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Strategies for Number Puzzles of all kinds
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Feedback and Questions

I've received a lot of interesting comments and questions from Sudoku fans over the last few years and this page is where I try to answer them. Please feel free to drop me a note on the side of the page or try the Facebook comment box. Or you can email me directly at .

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Many thanks to all the people who have helped improve the solvers and strategies with their feedback!

Friday 10-Apr-2015

... by: sundaresan, india

DEAR Mr.Andrew
WELL, THIS IS WONDERFUL.a complete one. I thankyou for the amazing guide opens all the doors. I donot think no more tips and tricks around.

thank you friend


Wednesday 8-Apr-2015

... by: LWNK, USA

Still...all daily killer suduko in archive are "GENTLE" please inspect your links.

Andrew Stuart writes (10-Apr-2015):

Yeah sorry about that. Upgraded the backend and didn’t pass a value. Fixed now

Saturday 28-Feb-2015

... by: Dale E. Kloss, Portland, Oregon, USA

About Unique Rectangles(I happen to like them)- I once read a statement(maybe this website) to the effect that Unique Rectangles can never be the only way left to solve a puzzle at a bottleneck and that there always has to be a way to solve them using some other strategy.

Is that true? it seems likely but I have always wondered.
This seems to be related to finding a U.R. exemplar.

Thanks. Dale Kloss

Andrew Stuart writes (2-Mar-2015):

There may be a tiny number of puzzles which are unsolvable using the strategies/implementation I have in my solver after you turn off UR strategies. I'd have to run quite a large test suit to know for sure. But I don’t know every possible logical strategy yet - no one does, so its impossible to state what % are true for your statement. But usually there are several ways to kin the cat at any one stage. Any strategy, unless it is wholly a sub-set of another - will increase the hit rate, even if only by a tiny amount

Tuesday 24-Feb-2015

... by: Chuck, Virginia

Load Sudoku:

Hello Andrew,

I have 2 questions. The first concerns the X-Cycles (Part 2) description. The third paragraph has a line that reads "Discontinuity' doesn't mean that the loop is broken or that it's a chain." Am I incorrect in thinking that it should read "Discontinuity' doesn't mean that the loop is broken or that it's NOT a chain"?

My second question concerns the Sudoku that I have included. If you select only the X-Cycle strategy and then step through the puzzle until it stops on the X-Cycle, everything looks good. Now, do a back step, deselect the X-Cycle, select Grouped X-Cycle, and do a step. The solver stops with the exact display as before, but the description at the bottom states that it found a Grouped X-Cycle. Is this a mistake in the solver?

Thanks for taking the time to look at this. I love your site and recommend it to all my friends and acquaintances that are in to Sudoku.

Chuck Bruno

Andrew Stuart writes (2-Mar-2015):

I'll go with that typo suggestion, makes more sense.
Grouped X-Cycles includes all X-Cycles so yes if you turn the first off then a normal X-Cycle will turn up in the grouped one. I suppose I could filter them but what I am doing is performing a search with additional flags (yes to grouped cells and other types of links) rather than negatively filtering the first. Grouped X-Cycles is a super set of X-Cycles

Wednesday 18-Feb-2015

... by: Mark, Australia

Hello, Andrew.

Thank you for creating and maintaining this website. Being shown how to solve a given puzzle, step by step, is wonderfully educational! In just a few minutes, with your step-by-step solver, I have learned more than I'd learned in hours, poring over static examples at other websites. Thank you for freely sharing this functionality!



Andrew Stuart writes (19-Feb-2015):

Very glad you like, thanks for the feedback!

Saturday 14-Feb-2015

... by: FallsOffRocks, UK

I've read your comments on simple colouring several times now and cannot get a handle on the significant difference between your rule 4 and rule 5.

Surely Rule 4 is just a constrained subset of Rule 5, with the constraint being that the two coloured candidates that the candidate to be eliminated can see must be in the same unit as the candidate to be eliminated?

I cannot really see a separate justification for rule 4.

Andrew Stuart writes (15-Feb-2015):

This is a very good observation, and I think you have to be a programmer trying to build the algorithm to spot this, so congrats. I'm certain Rules 4 came a long first and then - much later - further eliminations were spotted that Rule 4 failed to get and led to rule 5. What didn’t happen was a consideration that this rules was a super-set of another. Anyway, I've taken a couple of examples with plenty of instances of Simple Colouring and 3D Medusa and satisfied myself that Rules 5 does get all rules 4 instances plus it's addition ones.

This one had 2x Rules 4 and 2x Rules 5 3D Medusas, but I'm patching the solver tonight, so you wont see them unless yr quick. It now shortens the solution path.

This puzzle has many Simple Colorings - only the last right at the end does the new rule get two 4s instead of one.

Basically, all I need to do is remove the code for Rule 4 and let Rule 5 do the job. That's awkward because I now have to rename Rule 5 to Rule 4 and Rule 6 to Rule 5. Can't have a gap in the sequence. I'll try to update the documentation on Simple Colouring and 3D Medusa at the same time.

I'd be delighted to credit you on the pages.

It's rare to find a simplification, it's normally the case I have to add a complication

Friday 13-Feb-2015

... by: FallsOffRocks, UK

Thanks so much for the site and all the work that must have gone into it.

I was validating my own solver and loaded up your Y-Wing example. My own Y-Wing algorithm clearly scans in a different sequence from yours, as it showed up a completely different Y-Wing, a very nasty one to spot without assistance. Just rotate the puzzle and your solver gets the nasty one first.

Now I have to start on the chaining methods :(

Andrew Stuart writes (14-Feb-2015):

Yes, there are usually several examples of strategy X at any one point, and it depends on the search order. I'm sure you are going top left to bottom right and 1 to 9, which seems natural, but from then on it really depends on your pattern identifier. For chains I create a list of all possible chains and rank them according to "best", which is a set of rules about how long the chains are, how many eliminations they make, if they give a single cell solution, if they contain awkward links like grouped cells or ALSs. So there is a lot in the air and no two solvers will match.

Ideally I'd like to give the user an option to scroll through all the instances of a given strategy but it would greatly complicate the UI.

Monday 9-Feb-2015

... by: 0t0, europe

Load Sudoku:

I've found a Sudoku with a step with 16 solved cells at once:
My first 3D Medusa Sudoku!

Andrew Stuart writes (12-Feb-2015):

A very pretty Medusa! Nice catch

Monday 2-Feb-2015

... by: dan, florida

I'm doing one of your puzzles, a moderate one. but the solver has to use "diabolical" strategies.
How can it be moderate if you have to use xychain or some other diabolical method to solve?

Andrew Stuart writes (12-Feb-2015):

A single instance of a hard strategy does not a hard puzzle make. These are two different spectrums. It is possible to make trivial puzzles with a single very hard step (a bottleneck) and I try and filter those out when selecting for publishing, as they don’t make good puzzles. They are useful as exemplars, eg see X-Wings

Do let me know what puzzle it was, if you can find it again, I'd be happy to take a look at it.

For a fuller idea of how grading works, take a look at this write up.

Monday 2-Feb-2015

... by: anonym, europe

Kakuro is my FAVOURITE of logic number puzzles. I'm missing Kakuro Solver.

Andrew Stuart writes (12-Feb-2015):

There is some demand for that, and I do make those puzzles, but not quite enough yet to make a solver. On my wish list as well

Friday 23-Jan-2015

... by: DeBo, Germany

This is one of the best (may be: The BEST) solvers I have any seen.

Andrew Stuart writes (28-Jan-2015):

Thanks Debo.
Will be ten years old in May. Had a lot of helpful comments aloing the way, and much encouragement
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