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.

Post a Comment or Question here...

Tuesday 22-Aug-2006

... by: Larry Murphy, San Francisco

Andrew: Recovering from an operation after 5 days in hospital last year, I took up doing the Sudoku presented in our daily newspaper to assess any cognitive impairmant. After spending an hour or two doing the more difficult daily puzzles, I happened upon your solver site and now use it to save notation time and attack the most difficult versions. Saves a least 45 minutes a day and allows me to really test myself for 15-20 minutes without all the erasure and notation time. I try to not use the strategies beyond the first two steps until I fail to advance. As an occupational psychologist, I have even thought of incorporating Sudoku as a timed cognitive test of logical decision making. Thank you for your wonderful efforts, which I am sure are of great usefulness to many thousands of people, young and old. And happy flying! Cheers, Larry Murphy ps. The time I save is used to try to improve my lawn bowling, cycling, and skiing, and marital communication... extra time in life should never be used to spend more time at the office!

When I click solution count, it correctly gives me three possible solutions. However, if I click step at a time, it resolves to only one solution (In the BUG step it incorrectly eliminates candidates in H3)

2. In the advanced strategies, when it resolves a square, and I click "<<", to go back, and then "take step" to replay, it skips past, ie does not re-resolve it.

Andrew Stuart writes:

Hi Vijay

If your sudoku has more than one solution then the following strategies will create errors or misbehave:

Unique Rectangles, BUG, Empty Rectangles

These three rely on the sudoku being unique. They are called uniqueness arguments. You need to uncheck them. Even then, the solver will only give you one of the possible solutions.

On the Back button this is a known bug which I'm working to solve.

I use the following strategy to help eliminate possibilities.

Looking at the 2,3 chain located at I8, E8, D9, D5, it is possible to eliminate the 2,3 at I5 as follows. The 2,3 at I5 can be reached by both an even and odd number of steps starting at I8 (odd=I8-->I5; Even=I8-->E8-->D9-->D5-->I5; count number of arrows to determine even/odd). Since there is both an even and odd path, the 2,3 can be eliminated from I5. This can be "proved" by assuming that I5=2or3 and "solving" the puzzle to a contradiction.

This may well be a special case of one of the coloring or chain methods, but what is different is the notion of following even and odd number steps from a starting position to show that a possibility can be eliminated.

Note that you do not have to both numbers of the pair-chain in the taget cell where you are trying to eliminate them from. Just one of the numbers will do. For instance, if I5 only had a 2 or 3 (but not both) as a possibility, that single number could still be eliminated using the same logic.

Note the solver uses other strategies to solve this puzzle. The puzzle orginated from Michael Mepham, dtd 8/18/06 in the AZ Daily Star.

#8 is examined regardless of whether the checkbox is checked or not.

Andrew Stuart writes:

Your sudoku seems to contain two 6's in column 5. A typo I think

Friday 18-Aug-2006

... by: Chris Riesbeck, Chicago IL

The "email this board" feature doesn't work for some of the later puzzles like Grouped AIC and Riddle of Sho. The bd value is full of NaN's instead of 0's. Easy to fix with an editor but probably some really simple Javascript bug. The right value is generated for many of the easier puzzles.

Great site. Best collection of strategies and most useful helper/teacher I've seen.

Andrew Stuart writes:

Well spotted Chris. Fixed. Shouldn't have used dots instead of zeros in my example list.

I have a few puzzles that your solver solves via the X-cycles. When I click on the explanation link, there is no explanation of X-cycles. I've looking it up on other sites, like sudoku.org, etc but they do not explain it very well at all compared to how you explain things. I cannot figure out their logic because it is so complicated. Please help if you can (whenever you get free time of course).

I've run this Sudoku through your solver up to this point. The solver then says that the next step/strategy is "Hidden Unique Rectangle", on R1C6:R2C7. The explanation in the box says "Removes 3 from R1C5 because of R21C76 and two strong links on 5" What does this mean? I can't find any explanation in your documentation.

