The Magic Encyclopedia ™ DataBase

Pfeffermann's bimagic square puzzles
{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, to mimic that the puzzels and solutions listed in two seperate files, the reader might be tempted to solve the puzzles prior to downloading the solutions, 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 square puzzles
The here presented puzzles have the regular number range except for the second which consist of
numbers in arithmetic progression : 1, 4, 7, 10, ., 190.
Solutions of these puzzles can be found in: Pfeffermann Bimagic Squares
Puzzle #1 (order 8)

56 ?? 08 ?? 18 ?? 09 ??
?? 20 ?? 48 ?? 29 ?? 10
26 ?? 13 ?? 64 ?? 04 ??
?? 05 ?? 30 ?? 12 ?? 60
15 ?? 63 ?? 41 ?? 50 ??
?? 55 ?? 11 ?? 58 ?? 45
61 ?? 42 ?? 27 ?? 39 ??
?? 62 ?? 37 ?? 51 ?? 03
Puzzle #2 (order 8)

??? 121 004 ??? ??? 151 082 ???
034 ??? ??? 103 052 ??? ??? 169
187 ??? ??? 070 109 ??? ??? 040
??? 088 157 ??? ??? 022 139 ???
??? 010 127 ??? ??? 076 145 ???
097 ??? ??? 028 175 ??? ??? 058
064 ??? ??? 181 046 ??? ??? 115
??? 163 094 ??? ??? 133 016 ???
Puzzle #3 (order 8)

?? 61 ?? 60 23 38 18 35
42 27 47 30 49 ?? 56 ??
39 22 34 19 64 ?? 57 ??
?? 52 ?? 53 26 43 31 46
29 48 28 41 ?? 55 ?? 50
59 ?? 62 ?? 36 17 37 24
54 ?? 51 ?? 45 32 44 25
20 33 21 40 ?? 58 ?? 63
Puzzle #4 (order 8)

?? 42 ?? 53 52 ?? 47 ??
56 ?? 43 ?? ?? 46 ?? 49
?? 40 ?? 59 62 ?? 33 ??
58 ?? 37 ?? ?? 36 ?? 63
?? 51 ?? 48 41 ?? 54 ??
45 ?? 50 ?? ?? 55 ?? 44
?? 61 ?? 34 39 ?? 60 ??
35 ?? 64 ?? ?? 57 ?? 38
Puzzle #1 (order 9)

?? 03 81 42 ?? 47 17 59 ??
37 ?? 15 71 ?? 57 32 ?? 07
33 38 ?? 55 ?? 77 ?? 13 21
68 73 43 ?? ?? ?? 63 51 29
?? ?? ?? ?? 41 ?? ?? ?? ??
53 31 19 ?? ?? ?? 39 09 14
61 69 ?? 05 ?? 27 ?? 44 49
75 ?? 50 25 ?? 11 67 ?? 45
?? 23 65 35 ?? 40 01 79 ??
Puzzle #2 (order 9)

?? 13 57 ?? 31 ?? 20 77 ??
08 71 ?? 78 19 39 ?? 52 15
76 ?? 21 53 56 14 33 ?? 72
?? 36 04 40 ?? 27 47 11 ??
12 58 46 ?? ?? ?? 81 42 25
?? 26 80 10 ?? 60 06 64 ??
28 ?? 67 23 44 74 16 ?? 51
22 75 ?? 61 18 49 ?? 29 02
?? 50 17 ?? 69 ?? 43 24 ??
Puzzle #3 (order 9)

?? 35 05 57 ?? 40 10 76 ??
42 25 55 ?? 77 ?? 72 34 06
12 78 ?? 04 36 70 ?? 26 56
28 ?? 69 45 61 22 74 ?? 17
?? 51 16 68 ?? 29 24 63 ??
23 ?? 44 18 49 75 30 ?? 67
53 14 ?? 31 66 09 ?? 39 19
07 64 33 ?? 38 ?? 52 15 81
?? 37 21 79 ?? 54 08 65 ??