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 Post subject: Solving the Child's PlayPosted: Sun Aug 01, 2010 1:57 pm

Joined: Fri Mar 06, 2009 9:23 pm
There was a bit of discussion going on about solving the Child's Play in the New puzzle thread. I thought I would move the discussion to this board because it is more appropriate.

In the attached picture I try to explain visually why solving this (these?) puzzle is such a challenge. Going in with the knowledge that the orange layer is supposed to interact with the green layer when solve, it is a good place to start when trying to solve the puzzle. It is decently easy to set up shapes on the two respective faces of those layers so that they interact as they would when the puzzle is solved. The challenge the quickly arises is this: when solving just that face(on both 2x2x2's), the four adjacent faces (again on both 2x2x2's) must be considered. and when each one of those faces is trying to be solved, the adjacent faces must also be taken into account. The only concept that comes to mind is the programming concept called Recursion.

kastellorizo has mentioned that a puzzle with no coloring would be a much bigger challenge. I was well aware of this when designing the puzzle, but I decided to color it the way I did because I wanted to make the puzzle solvable. Even with he colored parts, the puzzle is still a challenge (at least to me it is). I will eventually make a version with coloring that will not make the solve any easier.

 Attachments: childs play solve 1.JPG [ 10.78 KiB | Viewed 2204 times ]

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Last edited by gingervergo on Sun Aug 01, 2010 2:28 pm, edited 2 times in total.
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 Post subject: Re: Solving the Child's PlayPosted: Sun Aug 01, 2010 2:18 pm

Joined: Fri Nov 04, 2005 12:31 am
Location: Greece, Australia, Thailand, India, Singapore.
Indeed, I guess we can always choose the level of difficulty.

The options are plenty for this puzzle, as it is based in the combination
of matching two twisty puzzles. Andreas has already done another nice
version, and I like both!

Moreover, this puzzle can be made even easier by presenting similar tilings
(i.e. more than once), as then, we may have the case of multiple solutions
even with different colorings!

And the plot thickens....

Pantazis

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 Post subject: Re: Solving the Child's PlayPosted: Sun Aug 01, 2010 3:20 pm

Joined: Fri Feb 20, 2009 6:38 pm
When solved, does each face have to interact with at least one other face? I was not able to determine from the pictures if each face had the same 4 shapes, how many repetitions of shapes there were, or if there was one repetition of shape per colored layer. If each face has the same 4 shapes, I am wondering how having each solved face have a unique shape would affect the solving or vice versa. I suspect that the puzzle would be easier if each face had a 4 unique shapes because the cube would then act as a blind man's cube. Also, would having each face a mix of male/female pieces or each cube having a mix of male/female faces have any effect on the solve? If I had to take a guess on which combination of the above would produce the most difficult solve, I would guess that a uniform cube with repetitions of shapes would produce the hardest puzzle to solve. This guess is based on a Sudoku 2x2 that I got from forum user SmaZ. It features 4 suits (as in a deck of cards) and one must solve so that each face has 1 of each suit. Such a situation as described above (uniform with repetition) presents an interesting concept: you could (as far as I can tell) just scramble a cube then solve the second to match it. This might be remedied by having each individual piece feature a specific shape. That way there is no individual solved state but together there are. I worry, however, that it would still not be difficult. I can see what is meant by needing the solution to one of the 2 puzzles in order to get the other .

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 Post subject: Re: Solving the Child's PlayPosted: Sun Aug 01, 2010 3:23 pm

Joined: Wed Jan 21, 2009 12:58 pm
Gingervergo,

The more I look at this puzzle, the more I realize there are great possibilities. I really like how every cubie in the first cube influences three cubies in the second cube.

I just realized what you did... You have eight shapes repeated six times each (three raised and three lowered). And what's most interesting is that the shapes are always oriented the same way in relation to the overall cube! That is mischievous! It would be very hard to know where to start if you didn't pay attention before scrambling. So yes, the colors definitely help. Again, kudos! What a great idea!

