Creation tools for spicy sudokus.
Spicy Sudokus? What's spicy about them?
Let's start with some non-spicy sudokus (the Korma of sudoku, if you will). Everyone knows about our venerable friend, the classic 9x9 sudoku:
But most sudoku enthusiasts will know that this isn't the only possible sudoku shape. We can also create 4x4 and 6x6 sudokus (i.e. the boxes are 2x2 and 2x3 respectively). However, these smaller puzzles are generally easy to the point of being boring. So easy, in fact, that I don't feel bad about not providing solutions 😉:
There are more square sudokus (16x16, 12x12, etc.), but they tend to be tedious to solve and aren't actually very spicy (perhaps something like a Pasanda).
Here's the thing: there's nothing about the definition of a sudoku that requires it to be square. Obviously, square sudokus are easy to print and visualise, but squareness is an arbitrary limitation imposed by humans. Computers, on the other hand, have no such qualms. And since this project is about programming computers, let's say goodbye to arbitrary restrictions and see what comes out!
At the end of the day, a sudoku is simply a set of cells. These cells are split into groups (usually rows, columns or boxes) where digits can't be placed into two different cells which share a group. For example, our venerable 9x9 has 81 cells and 27 groups (9 rows, 9 columns and 9 boxes). But why limit ourselves to square grids? Surely any set of equally sized groups is a sudoku?
Almost. Well technically, yes - by our definition they are all sudokus. But as humans, it would be nice if we could actually print the sudokus (onto paper or just the screen) for us to solve.
It's worth noting at this point that Kuudos itself doesn't care what we give it - it will happily generate and solve puzzles with any shape you feel like throwing at it - but it may be next to impossible for a human to digest the results if they can't be printed.
The easiest way to spice things up a little is to keep grouping our cells into boxes, but allow these boxes to be arranged in something other than a square grid. Thus, boxes now become quadrilaterals and we have already unlocked new possibilities, such as the 'star':
Here, each row/column is slightly curved, but the rules are still the same: digits can't be repeated in a box, and rows and columns are generated by following the opposite sides of edges. More complex and interesting shapes are also possible, such as the 'tear-drop':
<insert teardrop>
Whether or not these shapes are easy to solve is debatable (the star definitely is), but they are at least semi-intuitive for humans. I think that these are something equivalent to Tikka - a bit of a tingle for the little grey cells but really nothing too spicy.
As a fun aside, it turns out that both of these shapes are incredibly over-defined - i.e. there are very few ways to actually fill the cells with digits without violating one of the group constraints.
All the solvers in Kuudos are essentially searching all the possible ways of filling the puzzle grid (and faster solvers are only faster because they are better at skipping parts of the search space). Therefore, if there aren't very many solved grids then it's entirely possible for the solver to simply test them all. And if there's one thing computers are good at it's bashing out this kind of thing at super-speed. Humans, on the other hand, are terrible at this solving method.
And why would we be? There's no fun in blindly guessing solutions to a logic puzzle.
Couple this with the (relatively) small number of solutions, means that over-constrained are extremely easy for computers to solve, but painfully difficult for us poor humans. To make things even more fun, the puzzle generator in Kuudos tries to make interesting puzzles by taking away as many clues as possible whilst still having exactly one solution. I think you can see where this is going - the solver would merrily take out loads and loads of clues (it thinks: everything's fine, there's still one solution) but the result is nearly impossible for humans to solve.
Anyway, we're not done yet! In fact, we've barely got started...