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Strategies for Popular Number Puzzles
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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. I'm also directing Str8ts feedback here. Please feel free to drop me a note on the side of the page. 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!

Tuesday 18-May-2010

... by: Bob Kukla, Texas, USA

I use your Sudoku solver everyday. It's very helpful.

If you're looking for something else to do to improve it, you could add support for the arrow keys during the entry process. Most important one would be the down arrow but all directions would be valuable.

Keep up the good work!


Andrew Stuart writes:
Not the first to point this out and it’s a good idea. I have to go with what the browser provides in terms of GUI features in their forms and text boxes. A spreadsheet style widget would be overkill and overload an already busy page. I could add a javascript override but it might not be multi browser compatible and could create bugs. So it’s a web page thing I'm afraid. I'll do some research and see if anyone has a good solution. I usually stick with tabbing and enter in horizontal lines.

Wednesday 12-May-2010

... by: Julia, USA

I love the new configurations!! Well worth waiting for.

Sunday 9-May-2010

... by: David G. Stork, California

Your sudoku solver refers to "row 6" when instead it should be "row F".

HIDDEN PAIR: 1/6 in row 6: F6 - 1/3/6 -> 1/6

Andrew Stuart writes:
Sorry for the extremely late reply. You are quite correct. That’s a bug that's been there for quite a number of years. I've updated the javascript. Appreciate the correction

Saturday 1-May-2010

... by: Brad, Michigan

I am new to KenKen, but have been solving Sudoku's for years. I used your Sudoku Solver when I got stuck on really hard ones and when I started using KenKen, I was glad to see that you had a solver for that as well. Your Sudoku solver was fantastic and so far your KenKen solver is great as well. It is easy to use and it is really helping me figure out some of the more advanced KenKen logic. Thanks for providing this. I hope you continue to keep updating it.

Andrew Stuart writes:
Thanks Brad! There are some known and ready-to-go improvements for the KenKen/Kendoku, so it should get better. Appreciate the feedback :)

Sunday 18-Apr-2010

... by: Fred, Belfast

I'm new to Killer and have managed to solve some simple grids to get used to the techniques. Now getting to the more difficult grids and trying to use your solver. However, when I fill the grid and validate it and then send to the solver, nothing seems to happen. Should my new grid replace the demo grid that I see on the home page?

Andrew Stuart writes:
There was a bug that prevented modified or newly entered Killer puzzles being sent to the solver when using Internet Explorer. Seems to work for me now, let me know if there are still problems. Clear your cache if you see no change. Also fixed a bug that sometimes presented chains in the killer solver when it shouldn't have. Appreciate the feedback

Friday 26-Mar-2010

... by: Mike, UK

Used jigsaw solver today and it utilised a technique called "Digit forcing chain" which does not appear on the strategy list shown on the right.

The technique helped to solve the puzzle - just that it is not one of the listed strategies

Andrew Stuart writes:
Correct I'd missed this strategy from the list in Jigsaw. It's very recent. I've now added it and it seems to work fine. This is a document page as well - Digit Forcing Chains

Monday 22-Mar-2010

... by: Charlie, Nebraska

Would you provide an update on the availability of your book, The Logic of Sudoku, please? There are many of us who would like to order a copy. Thank you.

Andrew Stuart writes:
Quite right, I've updated the notice now. I'll be back in the UK end of April and I'll open the shop in the third week. I shoud be able to ship the day after I arrive. Thanks for the prompt

Friday 12-Mar-2010

... by: Bill Richter, Chicago

Andrew, I've always thought of you as a great puzzle-maker, from your days, and your ideas in 10-Jan-2010 about `patterns' vs `trial and error' is fine advice for beginners. But we also need contests for advanced Sudoku solvers, and your `blurry' ideas won't work there. The only reasonable criterion for evaluating Sudoku solutions is the mathematical elegance of the proofs of eliminations: proofs expressed e.g. as chains. That's all anyone ever posts anyway: their proofs. And grading solutions by mathematical elegance usually rules out the Nishio solutions anyway.

