cheesemeister wrote:afraid you raised more questions than you answered with that; what are turbot and nishio?

Turbot fish was first described

here by Nick70. It's a simple pattern to spot, but it's also just as easy to spot with complete coloring.

Nishio is a limited form of trial and error that tries to place a digit, and then looks to see if it can place the remaining positions for that digit based on "single" rules. If it finds a contradiction, the placement is invalid. It can also tell you if, for example, all possible placements of 2 in row 3 lead to a 2 being in (8,6), or if all possible placements of 5 in column 1 eliminate 5 from (4,2).

and whats different about supercolouring to the kind of colouring in the program simple sudoku

Well I haven't used simple sudoku, so I can't speak to that, but I can tell you the difference between simple coloring as commonly practiced,

complete simple coloring, and advanced coloring (which is also called supercoloring, multicoloring, ultracoloring, etc.).

Traditionally simple coloring involves taking the candidates of just a single digit, and then finding all sets of conjugates that you possibly can. If a color appears twice in the same house (box/column/row), it's false, and its conjugate must be true. If a color appears alongside two others that are conjugates (i.e., if b shares a house with a, but it also shares a house with A), it is also false. You can also look for colors which must be equivalent; if x and y appear together, and x' and y' (their conjugates) also appear together, then x=y' and x'=y. Finally, this form of coloring can also make eliminations based on places where conjugates intersect: For example, if you have x in (5,1) and x' (x's conjugate) in (9,6), you can't have the digit at (5,6) or (9,1).

Complete simple coloring, which is the form I've recently started using, operates on some extra rules used in supercoloring; in spite of that it's not hard. It looks at colors that share the same house, and says they exclude each other. For example if x and y are together, x!y. If one is true, the other must be false; nothing says either one is necessarily true, but at least one of them is false. Now with exclusions, if x!y, and y'!z, then x!z. You can say this because if x is true, y is false, and y's conjugate y' must be true; since y'!z, z must then be false. Complete simple coloring makes the following observation: If x!y, then x' or y' or both must be true. Therefore any placement where x' and y' intersect must be false. If that placement is labeled with a color, the entire color is false. I don't think many people do coloring this way, which is why I felt free to name it. If you're going to bother to use coloring, this is really the way to go, though, since it's not much harder to use this exclusion rule and it finds things you otherwise won't.

Supercoloring does not restrict itself to one digit; you don't color an entire cell, but merely a candidate. It can find conjugates not just in a box, column, or row, but also in a single cell with only 2 candidates. It uses the same logic rules as complete simple coloring. Typically I find this ends up with around 15-20 conjugate pairs (that's 30-40 colors!), and it's up to you to calculate the exclusions. Once you've calculated exclusions, you may notice that one of the colors excludes itself, in which case it is false. You can also look for intersections as in complete simple coloring, which may be difficult but is doable. This can provide some interesting insights, such as: "Either (4,1)=2 or (4,7)=5, or both. Therefore, (4,1)<>5, and (4,7)<>2."