A090573 -id:A090573 - cp's OEIS frontend

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.

1, 3, 6, 12, 24, 48, 93, 180, 351, 675, 1191, 1963, 3015, 3772, 3732, 2837, 1589, 572, 78, 18

Offset: 0

Hugo Pfoertner, Jan 14 2004

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

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

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.

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

# 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

A090576 Number of configurations of the 3-dimensional 3 X 3 X 3 sliding cube puzzle that require a minimum of n moves to be reached, starting with the empty space at mid-side of one of the 12 edges of the combination cube.

Original entry on oeis.org

1, 4, 12, 40, 128, 412, 1251, 4026, 12362, 39624, 120012, 379132, 1130914, 3530916, 10402781, 32112656, 93427431

Offset: 0

Hugo Pfoertner, Jan 15 2004

See under A090573.

			a(1)=4 because the empty space located at mid-edge of one of the 12 edges of the assumed initial configuration can be replaced in the first move by any of the adjacent 2 cubes from the same edge or by the adjacent mid-face cubes of the 2 faces forming this edge.

Cf. A090572 2 X 2 X 2 puzzle, A090573, A090574, A090575 3 X 3 X 3 puzzle with different initial configurations.

# uses alst(), swap() in A089473, moves3d() in A090573
moves = lambda p, shape: moves3d(p, shape)
start, shape = "1-23456789ABCDEFGHIJKLMNOPQ", (3, 3, 3)
print(alst(start, shape, maxd=12)) # Michael S. Branicky, Dec 28 2020

a(13)-a(16) from Michael S. Branicky, Dec 28 2020

A090574 Number of configurations of the 3-dimensional 3 X 3 X 3 sliding cube puzzle that require a minimum of n moves to be reached, starting with the empty space in the center of the combination cube.

Original entry on oeis.org

1, 6, 24, 72, 192, 624, 2004, 6504, 19776, 62760, 186000, 583712, 1720972, 5344088, 15565416, 47816092, 137916958

Offset: 0

Hugo Pfoertner, Jan 15 2004

See under A090573.

			a(1)=6 because the empty space in the center of the cube present in the assumed initial configuration can be replaced by any of the 6 adjacent cubes from the face centers in the first move.

A090572 2 X 2 X 2 puzzle, A090573, A090575, A090576 3 X 3 X 3 puzzle with different initial configurations.

# uses alst(), swap() in A089473, moves3d() in A090573
moves = lambda p, shape: moves3d(p, shape)
start, shape = "123456789ABCD-EFGHIJKLMNOPQ", (3, 3, 3)
print(alst(start, shape, maxd=12)) # Michael S. Branicky, Dec 28 2020

a(13)-a(16) from Michael S. Branicky, Dec 28 2020

A090575 Number of configurations of the 3-dimensional 3 X 3 X 3 sliding cube puzzle that require a minimum of n moves to be reached, starting with the empty space at the center of one of the 6 faces of the combination cube.

Original entry on oeis.org

1, 5, 17, 52, 164, 496, 1608, 5008, 16024, 48732, 153564, 460984, 1437632, 4263236, 13150544, 38498798, 117497284

Offset: 0

Hugo Pfoertner, Jan 15 2004

See A090573.

			a(1)=5 because the empty space located at the center of a face of the combination cube in the assumed initial configuration can be replaced in the first move by either the cube from the center of the combination cube or by one of the 4 adjacent cubes located at the edges of the face initially containing the empty space.

A090572 2 X 2 X 2 puzzle, A090573, A090574, A090576 3 X 3 X 3 puzzle with different initial configurations.

# uses alst(), swap() in A089473, moves3d() in A090573
moves = lambda p, shape: moves3d(p, shape)
start, shape = "1234-56789ABCDEFGHIJKLMNOPQ", (3, 3, 3)
print(alst(start, shape, maxd=12)) # Michael S. Branicky, Dec 28 2020

a(13)-a(16) from Michael S. Branicky, Dec 28 2020

A090578 Number of configurations of a variant of the 3-dimensional 3 X 3 X 3 sliding cube puzzle that require a minimum of n moves to be reached, starting with the empty space at mid-edge of one of the 12 edges of the combination cube.

Original entry on oeis.org

1, 4, 10, 30, 74, 222, 546, 1628, 3978, 11810, 28658, 84520, 203562, 596520, 1425924, 4150232, 9838116, 28418002, 66805554

Offset: 0

Hugo Pfoertner, Jan 19 2004

See under A090577.

			a(1)=4 because the empty space located at mid-edge of one of the 12 edges of the assumed initial configuration can be replaced in the first move by any of the adjacent 2 cubes from the same edge or by the adjacent mid-face cubes of the 2 faces forming this edge.

Cf. A090577, A091521 this puzzle with different initial configurations, A090572 2X2X2 puzzle, A090573 - A090576 configurations of the 3 X 3 X 3 puzzle with 26 movable blocks.

