What puzzles are there that are similar to Rubik's Cube?

I made an inventory of the puzzles I have with a description for most
of them.

Rubik's Fifteen:
On the first side of the black box there are 25 windows arranged in a
grid of 5x5.  Tiles carrying Roman numerals from I to XV are visible
through the windows.  The Roman numerals have to be arranged in
sequence with the * filling the last window in the corner of a 4x4
grid.  On the reverse side 9 windows form a grid of 3x3 and the tiles
carry the numerals 0 to 15.  The numerals have to form a 'Magic
Square' of 15.  The tiles are moved by push buttons from the 2 sides
of the box.  Most of the push buttons move a column or row of tiles.
One of the push buttons moves 3 rows of tiles all at once.

Rubik's Dice:
A hollow cube which has 7 plates inside it.  The plates are white with
red dots on them.  The plates are loose but adhere to the inner sides
of the cube.  By shaking and turning the cube the position and
orientation of the plates can be changed and this in turn alters the
colour of the spots of the dice. Re-arrange the plates within the cube
in such a way that the dice has white and only white spots.  If red is
shown anywhere on the dice even through the small control holes - the
puzzle is not complete.

Rubik's Tangle 1:
It has 25 square tiles.  Each tile has the same pattern of ropes but
the colour of the ropes varies.  Lay down the tiles in a 5x5 square, in
such a way that each colored rope forms its own continuous line.  There
are 4 different tangle puzzles.

Rubik's Triamid:
It is basically a 3 sided pyramid made up of 10 small 4 sided play
elements.  These elements are held together by 4 connectors, invisible
when the Triamid is complete.  Detach a small pyramid (4 elements) from
a base (6 elements) and reattach the small pyramid with a different
side or in a different orientation to the base.  To solve the puzzle
all you have to do is to bring Triamid back to its original state with
each side one single color.

Rubik's Rabbits:
It has the shape of a hat.  In the start position, you see no rabbits
in the hat.  The hat is divided into 6 rings, which can be turned.  By
turning the rings, the rabbits appear and disappear.  The objective is
to make all 9 rabbits visible at the same time.

Rubik's Maze:
It consists of 6 cubes which are connected in such a way that each cube
can turn around its neighbour.  The puzzle has only 2 colors.  The
yellow lines are walls and the black lines are the path of the maze.
Turn the cubes and make a continuous black line.

Rubik's Clock:
It has 3x3 clocks (T-W, 1-5 and A-E) on both sides.  Each clock has one
dial.  2x2 push buttons (p-r) are placed between the clocks.  The dials
of 4 clocks (T-W) can be turned directly.  Then the dials of the other
clocks will turn depending upon the state of the push buttons (up or
down).  The objective is to turn all dials on both sides to 12.

front:  back:
T 1 U   U A T
 p q     q r
2 3 4   D C B
 r s     s r
V 5 W   W E V

Abraxis:
It consists of 13 pieces (12 pieces of 5 cubes and 1 piece of 4 cubes)
which can be put together to form a 4x4x4 cube.  The pieces look like:

113   3   131   31  13   131  131  23    32  3    113   13  13
  1  111   1   11    11  1      1   11  11   111  1    11    1

1: a cube
2: a cube above no cube
3: a cube above a cube

Hungarian Rings:
It has 2 rings with 10 red, 10 black, 9 yellow and 9 blue beads.  The
rings intersect each other at 2 beads.  A ring of beads can be moved.
The objective is to get all the beads of one color together.

Whirligig Plate:
It has 3x3 overlapping circles.  One circle moves 4 segments.  The
puzzle has 24 segments divided over 6 colors.  The objective is to make
a nice pattern with the colored segments.

Gripple:
It has 5 overlapping circles.  One circle moves 4 segments.  The puzzle
has 16 segments divided over 4 colors.  The objective is to make a nice
pattern with the colored segments.

Masterball:
The ball consists of 8 colored segments.  Each segment is divided in 4.
Vertical 180 degrees and horizontal 45 degrees turns are possible.

