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 Post subject: Minimally Stickered Cube
PostPosted: Sat Dec 28, 2013 2:13 am 
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Joined: Mon Apr 20, 2009 5:24 am
I would like to present my sticker scheme for a 3x3x3:




It has only 30 stickers, 24 less than a fully stickered 3x3x3. But that's not the point. It only has one unique solution, even considering color scheme changes. Not considering center rotations, since the only way you can fix those is to use super stickers, and also since the normal 3x3x3 can have center rotations.

This is the most number of stickers I was able to remove. As a bonus, each face has the same number of stickers. Pretty eh?

"But I'm solving it now, and it looks nothing like your sticker scheme. I even tried a alternate color scheme. I'm almost done!"

Yeah, the cube is mean and will throw you issues like these:


(OLL Parity)


(PLL Parity)


(Corner rotation Parity)


(Sticker flip parity)

I used Cubesmith 3x3x3 tiles and a random cleaned 3x3x3 to make this. It's a great way to freshen up one of your unused cubes!

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*10 years later...*
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 Post subject: Re: Minimally Stickered Cube
PostPosted: Sat Dec 28, 2013 2:33 am 
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Location: Bay Area, California
Do you have a proof that 30 is minimal?

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 Post subject: Re: Minimally Stickered Cube
PostPosted: Sat Dec 28, 2013 3:41 am 
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This problem is actually really complicated, I tried to solve it in this thread. That thread died and I continued later.

Basically I solved reduced versions of the problem. I first made it so that the set of edges, the set of centers and the set of corners only has one solution, even if you disassemble.

The edges can only have up to 6 removed, otherwise two edges will be identical.
Taus used GAP to verify the minimal range of solutions for corners.
The centers can only have 4 removed, otherwise you can rotate 4 unstickered centers around

Then you are allowed one extra swap from one of the three sets. A legal position can only have an even number of permutations, so this extra permutation will mess up the cube.

I removed one more sticker from the corners. There were only a few ways to do this on Taus's minimal corners such that one extra swap was possible.

As for the fixed color scheme, I myself forgot how I accomplished this. I made the sticker scheme a while ago. I do know that any two colors cannot be interchanged on the specific arrangement of corners I chose.

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I'm going to try learning puzzle design!
*10 years later...*
Yes! I made a sphere! Now, what was step 2 again?


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 Post subject: Re: Minimally Stickered Cube
PostPosted: Sat Dec 28, 2013 7:24 am 
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Joined: Sun Mar 15, 2009 12:00 am
Location: Jarrow, England
Interesting solution to a rather complicated problem. I wonder how many stickers you can remove if you add the additional restriction that the sticker pattern on all faces must be the same (or perhaps rotations/reflections could be allowed)?

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 Post subject: Re: Minimally Stickered Cube
PostPosted: Mon Dec 30, 2013 7:22 am 
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Joined: Fri Jun 21, 2013 3:39 am
Location: Rye, East Sussex
I think I will give this a go on my CT DIY Bandaged kit tonight.

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How to sum up my solving skills..."I try, I try, I fail. I try, I try, PREVAIL!"


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 Post subject: Re: Minimally Stickered Cube
PostPosted: Tue Dec 31, 2013 8:19 am 
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Joined: Fri Jun 21, 2013 3:39 am
Location: Rye, East Sussex
I actually really enjoyed the above puzzle, it is a great example of parity in action combined with struggling to work out where everything goes.

You have to replicate the puzzle with little thought, scramble it fast and then forget the solution, much more fun like that.

I gave it to my daughter to make for me and scramble.

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How to sum up my solving skills..."I try, I try, I fail. I try, I try, PREVAIL!"


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 Post subject: Re: Minimally Stickered Cube
PostPosted: Fri Jan 03, 2014 10:26 pm 
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Nice to hear that, I can't experience such a feeling since I designed the sticker pattern :lol: . Still I find it much harder than a simple 3x3. When I show it to people, they think its just another 3x3 until I scramble it for them.

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*10 years later...*
Yes! I made a sphere! Now, what was step 2 again?


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