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 Three-dimensional Calcudoku (4x4x4) 
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Posted on: Mon Apr 09, 2012 9:04 pm




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Post Three-dimensional Calcudoku (4x4x4)
In a not far future we will have “3D” screens (virtual) in which we will move and manage the objects and images like in the real world, a much more advanced software than now indeed. As mentioned in the thread “The shape of the cages (structure and names)” (in the section “Solving strategies and tips”), a “3-cell cage” in 3D, for instance, has five different configurations (while in 2D has only two different shapes, 3 cells in-line and 3 in L-shape, excluding symmetries): two of the type “in-line” (one with the three cubes in the horizontal plane and the other “in vertical” like a monolith) and three of the type L-shape: the three cubes in the horizontal plane, the L “in vertical”, let’s say, in its natural position, and the L “in vertical” but in the upside-down position (let’s say “againts the gravity”).

Image

In this “experiment” I show how a 3D Calcudoku (4x4x4) would be. The numbers 1 to 4 must be different in any line, the two horizontal and the vertical, in other words, the x, y, z axis; keeping our actual coordinates system I have introduced a new set of capital letters W, X, Y, Z to define the planes: for instance, the “cells” (cubes) Wb1, Xb1, Yb1 and Zb1 must contain the numbers 1 thru 4, all different, regardless of their sequence.

The Calcudoku is not represented “in perspective”; instead, the horizontal projections are shown, moving them to make them visible (however we can imagine it in the 3D space); in this way these 3D Calcudokus could be developed and solved using our actual means and representations. The colours refer to the “cages” and connect the “cells” of the different planes, for instance, the “24x” in Wb1 along with the light violet colour means that Wb1, Xb1, Xb2 and Yb1 are related by that operator; while the “9+” in Wd1 and the gray colour means that “9+” is relating the “cells” d1-d2-d3 all corresponding to the plane W and without any connection to any other plane. But if you observe Ya1 or Za1, no operation is written on them, this meaning that “any” valid number can be there, these “cells” are individual (not related to any other in accordance to the their individual colour) (this puzzle has not any “Keops hole”, an individual cube totally isolated inside the big cube, though it has a 2-cube “hole”, the one in Yc2-Zc2).

With all the above conditions I believe (I can be wrong) the solution is unique, very easy in this case, but this is just an initial idea on how “in the future” the numerical puzzles could be.


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Posted on: Mon Apr 09, 2012 9:53 pm




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Post Re: Three-dimensional Calcudoku (4x4x4)
Interesting. And I found it to have a unique solution.


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Posted on: Tue Apr 10, 2012 12:09 am




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Post Re: Three-dimensional Calcudoku (4x4x4)
clm wrote:
But if you observe Ya1 or Za1, no operation is written on them, this meaning that “any” valid number can be there, these “cells” are individual

Why leave them as individual? Why not assign an operator and value? To make the puzzle more difficult? They are connected, after all.

I love this idea. Not surprising, perhaps, since it's a different twist on the triplet puzzle idea I've been pushing Patrick to create.

4x4x4 might be the sweet spot for this. I can imagine 5x5x5 much harder but doable, 6 to be exponentially more difficult, and 3x3x3 might need ManyOp/NoOp to be interesting enough.


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Posted on: Tue Apr 10, 2012 3:03 am




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Post Re: Three-dimensional Calcudoku (4x4x4)
I like this idea alot. i think there are two major technical challenges to overcome, that of the graphical interface and that of the user interface.

I wonder if it's possible to do this w/ current standard tech so there can be a non-dirty viewing of the puzzle. As for user interface, most keyboards do not come with Z-axis movement keys. I think it would be fairly easy to map pgup and pgdwn to that function, it would just leave it a little bit awkward to navigate.


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Posted on: Tue Apr 10, 2012 3:02 pm




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Joined: Fri May 13, 2011 6:51 pm
Post Re: Three-dimensional Calcudoku (4x4x4)
sneaklyfox wrote:
Interesting. And I found it to have a unique solution.


Thank for your comments and your verification of the unicity.

jake4 wrote:
clm wrote:
But if you observe Ya1 or Za1, no operation is written on them, this meaning that “any” valid number can be there, these “cells” are individual

Why leave them as individual? Why not assign an operator and value? To make the puzzle more difficult? They are connected, after all.

I love this idea. Not surprising, perhaps, since it's a different twist on the triplet puzzle idea I've been pushing Patrick to create.