Zauberkreuz (Magic cross):
It is a red cross (center 2x2, 4 legs of 2x4) with 20 squares.  A
square is colored half at one side of a diagonal.  There are 5 colors.
The squares can be moved with 2 slides of 2x6.  The objective is to get
the squares of the same color together.

Laby Cube:
A 6x6x6 labyrinth cube of transparent plastic.  A small metal ball can
enter the cube through a hole at a corner and has to be guided through
the labyrinth to a hole at the opposite corner.

Kaos:
6 transparent tubes of size 2, 4, 6, 8, 10 and 12, arranged in a circle
and in a staircase pattern, contain 1 black, 2 white, 3 blue, 4 yellow,
5 green and 6 red balls.  The puzzle is divided in 2 turnable halves.
The objective is to get the colored balls together in the correct tube.

Pla puzzle No. 783:
A 5x8 box contains 10 pieces.  Each piece consists of 4 squares.  There
are 5 different pieces.

Pla puzzle No. 0:
A box containing 13 circular pieces with protuberances.  The pieces are
arranged in a 4-5-4 pattern.  The circle with one protuberance occurs
twice.

Pla puzzle No. 5:
A 6x10 box containing 12 pentominoes.

Pla puzzle No. 6:
A box with sides 1, 6, 2, 5, 2 and 6, containing 12 hexiamonds.

Pla puzzle No. 7:
A box with 18 sides of 2, containing 24 heptiamonds.

Pla puzzle No. 8:
A 8x8 box containing 12 pentominoes and one 2x2 piece.

Pla puzzle No. 22:
A box with sides 11, 10, 11 and 10, containing 22 pieces.  Each piece
consists of 5 hexagonals.

Pla puzzle No. 600:
A 11x19 +1 box containing 35 hexominoes.  The extra square is present
at the middle of the 19 side.

Orb-it:
A sphere with 4 rings containing 8 blue, 20 red, 20 green and 8 orange
beads.  The beads can move in the rings.  Half of the sphere can make
45 degree turns.

Pyramid:
A tetrahedron, each side consisting of 9 triangles.

Meleda:
A rectangular slide has 7 turning buttons next to each other.  Each
button has 3 segments cut out at left, right and bottom.  The turning
circles of the buttons overlap.  The slide with buttons is contained in
a ruler. The ruler blocks the buttons from turning, except at the 7th
position where a segment is cut out from the ruler at the bottom.  At
this position, the button can be turned.  In the starting position with
all buttons upright, the slide can shift one position to the right.
The objective is to turn all 7 buttons 90 degrees to the left so that
the slide can be removed from the ruler.

Rubik's Cube 3x3x3
Rubik's Revenge 4x4x4
?'s Cube 5x5x5
Rubik's Magic 2x4 tiles
Rubik's Magic 2x6 tiles

-- Andre' Wilhelmus <awilhelm@hvsgg01.att.com>

In article <2e8o91INNda5@dns1.NMSU.Edu>, mwalls@nmsu.edu (Commander
Keen) writes:
|> Rubik's Cube:  The classic 3x3x3 puzzle.
|> Rubik's Revenge: Same as the cube, but 4x4x4.
|> Rubik Jr.:  Same as the cube, but 2x2x2 (and extremely easy)
|> Missing Link:  A rectangular prism with 4 panels on each side.  Each
|>                all sides but 1 have 4 pieces to make a colored chain.
|>                One side has only 3 pieces and an empty space to slide
|>                other pieces into.  The top and bottom 1/4 of the box
|>                turns.
|> Barrel/Whip-It: A cylindrical puzzle with 6 different colors.  Similar
|>                to the Missing Link, only with 3 pieces per color and
|>                no chain pattern to match--only colors.  Easy.
|> Orb:  A spherical puzzle that when solved has 2 small rings of beads
|>       near each pole and 2 large rings of beads near the equator.  It
|>       can be twisted to combine the rings into 1 or 2 continuous slots
|>       of beads.  Each ring is a different color and the beads slide.
|>       I found this one to be very difficult.
|> Pyramid:  A tetrahedron which has each face composed of 9 equilateral
|>           triangles.  Somewhat easy.  Also easy to take apart.
|> Star:  This one is hard to describe.  It is almost spherical, except
|>        each "face" has a star on it.  The sides of the points of the
|>        are parts of the "face" of another side.

