RUBIK’S MAGIC

ABOUT RUBIK’S MAGIC

Do you remember the old falling-book toy sometimes called“Chinese block”? perhaps 6 blocks are connected with alter-natingsingle and doubl straps.All except the end blocks have straps on both sides of the neighboring block below,a chin reac-tion occurs,wit each block falling in sequence until a new chain is formed.Sing straps move between double straps to the neighboring block.

Rubik’s magic can be thought of as very clever and elaborate design based on the same principle. The puzzle consists  of 8 plastic squares connected to each other by very thin filaments , or cords , that rest in grooves cut into the plastic squares. Each square is attached to 2 others by these cords.

The puzzle moves the way it does because of the clever way the cords are wrapped around the plastic squares. There are 16 separate cords holding the 8 squares together (you can verify this if you puzzle falls apart , as these puzzles sometimes do after misuse). The ends of each cord are attached to each other by a small metal clip to form a circle 5.5 inches in diame-ter. Pairs of cord cross each other .and where these crossings occur,the cords pass between each other as shown here

The puzzle moves by changes in the relative positions of cent squares. Squares are folded over on top of other squares and then pulled up so the different edges are touching when the move is done.

The move causes some of the segments of the cord to switch between 2 squares. During the move, parts of the cords ”jump” from one square to the other. During this jumping motion the part of the cords pass between each 

other in manner similar to the way the straps on the falling-block toy move. the puzzle with 8 squares can be thought  of as consisting of 4 overlapping sets  of 3 squares .

There are 4 cords attaching each set of 3 square,which means that alternating squares have 4 or 2 cords in each groove.

If you accidentally destroy one of these puzzles , you may be able to salvage one to salvage one of the 3-square pieces,which can be fun to play with your next 8-square puzzle.

Since the entire puzzle is built from smaller pieces in this way , it should be possible to construct larger versions. I wouldn’t be surprised to see such puzzles appear as this one becomes more popular. You may recall the large variety  of similar puzzles that appeared shortly after Rubik’s Cube. Perhaps Professor Rubik will also come up with other ways to wrap cords around different shapes to provide even more challenging puzzles.

TERMINOLOGY

Rubik’s Magic is made up of 8 squares connected by very thin cord. Each square has grooves cut into it in which the cords rest. Each square has 2 faces 4 edges.

 

BASIC MOVES

Rubik’s Magic can be changed from any of its shapes to any other by 1 or more moves in which 2 adjacent squares are folded together and unfolded on different edge.
The edges of the 2 squares that will become adjacent after the move are the ones on either side of the 2 small pieces of cord shown in the illustration. By looking for these 2 small pieces of cord, you can always tell the squares will move.

CORRECT AND INCORRECT OPENING.

*INDICATES 2 LAYERS OF SQUARES FOR QUICK REFERENCE

Squares can from patterns that you can move in useful ways when trying to change the shape of the puzzle.It is helpful to be able to recognize the following common patterns. Note that all these moves go both ways. Also, it is important to be aware of the position of the cords, since this determines the direction in which a move can be made. You might easily break the puzzle by trying to move it improperly.

OPEN A 4-SQUARES 2 WAYS.

A single square that pops up by itself I call a “flap.” Moving flaps is one way to change shapes.

MOVE A FLAP 2 WAYS.

There are 7 ways to move out of a double flap, making it one of the most versatile patterns.

ONE WAY OF OPENING DOUBLE FLAP.

SEQUENCE OF 2-FLAP MOVES.

If all else fails, just try folding and unfolding the puzzle without forcing it too hard. For a change to occur, 2 squares must be touching on 1 face.

What Can Go Wrong?

Avoiding Damage to the Puzzle 
The manufacturer has provided several very important suggestions to help you avoid damaging your puzzle. lf you ignore this advice, you risk ending up with a handful of plastic squares, colored paper, and loose cords. Unlike Rubik’s Cube, Rubik’s magic is not simple to reassemble. 

Keeping the puzzle Aligned 
It is also important to follow the manufacturer’s suggestion whenever the puzzle gets slightly out of alignment. When this happens, 2 adjacent squares will tend to overlap slightly, and the puzzle in its original 2-by-4 shape will not lie flat. Try pulling the overlapping squares apart and moving them up and down with respect to each other. I have found that these puzzles get slightly looser as they are used, so problems with alignment and stiffness tend to go away 

Cords out of Grooves 
A minor problem can occur when the longer cord segments fall slightly out of their grooves.When this happens, Justgently nudge the cord back and then jiggle 2 squares a little bit. 

Twisted Cords 
Sometimes twists in the cords will accumulate in one place and prevent the pairs of cords from passing between each other as they should, which can prevent otherwise permitted moves from being made. In a normal permitted move the small segments of cord pairs pass between each other. If there are twists in the outer pair of cords, this movement of the inner pair may be block, and the squares will not reopen all the way.

The feeling will be much the same as when you try to move the puzzle improperly. If you ever have trouble accomplishing what should be a permitted move, you should consider the possibility that cords are twisted.

TWISTS IN CORD AT CROSSING.

TWISTS BLOCK MOVEMENT OF CORDS THROUGH EACH OTHER.

To fix the problem you must carefully push the accumulated twisted cords through to the other side of the puzzle.

PUSH TWISTS THROUGH TO OTHER SIDE.