4x4x4 might be the sweet spot for this. I can imagine 5x5x5 much harder but doable, 6 to be exponentially more difficult, and 3x3x3 might need ManyOp/NoOp to be interesting enough.


Thank you for your ideas and comments. Not assignning a value is only a possibility, in this case it does not make the puzzle more difficult though certainly some softwares (like the Patrick’s) require those individual values.

I don’t think that this 3D concept is related to the triplets if I am understanding well your idea (from your previous posts on this subject), the triplets use the same distribution of numbers (in three different “puzzles” which work together, “in parallel”, like in the case of the twins) while here every plane has necessarily a different distribution of numbers, interactuating among the different planes.

In the other hand, I think that the triplet perhaps would provide excessive or redundant info, since even the twins give that excess in most cases (I referred to that in my post “The essential info in a puzzle” in the section “Solving strategies and tips”). In fact, you can do this test: Solve the yesterdays’s (Monday, Apr 09, 2012, Puzzle id: 445909) 6x6 difficult (twin) using only the right puzzle of the twin pair and you will see that you will obtain a unique solution (some more work is necessary than using the one in the left of course). Do the same with the Sunday's, Apr 08, 2012, 6x6 difficult (twin), Puzzle id: 445848, using the right puzzle of the twin, with the same conclusions, Patrick might confirm that both have a unique solution regardless of the left part of the twin. Its’ a good practice, even with all twins (5x5’s and 6x6’s) everytime they appear, I would affirm that in the 99% of the cases they can be solved using only one of them. The only thing that the other part of the twin does is making it easy the solution. Consequently, IMHO the triplets are excessive.

Yes, I was thinking of preparing a 5x5x5 for this initial 3D idea, but I had some problems with the graphics, to draw the 5 planes enough near, additionally I liked to initially transmit a very easy to understand idea.

picklepep wrote:
I like this idea alot. i think there are two major technical challenges to overcome, that of the graphical interface and that of the user interface.

I wonder if it's possible to do this w/ current standard tech so there can be a non-dirty viewing of the puzzle. As for user interface, most keyboards do not come with Z-axis movement keys. I think it would be fairly easy to map pgup and pgdwn to that function, it would just leave it a little bit awkward to navigate.


Yes, thank you for your comments, it looks like the graphical presentation can a be a problem. With respect to the interface, if some day one of these 3D puzzles is developed, probably the programmer would invent some other technique, I cann’t imagine that, I’m a very bad programmer.


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Posted on: Wed Apr 11, 2012 7:50 am




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Joined: Mon Mar 05, 2012 12:45 pm
Post Re: Three-dimensional Calcudoku (4x4x4)
If you are going to do it, I'd suggest another navigation feature to consider: The possibility to "rotate" the entire puzzle, i.e. to cut it along a different axis. The rationale is that neighbouring cells in the Z plane are very far from each other in the expanded view, thus it is difficult to see certain things (like that a certain row along Z has just one number missing). The ability to change the view and make those cells visible in a single square would help a lot. This means, of course, that the maker of the puzzle would really prepare three sets of diagrams, and some keys in the keyboard (x-y-z?) would switch between them.


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Posted on: Wed Apr 11, 2012 7:50 pm




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Joined: Fri May 13, 2011 6:51 pm
Post Re: Three-dimensional Calcudoku (4x4x4)
jotempe wrote:
If you are going to do it, I'd suggest another navigation feature to consider: The possibility to "rotate" the entire puzzle, i.e. to cut it along a different axis. The rationale is that neighbouring cells in the Z plane are very far from each other in the expanded view, thus it is difficult to see certain things (like that a certain row along Z has just one number missing). The ability to change the view and make those cells visible in a single square would help a lot. This means, of course, that the maker of the puzzle would really prepare three sets of diagrams, and some keys in the keyboard (x-y-z?) would switch between them.


I totally agree, until we have the "movement" in 3D, a very good alternative would be showing the three sets of diagrams with the projections on the horizontal plane and on the two vertical planes, for instance (as you well say the "cells" in the Z axis are very far in this type of representation and it requires spatial imagination not very intuitive for everybody). If we had the 3D "toy" in our hands to play with, it would be very different obviously.

(BTW, with 81 pieces for the numbers, nine sets of 1 to 9, some "sockets" or "recipients" with different shapes for the cages, and some "operators" to label the "sockets", perhaps an "horizontal" Calcudoku Toy would be an interesting educational toy [biggrin]).


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