 56 05
39 22 34 19 64 13 57 12
01 52 08 53 26 43 31 46
29 48 28 41 06 55 03 50
59 10 62 15 36 17 37 24
54 07 51 02 45 32 44 25
20 33 21 40 11 58 14 63 Puzzle #4 (order 8)
(july 15, 1891)

06 42 25 53 52 32 47 03
56 28 43 07 02 46 29 49
12 40 23 59 62 18 33 13
58 22 37 09 16 36 19 63
31 51 04 48 41 05 54 26
45 01 50 30 27 55 08 44
17 61 14 34 39 11 60 24
35 15 64 20 21 57 10 38
Puzzle #1 (order 9)
(august 1st, 1891)

22 03 81 42 34 47 17 59 64
37 54 15 71 76 57 32 20 07
33 38 08 55 72 77 52 13 21
68 73 43 12 26 04 63 51 29
02 16 58 46 41 36 24 66 80
53 31 19 78 56 70 39 09 14
61 69 30 05 10 27 74 44 49
75 62 50 25 06 11 67 28 45
18 23 65 35 48 40 01 79 60 Puzzle #2 (order 9)
(december 15, 1891)

54 13 57 09 31 70 20 77 38
08 71 32 78 19 39 55 52 15
76 37 21 53 56 14 33 07 72
66 36 04 40 79 27 47 11 59
12 58 46 65 05 35 81 42 25
41 26 80 10 48 60 06 64 34
28 03 67 23 44 74 16 63 51
22 75 45 61 18 49 68 29 02
62 50 17 30 69 01 43 24 73
Puzzle #3 (order 9)
(january 1st, 1892)

71 35 05 57 27 40 10 76 48
42 25 55 47 77 11 72 34 06
12 78 46 04 36 70 41 26 56
28 03 69 45 61 22 74 50 17
73 51 16 68 02 29 24 63 43
23 62 44 18 49 75 30 01 67
53 14 80 31 66 09 58 39 19
07 64 33 20 38 59 52 15 81
60 37 21 79 13 54 08 65 32

Pfeffermann's bimagic squares
The here presented squares have the regular number range except for the second which consist of numbers in arithmetic progression : 1, 4, 7, 10, ., 190. These squares where solutions to puzzles Pfeffermann can be found in: Pfeffermann Bimagic Square Puzzels
Puzzle #1 (order 8) (february 1st, 1891) 56 34 08 57 18 47 09 31 33 20 54 48 07 29 59 10 26 43 13 23 64 38 04 49 19 05 35 30 53 12 46 60 15 25 63 02 41 24 50 40 06 55 17 11 36 58 32 45 61 16 42 52 27 01 39 22 44 62 28 37 14 51 21 03	Puzzle #2 (order 8) (march 15, 1891) 118 121 004 043 184 151 082 061 034 013 136 103 052 091 166 169 187 148 073 070 109 130 007 040 055 088 157 178 025 022 139 100 037 010 127 112 067 076 145 190 097 142 019 028 175 160 085 058 064 079 154 181 046 001 124 115 172 163 094 049 106 133 016 031	Puzzle #3 (order 8) (april 15, 1891) 16 61 09 60 23 38 18 35 42 27 47 30 49 04 56 05 39 22 34 19 64 13 57 12 01 52 08 53 26 43 31 46 29 48 28 41 06 55 03 50 59 10 62 15 36 17 37 24 54 07 51 02 45 32 44 25 20 33 21 40 11 58 14 63	Puzzle #4 (order 8) (july 15, 1891) 06 42 25 53 52 32 47 03 56 28 43 07 02 46 29 49 12 40 23 59 62 18 33 13 58 22 37 09 16 36 19 63 31 51 04 48 41 05 54 26 45 01 50 30 27 55 08 44 17 61 14 34 39 11 60 24 35 15 64 20 21 57 10 38
Puzzle #1 (order 9) (august 1st, 1891) 22 03 81 42 34 47 17 59 64 37 54 15 71 76 57 32 20 07 33 38 08 55 72 77 52 13 21 68 73 43 12 26 04 63 51 29 02 16 58 46 41 36 24 66 80 53 31 19 78 56 70 39 09 14 61 69 30 05 10 27 74 44 49 75 62 50 25 06 11 67 28 45 18 23 65 35 48 40 01 79 60	Puzzle #2 (order 9) (december 15, 1891) 54 13 57 09 31 70 20 77 38 08 71 32 78 19 39 55 52 15 76 37 21 53 56 14 33 07 72 66 36 04 40 79 27 47 11 59 12 58 46 65 05 35 81 42 25 41 26 80 10 48 60 06 64 34 28 03 67 23 44 74 16 63 51 22 75 45 61 18 49 68 29 02 62 50 17 30 69 01 43 24 73	Puzzle #3 (order 9) (january 1st, 1892) 71 35 05 57 27 40 10 76 48 42 25 55 47 77 11 72 34 06 12 78 46 04 36 70 41 26 56 28 03 69 45 61 22 74 50 17 73 51 16 68 02 29 24 63 43 23 62 44 18 49 75 30 01 67 53 14 80 31 66 09 58 39 19 07 64 33 20 38 59 52 15 81 60 37 21 79 13 54 08 65 32