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 andrew@str8ts.com.

Hi, Andrew. This is a great site-it has turned me into a sudoku fanatic. I'm confused about x-cycles where strong links are considered weak. Can all strong links be considered weak when convenient to achieve candidate elimination? In the above puzzle your solver eliminates 7 at d3 as it has weak links to f1 and g3. I think f1-d3 is strong. Why am I wrong? Anyway, its all great fun. Geoff

Andrew Stuart writes:

You are right, have a look at the bottom section of this page: http://www.scanraid.com/X_Cycles_Part_2 I explain all there

Friday 3-Oct-2008

... by: RL Purple, UAS, Minnesota

Thank you. You have given a retired old professor a lot of insights and pleasure on taking up this hobby.

Andrew Stuart writes:

Thank you sir! My pleasure

Best of luck

Andrew Stuart

Tuesday 23-Sep-2008

... by: Larry orrick, U S

Would like to suggest you offer the option to print the "possibilities" along with the puzzle after buying the Puzzle Pack. This would save time as I don't like the job of doing that busy work. Thanks Larry

Andrew Stuart writes:

I've thought of that as well. It would not be appropriate for gentle or moderate puzzles since it would give away too many solved cells, but for diabolical and extremes, it might work. It would mean doubling up the puzzle packs or making them twice the size. That could be done if there was sufficient demand. Otherwise, I could provide a text file with the puzzles to link to the solver, Take Step once would give you the same effect

Sunday 21-Sep-2008

... by: John Robinson, Western North Carolina

Would it be possible to make the daily sudoku saveable and to be able to print out the puzzle plus the possible candidates that I have inserted? Thank You, JR

Andrew Stuart writes:

You can use the Email This Board function to save your sudoku at any stage of solving. Follow the instructions to copy into an email message and send the message to yourself.

It may be time to replace your brute force solution counter with a more efficient algorithm. It works fine in most cases, but the worst case is terrible. The maximum number of recursions for a valid sudoku is probably 15-30 billion, which is about a thousand times more than your counter can handle before is produces a "timed out" error.

Solving singles first and then bi-value cells reduces the number of recursions considerably (but each recursion takes longer time). I will include a counter is the next version of my own solver (Java applet), but I haven't decided yet how to implement it.

The example is a permutation of no. 32632 from Gordon Royle's list (of 47793 puzzles with 17 given) which requires 14,724,893,706 recursions.

Andrew Stuart writes:

Yes, the brute force algorithm could definitely be improved by having it solve as many squares as possible using basic strategies before applying the brute force approach. Your example solves completely using basic strategies, but times out using "Solution Count." As a workaround for the time out error, until "Solution Count" is made more efficient, I suggest using "Take Step" to solve a few squares and then try Solution Count again.

Thursday 11-Sep-2008

... by: PaulyPitts, New Jersey, USA

Would it be possible to add a button that would yield the instant puzzle solution ready for printout? While I'm working on a puzzle, like to verify my individual square solutions to check on my work. I also find this very instructive because it gives me instant feedback if my logic is faulty. If there was one button to click that would present the solved puzzle for printing, it would be of great help.

By the way, your Sudoku site is the very best. It just keeps on getting better and better. Keep up the good work.

PaulyPitts

Andrew Stuart writes:

I don't plan to add an "Instant Solution" button. However, click "Solution Count" and copy the solution string. Open a second solver window and click Import a Sudoku. Paste the string and click OK. Click either the Print 1 or Print 2 button and then print the page with the solution.

Consider 2 pairs; not in a box and not on any on any line. Those 2 pair define a square. The other two corners of the square cannot contain any possibilities of members of the pair.

Andrew Stuart writes:

That's an interesting observation but I don't think it is always true as a general principle. I've picked a random diabolical to look for an example:

D1 and E9 is the pair. E1 contains a 6/8 as well. It forms a short Remote Pair chain and E1 must contain a 6 or 8 as they are the only candidates left. Our pair must contain the same number (either 6 or 8).

So while both opposite corners of the pair cannot contain BOTH numbers they can contain ONE of the numbers - which one though cannot be determined without other strategies.

I have a question about "single's chains, type 1". I'm trying to solve the above puzzle, but I don't understand why the 8 is removed from D9 and not from the another of the cells in the chain (D2, G2, H3, H9)?

