## nice loops again

Advanced methods and approaches for solving Sudoku puzzles

### nice loops again

Good evening from Greece.. It’s with great interest and admiration that I attend all these conversations and tutorials about sudoku strategies, and I think that without all these extraordinary minds (like Myth Jellies, Jeff, Ronk, Havard, Mike Barker and some others) we would never be able to solve the REALLY difficult sudoku puzzles! I have already printed hundreds of pages out of the forum, in order to study them more carefully. At these days I try to learn everything about x-cycles, but I have a problem: although I learned very well (and I also use) the techniques of Alternative Inference Chains (continuous, discontinuous, grouped cycles etc) I stil can’t clear what other types of cycles are there, and what is in fact the exact / full meaning of Nice Loops – which are their other uses (beyond AICs)? I found the conversations about these strategies in the forum somewhat confusing. May someone of you guys help me distinguish and clearing these things? Thanks in advance.
andre43

Posts: 16
Joined: 03 September 2006

Nice Loops and AIC's are just two similar ways of looking at the same reduction.

Nice Loops originated as a means of documenting a bivalue & bilocation plot. It was named such because the lines on the plot that lead to an effective reduction show up as closed loops. Nice Loops uses cells as nodes and uses labelled linkages into and out of the cells. There are a few rules you need to learn to determine which kind of linkages to each cell are appropriate.

Alternating Inference Chains can document all the reductions that Nice Loops do (and vice versa). AIC's are based on the observation that all Nice Loops, as well as coloring, naked and hidden pairs, Almost Locked Sets, Sue de Coqs, finned fish, etc.; can be replicated by following the simple rule of starting and ending with a strong link, and alternating strong and weak links in between. AIC's use candidates as nodes and thus do not need to label the linkages, just note whether a strong (=) or weak (-) inference is being used.

It doesn't much matter which one you use, so try the one that seems most natural to you.
Myth Jellies

Posts: 593
Joined: 19 September 2005

Myth Jellies, thanks for the reply! I think that the key to distinguish the differences between AICs and Nice Loops in general is in your sentence, ” AIC's use candidates as nodes and thus do not need to label the linkages, just note whether a strong (=) or weak (-) inference is being used." As I get it (and, please, correct me if I'm wrong) the AICs (continuous or discontinuous) needs the alternative use of strong and weak links throughout the cycle (including the use of grouped cells as also the use of strong links in the role of strong and/or weak links) while in Nice Loops we don't interest in alternative strong/weak links, as they only focus in the cells as nodes (and not in a particular candidate). This means that we can use the bivalue cells as strong links, which in turn means that we may start the cycle with one candidate and then change it for others n numbers of candidates (whenever we have bivalue cells), ending the cycle in a different number of the starting one.
andre43

Posts: 16
Joined: 03 September 2006

Nice loops trades in the alternating links concept for a slightly more complex set of rules about linkages in and out of cells that in the end amounts to the same thing.
Myth Jellies

Posts: 593
Joined: 19 September 2005