Sources page biographical material

5.E.2.a. PANTACTIC SQUARES
Haubrich's 1995-1996 surveys, op. cit. in 5.H.4, include this.
B. Astle. Pantactic squares. MG 49 (No. 368) (May 1965) 144 152. This is a two dimensional version of the memory wheel. Take a 5 x 5 array of cells marked 0 or 1 (or Black or White). There are 16 ways to take a 2 x 2 subarray from the 5 x 5 array. If these give all 16 2 x 2 binary patterns, the array is called pantactic. The author shows a number of properties and some types of such squares.

C. J. Bouwkamp, P. Janssen & A. Koene. Note on pantactic squares. MG 54 (No. 390) (Dec 1970) 348 351. They find 800 such squares, forming 50 classes of 16 forms.

[Surprisingly, neither paper considers a 4 x 4 array viewed toroidally, which is the natural generalization of the memory wheel. Precisely two of the fifty classes, namely nos. 25 & 41, give such a solution and these are the same pattern on the torus. One can also look at the 4 x 4 subarrays of a 131 x 131 or a 128 x 128 array, etc., as well as 3 and higher dimensional arrays. I submitted the question of the existence and numbers of these as a problem for CM, but it was considered too technical.]

Ivan Moscovich. US Patent 3,677,549 -- Board Game Apparatus. Applied: 14 Jun 1971; patented: 18 Jul 1972. Front page, 1p diagrams, 2pp text. Reproduced in Haubrich, About ..., 1996, op. cit. in 5.H.4. 2pp + 2pp diagrams. This uses the 16 2 x 2 binary patterns as game pieces. He allows the pieces to be rotated, scoring different values according to the orientation. No mention of reversing pieces or of the use of the pieces as a puzzle.

John Humphries. Review of Q-Bits. G&P 54 (Nov 1976) 28. This is Moscovich's game idea, produced by Orda. Though he mentions changing the rules to having non-matching, there is no mention of two-sidedness.

Pieter van Delft & Jack Botermans. Creative Puzzles of the World. (As: Puzzels uit de hele wereld; Spectrum Hobby, 1978); Harry N. Abrams, NY, 1978. The colormatch square, p. 165. See Haubrich,1994, for description.

Jacques Haubrich. Pantactic patterns and puzzles. CFF 34 (Oct 1994) 19-21. Notes the toroidal property just mentioned. Says Bouwkamp had the idea of making the 16 basic squares in coloured card and using them as a MacMahon-type puzzle, with the pieces double-sided and such that when one side had MacMahon matching, the other side had non-matching. There are two different bijections between matching patterns and non-matching patterns, so there are also 800 solutions in 50 classes for the non-matching problem. Bouwkamp's puzzle appeared in van Delft & Botermans, though they did not know about and hence did not mention the double-sidedness. [In an email of 22 Aug 2000, Haubrich says he believes Bouwkamp did tell van Delft and Botermans about this, but somehow it did not get into their book.] The idea was copied by two manufacturers (Set Squares by Peter Pan Playthings and Regev Magnetics) who did not understand Bouwkamp's ideas -- i.e. they permitted pieces to rotate. Describes Verbakel's puzzle of 5.H.2.

Jacques Haubrich. Letter: Pantactic Puzzles = Q-Bits. CFF 37 (Jun 1995) 4. Says that Ivan Moscovich has responded that he invented the version called "Q-Bits" in 1960-1964, having the same tiles as Bouwkamp's (but only one-sided [clarified by Haubrich in above mentioned email]). His US Patent 3,677,549 (see above) is for a game version of he idea. The version produced by Orda Ltd. was reviewed in G&P 54 (Nov 1976) (above). So it seems clear that Moscovich had the idea of the pieces before Bouwkamp's version was published, but Moscovich's application was to use them in a game where the orientations could be varied.