... by: Dena, US

Load Sudoku: 509200006268719354004865009095480670406970005780056490807020960901607508600098007

Your solver found a unique rectangle with 1s and 7s in R1C2, R1C7, R3C2, and R3C7. I read the explanation on unique rectangles but I still don't understand. Which are the floor squares (only R1C2 has 2 candidates)? Which are the roof squares? Why is only a 1 eliminated? Why is it only eliminated from 1 square? What does it mean when it says 7s are strong candidates?

I love your solver but the explanations sometimes omit information. Maybe if you are really good at Sudoku it is obvious but I'm still a novice.

Thanks for your help!
Andrew Stuart writes (1-Feb-2009):
I've split this type of unique rectangle out because people were not finding the correct strategy page. This is at
/Hidden_Unique_Rectangles
and there is now a link to it from the solver. Hope that helps!

... by: JimF, Australia

Looking at the bottom diagram in the Avoidable Rectangles page, I can see that if you could put an 8 in B4, you would then have two possible solutions for BC47:

5..8 8..5
8..5 5..8

But if you can swap the 5/8 values after the puzzle is finished and still have a valid solution, how could we ever have deduced the values of 5, 8 and 5 for C4, C7, and B7 respectively in the first place? Any 5's or 8's in the bottom two thirds of the puzzle can restrict which columns can contain a 5 or 8 in the top third of the puzzle, but not which rows can contain them. i.e. they can't have any impact upon whether we have 5 in B7 and 8 in C7 as opposed to the other way around. The values of C4, C7 and B7 are dependent upon each other; we need to know one of them to be able to determine the other two. But if we know none of them, then C4/C7/B7 can have values of 5/8/5 or 8/5/8.

So my problem is that I don't see how this particular example could ever occur in real life.

If we undo those three cells, the possibilities for those cells are:

B4: 589 B7: 58
C5: 58 C7: 58

and we can then use the Unique Rectangles algorithm to determine that B4 is 9, which quickly allows lots of other cells to be solved.

Andrew Stuart writes (13-Mar-2009):
Yes and no is the short answer. Here is the orginal sudoku for that bottom diagram:
.8.7...5..9.523.6..........3.6...8.7.58... 62.9.4...1.5..........4.958.7..6...7.4.

There are infact many ways to crack the numbers in those four cells, I just turned off strategies that did so at that point and tried again. I don't have a facility to cycle through all URs for example, the solver only returns the first it finds and then insists on moving on. But yes you can use UR to solve it. However, its very common for strategies to overlap.

I feel ARs stand out more than URs and since it’s a very interesting strategy it's worth documenting. Also note I've not actually added Avoidable Rectangles to the program yet. What I need to do it implement it fully and run through a very large stock to see if it’s a necessary strategy, that is, if it is used when all other URs have been tested for.

Will add to my job pile :)

... by: Seong-OK, Korea

Load Sudoku: 002508100000602000400010008580000019001000300960000045300050001000304000009801400

Hi,

Thanks for an excellent slover. I got a lot of help from your tool..
While I'm trying to solve the puzzle above, your solver stoped after displaying results of pointing pair step..
Would you check if there is any problem in your tool ???

Thanks and Happy new year...

Andrew Stuart writes (11-Jan-2009):
Your Sudoku has 23 solutions, so it will never solve completely with logical strategies. Use the Solution Count button to check is what you enetered is correct or to check if the puzzle is faulty

... by: Stephen Hotchkis, Scotland

Load Sudoku: 800009406060240013000600005026300008380000050400807360908003000610082030203900001

I cant relate your swordfish rationale to solving this puzzle

Also not sure of the significance of the grren and yellow squares
Andrew Stuart writes (4-Jan-2009):
I've been meaning to expand and explain the Swordfish strategy a little better for some time and your example is a good one, so I've used it in the page. Have another look at http://www.sudokuwiki.org/Sword_Fish_Strategy

... by: Wayne, Canada

Congrats on building and sharing this awesome tool. User-friendly, intuitive and powerful - I'm sharing it with all my Sudoku solving friends. Nice job!
Andrew Stuart writes (4-Jan-2009):
Thank you Wayne!

... by: RIZDINA, USA

This site is amazing. In just one day I was able to pick up several new techniques that I was unable to master at other sites. Keep up the great work. I am regular to the site now.
Andrew Stuart writes (1-Jan-2009):
Appreciate the kind words! Have a great new year :-)

... by: julie, Australia

I have just spent many hours on a 5 star rated Sudoku in the local paper. Finally putting into a Sudoku solver I was frustrated to find it did not have a unique solution. You are right what a turnoff. Is there a way of determining if there is more than 1 solution.
Andrew Stuart writes (29-Dec-2008):
My guess is that some puzzle publishers don’t understand the puzzle or don’t know who to check their puzzles. Its also possible you might have transposed a clue incorrectly? Easily done. There is no way to determine how many solutions a puzzle has bar a brute force algorithm such as I employ with the "Solution Count" button.

... by: Ken Rizzo, Ft. Mill, SC - Just South of Charlotte NC

What an incredible Sudoku Site you've put together. Very indepth and detailed in different solving techniques. When I have time I'm planning on reading about the different strategies that you speak about. Your site is so much better than any other sudoku site I've been on. Well done Andrew.
Andrew Stuart writes (29-Dec-2008):
Most appreciated Ken, looking forward to putting lots of new stuff in 2009

... by: joconnor, US - Bailey, Colorado

Hi, In your section on Unique Rectangles it seems to me that you are not saying that the ambiguity results in invalid solutions but that the choices are not self-defined by the existing pattern. In your Type 1 Unique Rectangle you seem to be saying not that either choice of the "deadly pattern" would be wrong as a solution but that the puzzle is improper in allowing such a choice and you are selecting a third alternative (the additional characters after throwing out the deadly duo) as proper. Is this actually the only valid choice or is it simply a third alternative?
Andrew Stuart writes (29-Dec-2008):

Interesting question. It depends on your definition of a proper sudoku. If there are insufficient clues then you will have more than one solution, although any solution that fills the board and satisfies the rules could be said to be a completed sudoku. We make the choice that a sudoku should have only one solution to make it a satisfactory puzzle. Multiple solutions while valid in the logical sense are frsutrating to the puzzle solver who does not expect this nor wishes to find all solutions.

Unique rectangles take advantage of the implicit agreement between the puzzle maker and the puzzle solver that there will only be one solution. Sometimes its explicit - as in my introductions to puzzle books or in my packs. So you could incorporate the statement of one solution into the rules and therefore the deadly pattern leads to 'invalid' as opposed to 'alternative' solutions.

URs are very common in the harder puzzles and well worth looking into, but will break your solving route if the puzzle is faulty, which is why I included the "Solution Count" on my solver as a check.

... by: jbm, California

Many thanks for saving me from that first tedious, time-consuming, boring, mindless step that shows only the possible numbers in each square. Without that lovely shortcut I'd have given up on Sudoku long ago!
Andrew Stuart writes (23-Nov-2008):
Great to know its working for you :-)

... by: Bob Spessard, USA

Why are pointing pairs down the difficulty list. They seem to be much easier to spot than hidden pairs and triples?
Andrew Stuart writes (23-Nov-2008):
The order of the strategies is only roughly in order of complexity, there's a certain amount of user preference and that’s my list. I'd like to offer the chance of re-ordering them but it’s a bit of a programming job. So I don't disagree with you