This electronic puzzle consists of a ball with 12 large buttons on it, arranged symmetrically like the faces of a dodecahedron. Each button has a light in it as well. It is very similar to the Lights Out puzzle, in that by pressing the buttons the pattern of lights changes. The aim is to switch on all the lights.
There are 4 types of game play, which have very different ways of solving. These will be discussed separately below. By pressing and holding down two buttons at the same time you control the following aspects of the puzzle:
The Orbix was patented by Uwe Meffert on 15 October 1996, US 5,564,702.
If your browser supports it, you can play with the orbix by clicking this link:
This is a very simple type of game. Like Lights Out and Rubik's Clock, this is one of the few puzzles in which the order that the moves are performed is unimportant (i.e. the puzzle positions form an Abelian group). This means that it is not necessary to press any button more than once during the solution because we could change the order of the moves so that repetitions occur together. Since pressing a button twice will not change anything, a button need only be pressed at most once.
There are 12 lights, and each light can be switched on independently from all the others. There are therefore 212 = 4,096 positions, and at most 12 button presses are needed to solve it. Of course many of the positions are similar because rotations/reflections of the whole puzzle have not been taken into account.
In Sloane's On-Line Encyclopedia of Integer Sequences these are included as sequences A080559, A080560 and A080561.
The table shows the number of positions there are for each number of moves. In this case the numbers are simply the binomial coefficients, because of the nature of an Abelian group i.e. because the move order does not matter. The third column shows the number of positions if rotations are taken into account, the last if both rotations and reflections are taken into account.
Simply press a button if an even number of the adjacent buttons are lit. Repeat this until the puzzle is solved.
This type of game play is the same as type 1, except that only lit buttons can be pressed. Pressing an unlit button has no effect on the lights.
A simple computer search shows that 2079 positions are attainable, and that it can always be solved in at most 10 button presses.
In Sloane's On-Line Encyclopedia of Integer Sequences this is included as sequence A080562.
This is solved in a similar manner as before, except that you just press lit buttons. Simply press any lit button which has an even number of lit neighbours. Repeat this until the puzzle is solved. There are however 5 types of position which has no lit buttons with an even number of lit neighbours and these should be avoided if you want to use the minimum number of moves. These are:
With this type of game play only unlit buttons can be pressed, and then all buttons EXCEPT the adjacent ones change. Pressing a lit button has no effect on the lights.
A simple computer search shows that all positions are attainable, and that it can always be solved in at most 12 button presses.
In Sloane's On-Line Encyclopedia of Integer Sequences this is included as sequence A080563.
Solving this is very similar to type 2, except that now you only press unlit buttons, and the number of lit neighbours must be alternately odd and even. I do not know of an easy way to determine what the parity of your first move should be, odd or even. Simply choose any first move, and from then on alternate the parity. If you have done 12 moves and still have not solved it, then you must have started wrong. You may also come upon a position where there are no moves of the parity you are looking for.
Generally, in any position that is an odd number of moves from being solved, the next button pressed should have an odd number of lit neighbours. Similarly, positions an even number of moves from solved usually have an even next move. If there are moves of the right parity, then they will always be good moves. There are however a few exceptional positions where there are no moves of the correct parity. In all these cases, any single move of the wrong parity is good, and then just continue as if that move were the correct parity. These cases are:
A way to solve the puzzle in relatively few moves is therefore like this:
With this type of game play only lit buttons can be pressed. If the button opposite the pressed one is on then the effect is as type 1/2, i.e. the adjacent 5 lights change. If the button opposite the pressed one is off, then all buttons except the pressed one change. Pressing an unlit button has no effect.
In Sloane's On-Line Encyclopedia of Integer Sequences this is included as sequence A080564.
This shows that all positions can be solved in at most nine moves, except of course the position with no buttons lit which is impossible.
The following method is not the fastest, but it will solve the puzzle fairly quickly.