RUBIK'S CUBE VARIANTS -- INFORMATION AND QUESTIONS

What other puzzles are out there that are similar to Rubik's Cube?  I
suppose I'd require the following (only because you have to draw the
line somewhere):

    * Stationary axes of rotation (i.e., they rotate, but otherwise
        don't move) in at least 3 different planes.
        (Rubik's Magic, Whip-It, and the like fail here)

    * 1 or more kinds of interchangeable pieces which together make up
        most of the entire outer surface of the puzzle.
        (the Orb fails here, since the beads are the real pieces, but
        it's close)

I already know about the following (numbers in parentheses refer to
NOTES below):

NAME /              GENERAL         NUMBER AND                  NUMBER OF
DIFFICULTY (0)      SHAPE           TYPES OF PIECES             COLORS
------------------  --------------  --------------------------  ---------
Alexander's Star    dodecahedron    60 diamonds (double         6
    3 (1)           with stars on   triangles with a bend
                    each side       between them)
Masterball          sphere split    16 "polar" wedges           8/2
    7/4 (2)         by 8 longitude  16 "tropical" wedges
                    and 3 latitude
                    lines
Pyraminx            pyramid         4 corner pyramids           4
    3 (3)           divided into    4 edge pyramids
                    triangles of    4 "center" pieces
                    1/3 size
Rubik's Jr.         cube            8 corner cubes              6
    3               2x2x2
Rubik's Cube        cube            8 corner cubes
    7 (4)           3x3x3           12 edge cubes
                                    6 center pieces
Rubik's Revenge     cube            8 corner cubes              6
    8 (5)           4x4x4           24 edge cubes
                                    24 "center" pieces
Rubik's Wan         cube            8 corner cubes              6
    9 (6)           5x5x5           24 off-center edge cubes
                                    12 central edge cubes
                                    24 inner-corner pieces
                                    24 inner-edge pieces
                                    6 center pieces
Smart Alex          4 hexagons      24 triangles                4
    3 (7)           around a cube
Square 1            cube (almost)   8 "edge" triangles          6
    8 (8)                           8 "corner" kites
                                    2 pivot trapezoids

(0) My difficulty estimates on a scale from 1 (can be solved with
random twists in a short time) to 10 (paper and pencil will be useful).

(1) How much harder would this be if it had 12 colors?

(2) Masterball is arguably the best looking since it uses colored
plastic pieces instead of those mangy stickers.  Unfortunately, its
mechanism is one of the worst, which actually contributes to the
difficulty.  The 7 rating is for the 8 color Masterball.  The black and
white version gets a 4.

(3) How much harder would this be if it had an extra "row"?

(4) Very close variants like Rubik's World (just like the Cube, but
requiring the center pieces to be oriented correctly as well) aren't
as interesting, but I wouldn't mind hearing about them.  I also
remember an octagon variant which was simpler than the Cube.

(5) Any Rubik's Revenge hackers out there?  Does anyone have a "good"
solution for flipping a single pair of edge pieces?  My current (i.e.,
what I figured out about 10 years ago) solution takes ~43 moves.

In ascii:

        +--+--+--+--+                   +--+--+--+--+
        |\oo\oo\oo\oo\                  |\oo\oo\oo\oo\
        + +--+--+--+--+                 + +--+--+--+--+
        |\|\oo\oo\oo\oo\                |\|\oo\oo\oo\oo\
        + + +--+--+--+--+               + + +--+--+--+--+
        |\|\|\oo\oo\oo\oo\              |\|\|\oo\oo\oo\oo\
        + + + +--+--+--+--+             + + + +--+--+--+--+
        |\|\|\|\oo\xx\xx\oo\      ?     |\|\|\|\oo\oo\oo\oo\
        + + + + +--+--+--+--+    --->   + + + + +--+--+--+--+
         \|\|\|\|xx|oo|oo|xx|            \|\|\|\|xx|xx|xx|xx|
          + + + +--+--+--+--+             + + + +--+--+--+--+
           \|\|\|xx|xx|xx|xx|              \|\|\|xx|xx|xx|xx|
            + + +--+--+--+--+               + + +--+--+--+--+
             \|\|xx|xx|xx|xx|                \|\|xx|xx|xx|xx|
              + +--+--+--+--+                 + +--+--+--+--+
               \|xx|xx|xx|xx|                  \|xx|xx|xx|xx|
                +--+--+--+--+                   +--+--+--+--+