# uses alst(), swap() in A089473, moves3d() in A090573
moves = lambda p, shape: moves3d(p, shape, fixed=13)
start, shape = "1-23456789ABCDEFGHIJKLMNOPQ", (3, 3, 3)
print(alst(start, shape, maxd=13)) # Michael S. Branicky, Dec 28 2020

a(14)-a(18) from Michael S. Branicky, Dec 28 2020

A090577 Number of configurations of a variant of the 3-dimensional 3 X 3 X 3 sliding cube puzzle that require a minimum of n moves to be reached, starting with the empty space at one of the enclosing cube corners.

Original entry on oeis.org

1, 3, 9, 24, 72, 174, 519, 1284, 3813, 9300, 27462, 66666, 195674, 470886, 1372946, 3280224, 9495005, 22487511, 64615934, 151714911

Offset: 0

Hugo Pfoertner, Jan 19 2004

The sliding cube 3 X 3 X 3 puzzle under consideration has a fixed central block and 25 movable blocks that can be shifted in the space between the enclosing holder frame and the central block. A description is given in US patents 3845959 and 6513808.

			a(1)=3 because the empty space at one of the 6 corners in the assumed initial configuration can be replaced by any of the 3 adjacent cubes from the middle of the 3 edges meeting at the empty corner in the first move.

Chih Chung Fang, Cubic Puzzle. US Patent 6513808, filed May 09, 2001
Daniel Kosarek, Three-dimensional block puzzle. US Patent 3845959, filed Nov. 5, 1974

Cf. A090578, A091521 this puzzle with different initial configurations, A090572 2X2X2 puzzle, A090573 - A090576 configurations of the 3 X 3 X 3 puzzle with 26 movable blocks.

# uses alst(), swap() in A089473, moves3d() in A090573
moves = lambda p, shape: moves3d(p, shape, fixed=13)
start, shape = "-123456789ABCDEFGHIJKLMNOPQ", (3, 3, 3)
print(alst(start, shape, maxd=14)) # Michael S. Branicky, Dec 28 2020

a(15)-a(19) from Michael S. Branicky, Dec 28 2020

A091521 Number of configurations of a variant of the 3-dimensional 3 X 3 X 3 sliding cube puzzle that require a minimum of n moves to be reached, starting with the empty space at the center of one of the 6 faces of the combination cube.

Original entry on oeis.org

1, 4, 12, 28, 84, 212, 632, 1544, 4584, 11220, 33060, 80152, 234648, 565192, 1643552, 3926832, 11337422, 26852656, 76981660

Offset: 0

Hugo Pfoertner, Jan 19 2004

See under A090577.

			a(1)=4 because the empty space located at the center of a face of the combination cube in the assumed initial configuration can be replaced in the first move by one of the 4 adjacent cubes located at the edges of the face initially containing the empty space. The cube at the center of the combination cube cannot replace the empty space because the construction of this puzzle inhibits the movement of the central cube.

Cf. A090577, A090578 this puzzle with different initial configurations, A090572 2 X 2 X 2 puzzle, A090573 - A090576 configurations of the 3 X 3 X 3 puzzle with 26 movable blocks.

# uses alst(), swap() in A089473, moves3d() in A090573
moves = lambda p, shape: moves3d(p, shape, fixed=13)
start, shape = "1234-56789ABCDEFGHIJKLMNOPQ", (3, 3, 3)
print(alst(start, shape, maxd=13)) # Michael S. Branicky, Dec 28 2020

a(14)-a(18) from Michael S. Branicky, Dec 28 2020

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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.

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A090576 Number of configurations of the 3-dimensional 3 X 3 X 3 sliding cube puzzle that require a minimum of n moves to be reached, starting with the empty space at mid-side of one of the 12 edges of the combination cube.

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A090574 Number of configurations of the 3-dimensional 3 X 3 X 3 sliding cube puzzle that require a minimum of n moves to be reached, starting with the empty space in the center of the combination cube.

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A090575 Number of configurations of the 3-dimensional 3 X 3 X 3 sliding cube puzzle that require a minimum of n moves to be reached, starting with the empty space at the center of one of the 6 faces of the combination cube.

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A090578 Number of configurations of a variant of the 3-dimensional 3 X 3 X 3 sliding cube puzzle that require a minimum of n moves to be reached, starting with the empty space at mid-edge of one of the 12 edges of the combination cube.

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A090577 Number of configurations of a variant of the 3-dimensional 3 X 3 X 3 sliding cube puzzle that require a minimum of n moves to be reached, starting with the empty space at one of the enclosing cube corners.

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A091521 Number of configurations of a variant of the 3-dimensional 3 X 3 X 3 sliding cube puzzle that require a minimum of n moves to be reached, starting with the empty space at the center of one of the 6 faces of the combination cube.

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Author

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Python

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