%I #22 Jan 01 2021 03:21:33

%S 1,3,6,12,24,48,93,180,351,675,1191,1963,3015,3772,3732,2837,1589,572,

%T 78,18

%N Number of configurations of the 3-dimensional 2 X 2 X 2 sliding cube puzzle that require a minimum of n moves to be reached.

%C This puzzle is a 3-dimensional generalization of the so-called "Sam Loyd" 15-puzzle. A description is given in the now expired German patent 2152360 (see link).

%C Same as the number of configurations for the Varikon Box (see Jaapsch link) and others 2 X 2 X 2 sliding cube puzzles. The basic idea for this sliding block puzzle seems to be very old, long before Mr. Lurker's patent (see van der Schagt's article for details): Charles I. Rice patented a 2 X 2 X 2 version with peepholes in the faces in 1889. US Patent 416,344 _ Puzzle. Applied 9 Sep 1889; patented 3 Dec 1889. 2pp + 1p diagrams. Described in L. Edward Hordern. Sliding Piece Puzzles. OUP, 1986, pp. 27 & 157-158, G2. - Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 21 2006

%C In the late 1970's the Hungarians produced 2 X 2 X 2 versions within transparent cubes: Naef's beautiful 2 X 2 X 2 one, Vadasz 2 X 2 X 2 Cube, ... First one 2 X 2 X 2 sold commercially was designed by Piet Hein around 1972 and named Bloxbox. Martin Gardner described it for first time (Scientific American Feb, 1973, page 109). - Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 21 2006

%C The puzzle was made and sold in Japan under the name Qrazy Qube by Kawada in 1981. Another version was made and sold in Japan by Maruhaya (2 X 2 X 2) in 1981. The Varikon Box'S 2 X 2 X 2 puzzle of 1982 was invented by Csaba Postasy, Gabor Eszes and Miklos Zagoni. German patent, DE 3,027,556, published on Jun 19 1981. - Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 21 2006

%H Jaap's Puzzle Page: <a href="http://www.jaapsch.net/puzzles/varikon2.htm">Varikon Box 2 X 2 X 2</a>.

%H Werner Lurker, <a href="http://v3.espacenet.com/origdoc?IDX=DE2152360">Dreidimensionales puzzleaehnliches Spielzeug</a>. German Patent 2152360, filed Oct 21 1971

%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a090572.txt">List of the most distant configurations for the 2X2X2 sliding cube puzzle.</a>

%H Ad van der Schagt, <a href="http://www.twistypuzzles.com/articles/puzzle-petersblackhole/puzzle-petersblackhole.pdf">The History of Sliding Block puzzles before Peter's Black Hole</a>.

%e a(19) = 18 because 18 of the total 20160 possible configurations cannot be reached in fewer than 19 single-cube moves.

%o (Python) # uses alst(), swap() in A089473, moves3d() in A090573

%o moves = lambda p, shape: moves3d(p, shape)

%o print(alst("-1234567", (2, 2, 2))) # _Michael S. Branicky_, Dec 31 2020

%Y Cf. A090573 - A090578 configurations of 3 X 3 X 3 sliding cube puzzles, A089484 4 X 4 (15-)puzzle.

%K fini,full,nonn

%O 0,2

%A _Hugo Pfoertner_, Jan 14 2004