By the way, the name Child's Play is growing on me.

kastellorizo wrote:
Moreover, this puzzle can be made even easier by presenting similar tilings (i.e. more than once), as then, we may have the case of multiple solutions even with different colorings!
Like I said above, the shapes do repeat so... There is a possibility that this puzzle might have more than one solution if you ignore the coloring...

Skarabajo.

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 Post subject: Re: Solving the Child's PlayPosted: Sun Aug 01, 2010 8:06 pm

Joined: Fri Mar 06, 2009 9:23 pm
quicksolver wrote:
When solved, does each face have to interact with at least one other face? I was not able to determine from the pictures if each face had the same 4 shapes, how many repetitions of shapes there were, or if there was one repetition of shape per colored layer. If each face has the same 4 shapes, I am wondering how having each solved face have a unique shape would affect the solving or vice versa. I suspect that the puzzle would be easier if each face had a 4 unique shapes because the cube would then act as a blind man's cube. Also, would having each face a mix of male/female pieces or each cube having a mix of male/female faces have any effect on the solve? If I had to take a guess on which combination of the above would produce the most difficult solve, I would guess that a uniform cube with repetitions of shapes would produce the hardest puzzle to solve. This guess is based on a Sudoku 2x2 that I got from forum user SmaZ. It features 4 suits (as in a deck of cards) and one must solve so that each face has 1 of each suit. Such a situation as described above (uniform with repetition) presents an interesting concept: you could (as far as I can tell) just scramble a cube then solve the second to match it. This might be remedied by having each individual piece feature a specific shape. That way there is no individual solved state but together there are. I worry, however, that it would still not be difficult. I can see what is meant by needing the solution to one of the 2 puzzles in order to get the other .

I Hope This video will answer any questions you have

Skarabajo wrote:
Gingervergo,

The more I look at this puzzle, the more I realize there are great possibilities. I really like how every cubie in the first cube influences three cubies in the second cube.

I just realized what you did... You have eight shapes repeated six times each (three raised and three lowered). And what's most interesting is that the shapes are always oriented the same way in relation to the overall cube! That is mischievous! It would be very hard to know where to start if you didn't pay attention before scrambling. So yes, the colors definitely help. Again, kudos! What a great idea!

By the way, the name Child's Play is growing on me.

kastellorizo wrote:
Moreover, this puzzle can be made even easier by presenting similar tilings (i.e. more than once), as then, we may have the case of multiple solutions even with different colorings!
Like I said above, the shapes do repeat so... There is a possibility that this puzzle might have more than one solution if you ignore the coloring...

Skarabajo.

It's nice to see that people are starting to realize the effort I put into the design of this puzzle. The orientation of the shapes on the puzzle was done deliberately to change the complexity. Maybe I should have done a more detailed explanation of the puzzle. There is still one small thing no one has picked up on yet. As far as I can tell there is only one solution, but I could be mistaken.

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--Eric Vergo

My Shapeways shop

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 Post subject: Re: Solving the Child's PlayPosted: Sun Aug 01, 2010 8:15 pm

Joined: Sun Jun 13, 2010 1:00 am
Could 4 of each puzzle be pressed against eachother to make a solid 2x2x2 grid of 2x2x2s?

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 Post subject: Re: Solving the Child's PlayPosted: Sun Aug 01, 2010 8:30 pm

Joined: Sun Nov 16, 2008 5:18 pm
Location: MA, USA
PuzzleMaster6262 wrote:
Could 4 of each puzzle be pressed against eachother to make a solid 2x2x2 grid of 2x2x2s?

Unless I'm very mistaken, yes.

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 Post subject: Re: Solving the Child's PlayPosted: Sun Aug 01, 2010 8:56 pm

Joined: Fri Feb 06, 2009 2:57 pm
Location: Pittsburgh
I was genuinely surprised at how many people looked at this and thought it would be easy! I looked at it and thought "Oh goodness, please don't try to time me figuring it out."

