I solved the 4D sudoku puzzle: 129 543 876 485 762 391 637 918 254 354 687 912 276 139 548 891 425 763 768 291 435 913 854 627 542 376 189 Joseph DeVincentis ---------------------------------------------- Not so unsolvable after all, Ed. :-)) 129543876 485762391 637918254 354687912 276139548 891425763 768291435 913854627 542376189 Nice challenge, though. Cheers, Jon Braunhut ----------------------------------------------- Answer 129 543 876 485 762 391 637 918 254 354 687 912 276 139 548 891 425 763 768 291 435 913 854 627 542 376 189 -- Munira Lokhandwala ------------------------------------------------ 129 543 876 485 762 391 637 918 254 354 687 912 276 139 548 891 425 763 768 291 435 913 854 627 542 376 189 ~ James L Melby ------------------------------------------------- This is a very interesting Sudoku problem. Here is the answer: *---*---*---* *---*---*---* *---*---*---* / 1 / 2 / 9 / / 5 / 4 / 3 / / 8 / 7 / 6 / *---*---*---* *---*---*---* *---*---*---* / 4 / 8 / 5 / / 7 / 6 / 2 / / 3 / 9 / 1 / *---*---*---* *---*---*---* *---*---*---* / 6 / 3 / 7 / / 9 / 1 / 8 / / 2 / 5 / 4 / *---*---*---* *---*---*---* *---*---*---* *---*---*---* *---*---*---* *---*---*---* / 3 / 5 / 4 / / 6 / 8 / 7 / / 9 / 1 / 2 / *---*---*---* *---*---*---* *---*---*---* / 2 / 7 / 6 / / 1 / 3 / 9 / / 5 / 4 / 8 / *---*---*---* *---*---*---* *---*---*---* / 8 / 9 / 1 / / 4 / 2 / 5 / / 7 / 6 / 3 / *---*---*---* *---*---*---* *---*---*---* *---*---*---* *---*---*---* *---*---*---* / 7 / 6 / 8 / / 2 / 9 / 1 / / 4 / 3 / 5 / *---*---*---* *---*---*---* *---*---*---* / 9 / 1 / 3 / / 8 / 5 / 4 / / 6 / 2 / 7 / *---*---*---* *---*---*---* *---*---*---* / 5 / 4 / 2 / / 3 / 7 / 6 / / 1 / 8 / 9 / *---*---*---* *---*---*---* *---*---*---* Kind regards, Dr. Roland Studer --------------------------------------------- Hi Ed, Well done. I hope you enjoyed it. I note that the extra constraints relative to a normal Sudoku do rather restrict the richness of the possible solutions. Here, for instance, you may spot that the top, fourth and seventh rows have 129 543 876, 354 687 912 and 768 291 435 respectively. The corresponding triplets are all cyclic permutations of one another. Thus, if you know, say, that row 1 has 543 in it, you can be sure that rows 4 and 7 must have 354 and 435. The same applies to all triplets in the other rows, columns and other dimensions. This is unavoidable - I'm almost certain it is inherent in the 4D rules. So, it has great elegance and symmetry in being truly four dimensional, but is a less challenging puzzle than the standard Sudoku. But, by analogy with magic squares, where 3x3 is very limited but 4x4 isn't, I imagine a 4x4x4x4 hypercube would have far greater richness. As far as making a good quality puzzle is concerned, I find the "colour number place" with standard Sudoku rules plus sets containing each square in a certain position within a 3x3 block to be the most satisfactory. A similar extension of Sudoku rules is to ask if a Sudoku can be magic, in that every triplet parallel to any of the four axes sums to 15? Well, yes it can: 168 573 924 573 924 168 924 168 573 681 735 249 735 249 681 249 681 735 816 357 492 357 492 816 492 816 357 But, as you can easily see, this is even more constrained, so doesn't make for a rich puzzle. Best wishes Chris Lusby Taylor --------------------------------------------------- see: http://www.sudoku.com/forums/viewtopic.php?p=13485#13485 how the constraints form a graph with the 6 unit vectors in the 6 dimensions. Dimensions 5 appears, when you write the entries 1,2,..,9 in base 3. Dimension 6 appears, when you view the entry itself as another coordinate thus converting it to a nonattacking-pieces-problem. So, I think it should be viewed as 6-dimensional {1,2,3}^6-->{0,1} My computer says there is a single solution: 129543876 485762391 637918254 354687912 276139548 891425763 768291435 913854627 542376189 Guenter Stertenbrink