With another words, if I start the chain at D9->H9->H3->G2->D2, why is not the 8 removed from D2? (D2 = 8 in the solution and the solution count = 1)

Arne

ps. The puzzle is from a Sudoku-book

Andrew Stuart writes:

Do have a look at http://www.scanraid.com/Singles_Chains Which explains it more fully, but your example is a nice clear one. Either the two YELLOW cells will be the solution or the two BROWN cells will be. We don't know which was round. But that means any 8 that can see both colors can't be a solution. It can be removed. Type 1 works off the chain.

Sunday 10-Aug-2008

... by: Bernard Skehan, USA

This is the very best site on sudoku. It is better than any of the published books. I hope that someday you put all this in a book form, which would help when studying the strategies.

Please keep up this site, it is invaluable to beginners and advanced players.

Andrew Stuart writes:

Thanks Bernard!

Saturday 28-Jun-2008

... by: Doug, Hong Kng

Your site is great. Have you produced a solver for the sudoku puzzles where the diagonals also have 1 -9 in them?

## Saturday 4-Oct-2008

## ... by: Geoff, Australia

Load Sudoku: CLICK TO LOADhttp://www.scanraid.com/X_Cycles_Part_2

I explain all there

## Friday 3-Oct-2008

## ... by: RL Purple, UAS, Minnesota

You have given a retired old professor a lot of insights and pleasure on taking up this hobby.

Best of luck

Andrew Stuart

## Tuesday 23-Sep-2008

## ... by: Larry orrick, U S

Thanks

Larry

I've thought of that as well. It would not be appropriate for gentle or moderate puzzles since it would give away too many solved cells, but for diabolical and extremes, it might work. It would mean doubling up the puzzle packs or making them twice the size. That could be done if there was sufficient demand. Otherwise, I could provide a text file with the puzzles to link to the solver, Take Step once would give you the same effect

## Sunday 21-Sep-2008

## ... by: John Robinson, Western North Carolina

Thank You, JR

## Wednesday 17-Sep-2008

## ... by: Mats Anderbok, Sweden

Load Sudoku: CLICK TO LOADSolving singles first and then bi-value cells reduces the number of recursions considerably (but each recursion takes longer time). I will include a counter is the next version of my own solver (Java applet), but I haven't decided yet how to implement it.

The example is a permutation of no. 32632 from Gordon Royle's list (of 47793 puzzles with 17 given) which requires 14,724,893,706 recursions.

## Thursday 11-Sep-2008

## ... by: PaulyPitts, New Jersey, USA

By the way, your Sudoku site is the very best. It just keeps on getting better and better. Keep up the good work.

PaulyPitts

Lastly, thanks for the compliment!

## Sunday 31-Aug-2008

## ... by: pjf, Ontario, Canada

Load Sudoku: CLICK TO LOADConsider 2 pairs; not in a box and not on any on any line.

Those 2 pair define a square.

The other two corners of the square cannot contain any

possibilities of members of the pair.

That's an interesting observation but I don't think it is always true as a general principle. I've picked a random diabolical to look for an example:

D1 and E9 is the pair. E1 contains a 6/8 as well. It forms a short Remote Pair chain and E1 must contain a 6 or 8 as they are the only candidates left. Our pair must contain the same number (either 6 or 8).

So while both opposite corners of the pair cannot contain BOTH numbers they can contain ONE of the numbers - which one though cannot be determined without other strategies.

## Wednesday 13-Aug-2008

## ... by: Arne Hajonides, Wilnis, Netherlands

Load Sudoku: CLICK TO LOADTo start with, this is great site.

I have a question about "single's chains, type 1". I'm trying to solve the above puzzle, but I don't understand why the 8 is removed from D9 and not from the another of the cells in the chain (D2, G2, H3, H9)?

With another words, if I start the chain at D9->H9->H3->G2->D2, why is not the 8 removed from D2? (D2 = 8 in the solution and the solution count = 1)

Arne

ps. The puzzle is from a Sudoku-book

http://www.scanraid.com/Singles_Chains

Which explains it more fully, but your example is a nice clear one. Either the two YELLOW cells will be the solution or the two BROWN cells will be. We don't know which was round. But that means any 8 that can see both colors can't be a solution. It can be removed. Type 1 works off the chain.

## Sunday 10-Aug-2008

## ... by: Bernard Skehan, USA

Please keep up this site, it is invaluable to beginners and advanced players.

## Saturday 28-Jun-2008

## ... by: Doug, Hong Kng

http://www.sudokuwiki.org/SudokuX.htm