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 Post subject: Re: Solving the Child's PlayPosted: Sun Aug 01, 2010 8:58 pm

Joined: Sun Jun 13, 2010 1:00 am
So then the outer faces of that giant cube could be made flat, resulting in an even harder version of this

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 Post subject: Re: Solving the Child's PlayPosted: Mon Aug 02, 2010 1:00 am

Joined: Fri Nov 04, 2005 12:31 am
Location: Greece, Australia, Thailand, India, Singapore.
Skarabajo wrote:
kastellorizo wrote:
Moreover, this puzzle can be made even easier by presenting similar tilings (i.e. more than once), as then, we may have the case of multiple solutions even with different colorings!
Like I said above, the shapes do repeat so... There is a possibility that this puzzle might have more than one solution if you ignore the coloring...

Exactly. So there are a few possibilities:

1. The shapes are repeated on each side. Then depending on their (a) coloring, (b)orientation,
(c) position on the tiles*, (d) position on the faces**, and (e) strict or relaxed definition of matching

of all the pieces we can get more solutions.
2. The shapes are not repeated. Then depending on the coloring, orientation and/positions
(as described above), we have a similar effect as above. Just imagine orienting two or more pieces
of both cubes at the same time. Then based on how we define the matching, we can get more solutions.
3. A mixture of the two cases above. Again, depending on how we define and create the matching,
we can get many solutions or less solutions.

* i.e. shifting the too symmetrical ones a little near or far to the edge.
** i.e. depending on how we wish to define the matching.

Yes, we may also get a unique solutions (still not sure about it though I believe we can), but more research
has to be done for each individual case.

In other words, the level of the puzzle depends on many more facts, not just the colors.
And the colors help to make it significantly easier. Now, if we wish to keep it as difficult
but also colorful, maybe coloring each piece a specific color would be more interesting.

Pantazis

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 Post subject: Re: Solving the Child's PlayPosted: Mon Aug 02, 2010 2:42 pm

Joined: Tue Jul 13, 2010 12:50 pm
kastellorizo wrote:
Now, if we wish to keep it as difficult
but also colorful, maybe coloring each piece a specific color would be more interesting.

Coloring each piece would make the puzzle much easier, as one could memorize the order of the colors, leaving only orientation.

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 Post subject: Re: Solving the Child's PlayPosted: Mon Aug 02, 2010 2:54 pm

Joined: Fri Nov 04, 2005 12:31 am
Location: Greece, Australia, Thailand, India, Singapore.
Arkanoid0 wrote:
kastellorizo wrote:
Now, if we wish to keep it as difficult
but also colorful, maybe coloring each piece a specific color would be more interesting.

Coloring each piece would make the puzzle much easier, as one could memorize the order of the colors, leaving only orientation.

I am always focusing on the case where someone solves it for the first time.

Regarding memory and solving it for the second time, someone could easily
remember not just the colors (if there are any) but the entire patterns of say
the top face and one neighbouring face (which in most circumstances should
be enough), regardless if it has one or more colors.

Pantazis

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 Post subject: Re: Solving the Child's PlayPosted: Mon Aug 02, 2010 4:09 pm

Joined: Tue Jul 13, 2010 12:50 pm
Ok, I have figured out a solution to this puzzle. It is not a method per se, but more of a mathematical representation of the relationship of these two 2x2x2's. The idea is actually very simple:
First, imagine a babyface 2x2x2.
Next, move each babyface to the opposite side of the cube.
Connect the babyfaces to their original side, so when you make a U move, the U face doesn't move, but the D face does. Do this for all sides.

This weird cube is what I call the Anti-Cube. if you were to mix up one of the child's play cubes, and this Anti-cube(if the anti-cube had the same pattern as the other child's play cube) like using the same moves(U on the regular cube is the U layer not U face), then if the Anti-cube's position was a solvable position(for the corresponding Child's Play cube) then the puzzle is solved.

