After seeing 16×16 and even 25×25 sudoku grids, Dave and I have joked about the next logical step being three-dimensional sudoku puzzles — a series of nine 9×9 grids that would represent the layers of a 9×9×9 cube, creating 27 intersecting arrays. It would be difficult just to visualize clearly what was going on, of course, which is what made the idea so silly.
It didn’t occur to me, though, that on a computer you could make the intersecting arrays easier to visualize. Someone has gone and created a very attractive three-dimensional sudoku game called 3Doku, and the interface does make it relatively effortless to see what’s going on. You can look at three mutually intersecting cross-sectional views at a time. Double-clicking on a cell instantly brings up the three cross sections that contain that cell, and highlights all the other cells that are in the same line or 3×3 box with that cell (that is, all the cells that cannot contain the same digit). A fourth view shows the entire cube from an angle, and indicates the location of the cross sections you’re looking at in the other three views.
I played it for a while on my commute this morning. It’s kind of pleasant to wander through the grid looking for places where you can make a deduction, but even at the medium difficulty level I think I was averaging maybe one deduction per three to five minutes of searching. With 729 cells to fill instead of the usual 27, and two more difficulty levels above that one, I have the feeling this is the sort of problem you shouldn’t get too wrapped up in without a government grant.
It’s a lovely thing to contemplate, though.
Later: I’ve played more with this, and it turns out it’s not nearly as impossibly time-consuming as I thought it would be. After you get to a certain tipping point, there are enough numbers filled in that there are easy deductions to be made all over the place.
Even after you get to that point, though, there are hundreds of cells yet to be filled in, which is an awful lot of tedious mopping up to do.