 
This has the effect of putting the twists into the larger cord segment where they can be somewhat dissipated.

  

Questions and Answers

Whenever I get a new puzzle like this one, besides trying to solve it I like to figure out how complicated it is. What moves? What changes? What stays the same? How difficult is it? And so on. 

Can All 8 Squares Be Switched Around?

The answer is that eight squares can all be moved to any position, but not in all possible ways. In other words, it is possible for each of the 8 squares to be on any corner or anywhere in the interior of the original 2-by-4 shape. But if you look carefully at the puzzle, you will notice that each square is always attached to the same 2 neighbors no matter hoe many times it is moved. In effect, the 8 squares form a necklace held together with the thin cords. This is why the squares cannot be moved to all positions in all possible combinations.

Can the 8 Squares Be Rotated?

The answer is that all the squares can be rotated, but there are restrictions on the combinations of rotations that can occur. In other words, the design on a square can point in four different several others at the same time.

Can the Squares Be Turned Over?

The answer is so, unless all 8 squares are flipped. There are 2 sides to the puzzle, as you can see when it is first opened. One side has the design that forms the3 separate ovals. The other has the design that forms the 3 interlocked ovals of the solution. It is not possible to get a “mixed” design on the 2-by-4 shape.

What Shapes Can’t Be Made?

One of the first things I tried to do with this puzzle after solving it was to make a flat window shape.

After considerable unsuccessful effort I decided to try to figure out whether or not it was even possible to make this shape. It turns out to be impossible, and I could have saved myself a lot of wasted effort if I had known this ahead of time. There is enough frustration with these puzzles without trying to do things that are impossible.

I know from experience that I cannot claim that something cannot be done in a puzzle solution book without backing it up, so I will give a brief explanation.

In this illustration, the number in the upper left corner of each square is the number of cords in each groove on the square. The number in the lower right is the number of the square. Starting at number 1 let’s travel to all 8 squares and back to number 1. If we make a right turn through a square with 4 cords, let’s add 1. If we make a left turn through a square with 4 cords, let’s subtract 1. If we make a light turn through a square with 2 cords, let’s subtract 1. If we make a left turn through a square with 2 cords, let’s add 1. If we go straight, let’s add 0. The numbers in the centers of the squares are the values we get by traveling around the square in this way. Notice that they add to 0, no matter how we might change the shape of the puzzle by making moves.

If we do the same calculation on the window shape, we get a total of 4! Therefore, the window shape cannot we made. You can use this method to decide if other shapes can be made. If you find this kind of thing interesting, try to figure out the effect of “flaps” on the method.

How Difficult Is It to Solve?

A quick answer here is that the puzzle is easier than Rubik’s Cube, but the many possible shapes make it more interesting to play (or work) with.

One way to gauge difficulty is to try to count the number of possible arrangements and shapes. There are 43 quintillion possible arrangements of Rubik’s Cube. In the case of Rubik’s Magic, there is no obvious definition of what makes shapes different. Since the puzzle can be moved gradually to make slightly different shapes, it may make sense to just say there are infinitely many shapes possible.

Nevertheless, one way of counting possible shapes is based on the number of right turns, left turns, and flaps—similar to the method used to decide if a shape is possible (see page 18). This method ignores the geometric shape, mirror images, the position of the cords, the design, and whether the shape is turned inside out. There are no more than 1,351 possible shapes, counted this way, and only 59 of these do not have flaps.

An Important Different

This puzzle is unlike its predecessors in an important way. According to how the puzzle is made, the thin cords can be in a different position relative to the design on the puzzle. This is possible even when puzzle have exactly the same design, and the difference has a serious impact on a written solution. These two illustrations differ only by the position of the cords with respect to the design:
 

When you turn ever the left 2 squares, the result depends on the location of the cords. This difference is far more subtle than the differences that plagued attempts to provide general solutions for Rubik’s Cube and its imitators. For this puzzle, a written solution must take this possible difference into account. The step-by-step solution presented in this book dose that.

SOLVING RUBIK’S MAGIC

When you first get a Rubik’s Cube, it is already solved. The objective is to scramble it and then solve it again yourself. Aft least this way you see the thing solve once, even if you never manageto solve it again. By contrast Rubik’s Magic comes out of the box unsolved, and if you wish to see it solved, you have to do it yourself. To solve this puzzle you really have to do 2 things. You must correctly arrange the design so that the chain pieces are linked and you must change the shape of the puzzle.

CHANGE THE UNLINKED CHAIN ON THE STARTING 2-BY-4 SHAPE TO THE LINKED CHAIN ON THE FINAL SHAPE, A 3-BY-3 SHAPE MISSING A CORNER.

  

Overall Strategy

The step-by-step solution given in the next section will allow you to change the puzzle with any desingn on the 2-by-4 shape to the correct design on the final shape.

YOU CAN SOLE THE PUZZLE FROM ANY SCRAMBLED DESIGN.

Methods for converting many other shapes into the 2-by-4 shape without regard to the design are given in the sec-tions following the step-by-sep solution.

SUMMARY OF THE SOLUTION

The solution has 5 main step:

1 Find the square that will be the center of the design.

2 Position the center square next  the upper right corner of the 2-by-4 shape.

3Orient  the center  square so it points the right away.

4  Correctly position neighbors of center square.  

5 change the shape to reveal the solution.

 

CORRECTLY ORIENT CENTER SQUARE.