(6) I got Rubik's Wan from a friend who went to Hong Kong, so it's
probably not an "official" product.  Wan means 10,000 in Chinese.  This
really isn't much harder than the Revenge, but nonetheless it takes a
while to solve even if you know what you're doing (it takes me
approximately 4 times longer to solve the Revenge than the Cube, and 4
times longer to solve the Wan than the Revenge).

(7) This puzzle is basically 2 dimensional, so adding the missing two
hexagons wouldn't change much (in fact, removing 2 hexagons doesn't
either!).

(8) Square 1 stands out the most of all of these, since it changes
shapes all the time.  This is a major part of the difficulty, because
it makes remembering sequences harder.

I am hesitant to offer any solutions for any of these, since sometimes
they are very difficult to describe, but I can give general hints if
anybody wants them.

Corrections and additions?

-- Robert Jen <rjen@ctp.com>

[ Editor: see also competition/games/rubiks/ (rubiks.clock,
rubiks.magic, rubiks.tangle) and competition/games/square-1. ]

[ Editor: a June 1994 list of puzzles bearing Rubik's name, in reply to
a question about Rubik's Magic; it overlaps the inventories above but
gives the solver's impressions. ]

Here's an updated list of what sort of stuff has Erno Rubik's name on
it.  I believe most of them are licensed by Matchbox, although I have
this nagging feeling that the original cube was marketed by Ideal.

Rubik's Cube: a 3x3x3 cube.  We all know what this is.
Rubik's Revenge: a 4x4x4 cube.
Rubik's Cube Fourth Dimension: The old cube with pictures on the
   center of each face that you have to align.  This is not that much
   harder to solve if you know how.
Rubik's Snake: not really a "puzzle."  The most common shape is the
   "ball," or the rhombocubicoctahedron.
Rubik's Magic (original): Eight plastic squares linked by fishing
   wire.  Goal: to "link" three rings drawn on the surface.
Rubik's Magic (colored): Eight plastic squares linked by fishing wire.
   Each square is divided into four colored squares of blue, green,
   red, and yellow.  Goal 1: Find out what arrangement you're supposed
   to put it in (this part is easy if you have the instruction booklet
   that I've never seen!!)  Goal 2: get it into a cube with a two
   square handle so that each vertex has only one color surrounding
   it.  (I think this was much harder than the three rings version.)
Rubik's Master Magic: Twelve plastic squares.  Link five rings on a
   silver background.  Easier than the previous two.
Rubik's Clock: eighteen twelve-position dials, four gears and four
   buttons to control.

The new collection:
Rubik's Tangle: Pieces with pictures of ropes on it that you have to
   form closed loops with.  Four variations.
Rubik's Triamid: A take-apart puzzle that is much harder to solve if
   you follow the rules.  Still easier than the 3x3x3, though.
Rubik's Dice: A hollow dice with metal slabs inside that stick to the
   faces.. unfortunately, each slab has red dots on it.  Goal: to stick
   a slab on each face yet not let any red show.  Really ingenious,
   but a bit on the easy side.  Is somewhat unique in that you can also
   take a "skill" approach to the puzzle.
Rubik's Fifteen: This claims to be a variant of Sam Loyd's old 14-15
   puzzle.  It is actually much harder since you slide entire rows and
   columns at times.  I haven't played with it yet.

Any additions would be appreciated.  I know 5x5x5 exists, but I'm not
sure if Rubik's name is on them.

I can consistently solve all of them except Fifteen (which I've never
touched) and Tangle (I've never even physically seen this.)

-- Wei-Hwa Huang <whuang@cco.caltech.edu>