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 Post subject: Re: Solving the Child's PlayPosted: Tue Aug 03, 2010 1:33 pm

Joined: Wed Jan 21, 2009 12:58 pm
gingervergo wrote:
It's nice to see that people are starting to realize the effort I put into the design of this puzzle. The orientation of the shapes on the puzzle was done deliberately to change the complexity. Maybe I should have done a more detailed explanation of the puzzle. There is still one small thing no one has picked up on yet. As far as I can tell there is only one solution, but I could be mistaken.
Yes, you have put a heck of a lot of effort into this design, every time I take another look at this puzzle, I find something new...

I have found that there are two "loops" of connections between the cubies. In other words, there are two groups of eight cubies that are interconnected (each group of eight is composed of four cubies with raised shapes and four cubies with lowered shapes, so all colors are present). Which means that there are cubies that never interconnect! On top of that, you decided to use only six of the available eight shapes per group. Knowing all of this would really help to find a solution, even if it is a version with no colors. I understand that all these connections can only be mapped out on paper or on one's mind and they won't directly help the solver (unless he/she unglues the pieces from the Eastsheen Minis).

Also, a thought came to mind... Before gluing the pieces to the Eastsheen Minis, you could have connected these two groups of cubies together into two 2x2x2 cubes where the shapes would have been hidden on the inside and these two temporary cubes would have look like simple cornerless cubes (square cross in every face).

Are any of these the "small thing on one has picked up on yet"?

I have mapped the connections to show the two distinct "loops". Let me know if you don't want this graphic here and I will take it down.

(The word "group" is used here loosely and it shouldn't be taken into the advanced meaning of the word)

Skarabajo.

 Attachments: File comment: Child's Play connections showing two distinct "loops" childsplay_connections.gif [ 99.6 KiB | Viewed 1972 times ]

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 Post subject: Re: Solving the Child's PlayPosted: Tue Aug 03, 2010 4:33 pm

Joined: Fri Mar 06, 2009 9:23 pm
Skarabajo wrote:
I have found that there are two "loops" of connections between the cubies. In other words, there are two groups of eight cubies that are interconnected (each group of eight is composed of four cubies with raised shapes and four cubies with lowered shapes, so all colors are present). Which means that there are cubies that never interconnect! On top of that, you decided to use only six of the available eight shapes per group. Knowing all of this would really help to find a solution, even if it is a version with no colors. I understand that all these connections can only be mapped out on paper or on one's mind and they won't directly help the solver (unless he/she unglues the pieces from the Eastsheen Minis).
Skarabajo.

Indeed this is the little secret I was talking about! It's nice o see someone picked up on it. By all means, leave the graphic up. When I start selling these I will provide something similar, and also a full solution.

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--Eric Vergo

My Shapeways shop

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 Post subject: Re: Solving the Child's PlayPosted: Sun Apr 01, 2012 5:36 pm

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
A few month ago I borrowed the Child's Play from Brandon. It's a quite challenging puzzle. So it was sitting on my desk for a long time, before I decided to give it a serious try yesterday.

After about two hours of work I found a solution. Based on it, I also quickly derived another solution: Given any solution, if we swap UFR<->UBL (U "stickers" stay on the U face) and DFL<->DBR (D "stickers" stay on the D face) on cube 1, and swap UFL<->UBR and DFR<->DBL on cube 2, we always get another solution. So the solutions always come in (at least) pairs. If we ignore the color, there are more related solutions.

Then I checked Vergo's video on Youtube. Interestingly, the solution he's got in the video is neither of my solution. For example in his solution there's a triangle on the pure green face, but it's not true in either of my solution.

I'm wondering how many solutions are there? Does any one know? There should be at least four.

Here's one of my solution. In each view, the center square represents the U face. btw I call the orange-red color as "red".

 Attachments: photo 1.JPG [ 105.66 KiB | Viewed 1372 times ]
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