The obvious reason to use mathematical elegance rather than pattern spotting as the criterion is to avoid shouting match about who spotted patterns and who asked the question "If I remove/add a number here - what is the consequence?". Furthermore, there is no reason why we should care if folks ask the consequences of plugging in numbers. Chess players do this routinely (If I move my rook, they'll move the bishop, then I can take the pawn), and no one scolds them for it. Our actual opposition to plugging in numbers is that is the inelegant proofs that folks post as a result of plugging in numbers. We want to rule out solutions using inelegant proofs like "I plugged 6 into B5, and 30 moves later, I have two 5s in box 8, so 6 can't go there!" We want simple proofs that we can draw nice pictures of. If we drew a picture of this inelegant proof, we could make the 6 in B5 blue, and candidates turned off red, and andidates turned on green, but we would also need subscripts to show at which time the candidates were turned on or off. That's much more complicated than the pictures your solver draws, and so not elegant.

But let me expand on your point that the line between 'trial and error' vs determinism is blurry. On a hard puzzle, folks often prove a statement X is true by using an OR/NAND chains of the form
A1 OR B1 NAND A2 OR B2 ... An OR Bn,
for statements Ai & Bi, where X NAND A1 and Bn NAND X are true. But how does one find such a useful chain? If the OR statements Ai OR Bi are, say, of the ALS/AAHS form, there may be 10s of thousands of such chains. Nobody is going to form all possible such chains and then see if any of them work. Let's say they start with the first OR statements A1 OR B1. They have to glue another OR statements A2 OR B2 to it, meaning that B1 NAND A2 is true. But that's the same thing as saying that B1 => B2, and that the deduction B1 => B2 is of the ALS/AAHS form, meaning that it's a relatively simple deduction. So we can get into truly ludicrous discussions of whether the solver spotted the ALS/AAHS pattern which gave the OR statement A2 OR B2, or whether the solver _really_ noticed that the deduction B1 => B2 was simple. There's also the ludicrous discussion of whether the solver was looking for a chain which proved X, but that is perhaps a meaningful question, even though we can never know what the solver was _really_ thinking.

So I contend we should just concentrate on the mathematical proofs of eliminations, and leave off considerations of the solver's mental states, which we can't study, can't describe precisely, and shouldn't care about. As examples of elegant mathematical solutions of mine in which I explicitly violated the blurry rules, see my solution of Mepham's puzzle Unsolvable #14 ( and Unsolvable #30 (, which I believe you wrote. It was a nice puzzle, and Steve Kurzhals liked my solution

Andrew Stuart writes:
Thansk for writing again Bill. I'm probablu going to have to pick this up on a page on its own as the issues are quite lengthly, but very interesting.

Friday 12-Mar-2010

... by: sss, usa

Sudoku Solver not working -- giving all sorts of crazy values. I cleared my history and temporary files in IE. Also when load in solver from Daily Sudoku, just blank board.

Andrew Stuart writes:
Pleas clear your cache! 99% of the problems are related to updated scripts

Saturday 6-Mar-2010

... by: Oliver Buckley, London

Load Sudoku:

This puzzle is one grid (top right) from today's Samurai in The Times.
At this stage in solving the puzzle, your Solution Count records three viable solutions. Your main program eliminates two of these by referring to Uniqueness (Type 1), however this is incorrect. The uniqueness referred to cannot eliminate any solution, as both the other two solutions are equally valid and in fact clues from other grids in the Samurai confirm that one of the solutions your Uniqueness strategy eliminates, is in fact the correct one. I suspect there is a bug in the Uniqueness process.

Andrew Stuart writes:
The test for the number of solutions is separate from the solver. The solver assumes uniqueness and will give an unpredictable result when non-unique. All works by design.
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Thank-you everyone for all your questions and contributions.