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 Author: clm  [ Mon Apr 09, 2012 9:04 pm ] Post subject: 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”). 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.

 Author: sneaklyfox  [ Mon Apr 09, 2012 9:53 pm ] Post subject: Re: Three-dimensional Calcudoku (4x4x4) Interesting. And I found it to have a unique solution.

 Author: jake4  [ Tue Apr 10, 2012 12:09 am ] Post subject: 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 individualWhy 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.

 Author: picklepep  [ Tue Apr 10, 2012 3:03 am ] Post subject: 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.