A090572 -id:A090572 - cp's OEIS frontend

A090573 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 one of the enclosing cube corners.

1, 3, 9, 30, 102, 324, 1029, 3096, 9960, 30732, 97932, 295924, 929202, 2766958, 8590731, 25271897, 77575820

Offset: 0

Hugo Pfoertner, Jan 15 2004

The 3 X 3 X 3 sliding cube puzzle is a generalization of the 2 X 2 X 2 3-D puzzle A090572. There are various designs of this 3 X 3 X 3 puzzle, but in most of them the central cube is not freely accessible and the empty space cannot be moved to the central location of the cube. The design treated in this sequence assumes full accessibility of the central location.

Ji-Ha You, Three dimensional puzzle with blocks - has cube frame with hollow interior and movable blocks filled on one side with magnet. German Patent application DE-4106826 A1, March 4, 1991 - see link

Ji-Ha You, Dreidimensionales Spielgeraet. Offenlegungsschrift DE-4106826 A1.

Cf. A090572 2 X 2 X 2 puzzle, A090574, A090575, A090576 3 X 3 X 3 puzzle with different initial configurations.

# uses alst(), swap() in A089473
def moves3d(p, shape, fixed=None): # n x m x r puzzle
  nxt, (n, m, r) = [], shape
  L, z = n*m, p.find("-") # z: location of blank
  zq, zr = divmod(z, L)
  if zr > n - 1:  nxt.append(swap(p, z, z-n)) # blank up
  if zr < n*m-n:  nxt.append(swap(p, z, z+n)) # blank down
  if zr%n != 0:   nxt.append(swap(p, z, z-1)) # blank left
  if zr%n != n-1: nxt.append(swap(p, z, z+1)) # blank right
  if zq > 0:      nxt.append(swap(p, z, z-L)) # blank in
  if zq < r - 1:  nxt.append(swap(p, z, z+L)) # blank out
  return [m for m in nxt if m.find("-") != fixed]
moves = lambda p, shape: moves3d(p, shape)
start, shape = "-123456789ABCDEFGHIJKLMNOPQ", (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

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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A090573 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 one of the enclosing cube corners.

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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

Keywords

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Python

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