This is my Switch Box puzzle. It's a 3x3x3, but some edges and corners are bandaged together with a red part, that can slide along the edge. However, the switch can only slide in to a corner with an appropriate gap and only one switch can slide in to a given corner at a time.
This means endless variations are possible: a corner can have 1, 2, 3 or no cutouts at all. You can vary the position and count of edges with(-out) a switch. Of course it is also possible to make a variation where multiple switches can occupy a corner at once.

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The particular variation I made uses at least one of every part, but otherwise it's a bit of a mistake: it has quite little freedom. As a puzzle it's very good (hard!) but as a demonstration puzzle it's hard to find moves you can do.

I've build a slight little click in to the sliding action so the switches do not move on their own. This has worked out very well. The sliding pieces have slight tapers at their ends so they can move in easily without requiring perfect alignment. Over all I put a lot of thought in to the design and it really shows. I'm very happy with how this turned out.
In my copy of this puzzle I have colored the sliders with permanent marker and spray lacquered them. This worked quite well though I'm sure that red, polished strong and flexible is a good (and less labour intensive) option.



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Since I would like to give you the option to choose your own variation, I have not yet put up this item in my Shapeways shop. I considered making it as a co-creator so you could specify your preferences during the order process but due to technical reasons this would make the puzzle more expensive.
Instead, you can contact me specifying your own preferences and I will prepare a model that you can purchase from Shapeways. Over time I will add the more popular choices to my shop.

The base price is around $130/€125. Depending on which variation you choose this can vary by about $10 up or down. Edges with sliding connectors take up more material, regular corners are quite cheap while the corner with only 1 slot is the most expensive. The variations shouldn't be too great and the $10 figure is based on extreme cases.
To order, simply send me the following info:
- How many edges should have a slider (at most 7)
- How you want the corners to be distributed (how many with 3 gaps, how many with 2, with 1 and with 0 (no) gaps)
- Whether you want the sliders in a separate model (so you can have them dyed separately). It will add a little (about $5-$7) to the cost if you have them separated.
Of course you should make sure you have enough open corners for every slider to go in.

Of course assembled versions of this puzzle are available as usual.

Very clever design! Perhaps you could simply sell extra sliding bandages separately, that way the solver can add his/her own variation to the puzzle. Again, excellent job!

Of course I will honor such a request: if somebody wants to get more parts than those required for the base puzzle so they can swap them out that is an option but keep in mind (dis-)assembly it not easy and it is tricky to deal with the stickers if you want to assemble it in a different configuration.

Whoops haha you are absolutely correct! I simply was not thinking about disassembly, I could imagine that would be difficult.

Very clever and very well presented. I'm curious how many (non-trivial) versions are possible via this method. May I ask why there is a limit on only allowing 8 sliders? There is probably a very good reason but its not jumping out at me.

If the number of variations is something that could be reasonably counted any idea how much a kit would be that could be used to make all possible variations? The sticker issue could potentially be addressed by using tiles that weren't permanently attached to the faces. They could either pop into a recess or even be held on by magnets.

Carl

Won't a careful application of Burnside's lemma give us this answer?

If that's too much work, computer code to brute force it would be pretty trivial too.

EDIT: maybe not too trivial. There are a lot of combos so time and memory could be an issue. It might take more thinking to count this.

There are only 8 corners on a cube so you can only have 8 sliders. Though then you couldn't move any so 7 is a better figure.

Very cool, could you use this same method to bandage the center pieces to the edges as well?

Yes, that would be a very clever variation on this. You could have a piece sliding through a center that could either slot in to one edge or the other.

D'oh! I should have seen that. I guess I was thinking about this quote from the first post:But the key here is this ISN'T that variation. If it were I think you could allow up to 12 sliders.

Carl

Extremely cool!

Hey Tom-

Looks like the work you put into the details really show!
Congrats. It looks very nice. Also, great name!

Great work Tom
What if you order a whole bunch of these sliders all at once for your costumers?
(for the ones that directly buy from you)

Really nice puzzle Tom! Looks like such a fun puzzle to play around with and solve!
Great job!

simple, but cool.

i like the name.

I tried to analyze this puzzle in the past and the program wrote 1GB of data onto my HDD in no time.
Way to many variants. Sorry.

I have just made two variants of the Switch Box available on Shapeways. Don't forget to take advantage of their black Friday promotion by entering coupon code tdzmu on checkout to get 20% off.

You can either purchase the original variant or a new variant which has all corners open (I think this one will be more fun, the original was a bit too difficult for my taste).

You can also purchase the switches separately so you can have them dyed in a different color. Especially if you order the puzzle in BSF then ordering the switches together would make the switches black as well. By default you get both together (this is the cheaper option) but there is a link in the model description that will add the two separate models to your cart.