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A090572
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.
8
1, 3, 6, 12, 24, 48, 93, 180, 351, 675, 1191, 1963, 3015, 3772, 3732, 2837, 1589, 572, 78, 18
OFFSET
0,2
COMMENTS
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).
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
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
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
EXAMPLE
a(19) = 18 because 18 of the total 20160 possible configurations cannot be reached in fewer than 19 single-cube moves.
PROG
(Python) # uses alst(), swap() in A089473, moves3d() in A090573
moves = lambda p, shape: moves3d(p, shape)
print(alst("-1234567", (2, 2, 2))) # Michael S. Branicky, Dec 31 2020
CROSSREFS
Cf. A090573 - A090578 configurations of 3 X 3 X 3 sliding cube puzzles, A089484 4 X 4 (15-)puzzle.
Sequence in context: A002910 A001668 A080616 * A163876 A033893 A006851
KEYWORD
fini,full,nonn
AUTHOR
Hugo Pfoertner, Jan 14 2004
STATUS
approved