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Creating Sudoku 3x3x3x3
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Let's take another look at this: [code] cube0: 012 120 201 201 012 120 120 201 012 120 201 012 372 480 561 804 615 723 156 237 048 [/code] How did I come up with that in no time at all? Because I've done the 2d version a long time ago. Plus I have been playing with latin squares and orthos on-n-off for a few years. Interesting little basterds, aren't they? The very first square is just a regular 3x3 latin square. The one to the right of it, the one in the middle, is just the first square with +1%3. And the last square, top row on the right, is another +1%3 (or +2%3 on the first square). And then we have the ortho all by itself in it's own row. It is orthogonal to the first square. And, because of how the top row was created, it is also orthogonal to the other two in the top row. That lonely little ortho is orthogonal to all squares in the top row. Pretty slick, eh? So, what's the deal? Well, going to use that lonely little ortho as a mask of sorts. Copy the nums, in a matter of speaking, and put it all together. Follow this: [code] phase0: ..2 ..0 ..1 .0. .1. .2. 1.. 2.. 0.. ..0 .0. 0.. ..2 ..0 ..1 .0. .1. .2. 1.. 2.. 0.. [/code] That was 0 in the ortho mask for (0,1,2). Let's do the next phase for (3,4,5): [code] phase1: 0.. 1.. 2.. ..1 ..2 ..0 .2. .0. .1. 1.. ..1 .1. 3.. 4.. 5.. ..4 ..5 ..3 .5. .3. .4. [/code] And now the last phase for (6,7,8): [code] phase2: .1. .2. .0. 2.. 0.. 1.. ..0 ..1 ..2 .2. 2.. ..2 .7. .8. .6. 8.. 6.. 7.. ..6 ..7 ..8 [/code] Okay, we got all that. Now let's put it all together: [code] ..2 ..0 ..1 .0. .1. .2. 1.. 2.. 0.. 3.. 4.. 5.. ..4 ..5 ..3 .5. .3. .4. .7. .8. .6. 8.. 6.. 7.. ..6 ..7 ..8 372 480 561 804 615 723 156 237 048 [/code] Latin squares, ortho, and modulo magic = awesome sudo sub-cube. But I made 3 of these, and all I changed was the ortho. For changing the ortho, all I did was the exact same +1%3 trick that I used for the first latin cube. These tricks are simple. Baubles, really. And yet something awesome is popping out of the other end. This is why I love the original KPT. A small handfull of simple tricks put together in an amazing way. And I did the above on graph paper. That still cracks me up. Small pieces of understanding making something so much more. Love it. [small](Edited by [url=http://ozoneasylum.com/user/351]warjournal[/url] on 08-12-2019 03:13)[/small]
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