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.

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:

I've split this type of unique rectangle out because people were not finding the correct strategy page. This is at

and there is now a link to it from the solver. Hope that helps!

Thursday 22-Jan-2009

... 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:

Yes and no is the short answer. Here is the orginal sudoku for that bottom diagram:

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.

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:

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

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:

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

Saturday 3-Jan-2009

... 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!

## Wednesday 28-Jan-2009

## ... by: Dena, US

Load Sudoku: CLICK TO LOADI 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!

/Hidden_Unique_Rectangles

and there is now a link to it from the solver.

Hope that helps!

## Thursday 22-Jan-2009

## ... by: JimF, Australia

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.

.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 :)

## Friday 9-Jan-2009

## ... by: Seong-OK, Korea

Load Sudoku: CLICK TO LOADThanks 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...

## Sunday 4-Jan-2009

## ... by: Stephen Hotchkis, Scotland

Load Sudoku: CLICK TO LOADAlso not sure of the significance of the grren and yellow squares

http://www.sudokuwiki.org/Sword_Fish_Strategy

## Saturday 3-Jan-2009

## ... by: Wayne, Canada

Thank you Wayne!