

A090572


Number of configurations of the 3dimensional 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
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OFFSET

0,2


COMMENTS

This puzzle is a 3dimensional generalization of the socalled "Sam Loyd" 15puzzle. 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 & 157158, 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


LINKS

Table of n, a(n) for n=0..19.
Jaap's Puzzle Page: Varikon Box 2 X 2 X 2.
Werner Lurker, Dreidimensionales puzzleaehnliches Spielzeug. German Patent 2152360, filed Oct 21 1971
Hugo Pfoertner, List of the most distant configurations for the 2X2X2 sliding cube puzzle.
Ad van der Schagt, The History of Sliding Block puzzles before Peter's Black Hole.


EXAMPLE

a(19) = 18 because 18 of the total 20160 possible configurations cannot be reached in fewer than 19 singlecube 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
Adjacent sequences: A090569 A090570 A090571 * A090573 A090574 A090575


KEYWORD

fini,full,nonn


AUTHOR

Hugo Pfoertner, Jan 14 2004


STATUS

approved