PS That should read :- "Removes 3 from R1C6 because of R21C76 and two strong links on 5" What does this mean? I can't find any explanation in your documentation.

This is from sudoku.com.au and is their Tough Sudoku for 2 August 2006. (Tough is their hardest category.) If one runs the through your solver, one reaches the position in the sudoku linked above. After a few more steps, the solver reaches an alternating inference chain, with the following narrative: AIC Rule 2, on 5 (Alternating Inference Chain, length 10): 3[r1c3]=3[r1c8]-3[r8c8]=3[r8c7]-3[r2c7]=5[r2c7]-5[r2c9]=5[r7c9]-5[r7c1]=5[r3c1]- - Chain ends R1C3 cannot be 5 and R3C1 cannot be 3 I am confused by the narrative and the notation. Isn't the starting point 5[r1c3], not 3[r1c3]? And why conclude that R3C1 cannot be 3, when 3 was never a possibility? To me a better way of understanding it is this: If R1C3=5, then R1C8=3 and then R1C6=1. Then R1C5 is stranded as 4 or 5, with nowhere else for the other 4 or 5 to go. So R1C3 can not be 5. There is no need to go all the way round the board to reach that conclusion.

Andrew Stuart writes:

I'm a bit behind in updating the documentation so I'll get onto that as soon as possible. However, it's worth illustrating this example

- Chain ends R1C3 cannot be 5 and R3C1 cannot be 3

The easy part of the claim is

R3C1 cannot be 3 if R1C3 is 3

R1C3 cannot be 5 is R3C1 is 5

The AIC links these two candidates and it works in both directions. Starting from R1C3, if R1C3 is NOT 3, then R3C1 will be 5, therefore 5 cannot exist in R1C3 (whether 3 is or is not there, 5 cannot be there).

It's not important that there is no 3 in R3C1 but the logic is the same. Starting from R3C1, if R3C1 is NOT 3, then R1C3 will be 3, therefore 3 cannot exist in R3C1 (whether 5 is or is not there, 3 cannot be there).

You're second method is perfectly valid and is shorter. Searching for an AIC, especially with Almost Locked Sets embedded in them - which is your method, can take a long time so in this strategy I return the FIRST solution I find which is rarely the SHORTEST. I would like to find all candidate eliminations and return the shortest but it could take a while. The next update will go a small way to addressing this issue.

I think it's a little unfair of publishers to publish sudoku's requiring AICs since they are a long way from human-solvable using pencil and paper except for the most dedicated.

Friday 11-Aug-2006

... by: Thomas, Germany

Again me; again a question:

the "Take Step" Button is good, so see step-by-step which solution works.

how about a button, which does all strategies on an on, so long untin the sudoku is done or no strategie works ? this will help, if i need a "fast" solution and don´t want to press the Enter-Button again an again, or click 100-time on the Button...

hi... your site ist great ! but i have problems to read the "infos" under the sudoku...

this is not a "bug" but a "thing to make better perhaps": the sudoku is listet in Colums 1-9 and rows from A to J.

in the beginning "#6 Pointing Pairs" works: and the sudoku says: "POINTING PAIR: 9s at C2/C3 points to C4, removing 9 POINTING PAIR: 9s at C2/C3 points to C6, removing 9"

but later for example "#28 almost locked sets" brings some information: "ALS/ALS: [r1c1|r9c1] and [r6c1|r6c3|r6c7], 3 is restricted common, other common candidate 5 can be removed from R4C1 " R means row and C means column. OK. but why don´t write: A1, J1 and F1, F3 and F7 ?

Later on with "#33" the same; "BOWMAN BINGO: R4C6 cannot be 3 because R5C2 and R6C1 are both 3 "

BUT: again: Thank you for your time investet in this site !!! it gave me much, an i´ve learnd much about sudoku !!! Greetings, Thomas...

Tuesday 8-Aug-2006

... by: Paul McIlfatrick, Northern Ireland

Andrew

I reALY like the changes you have made with v1.32 allowing various strategies to be selected/unslected when solving a Sudoku.

Suggestion for a minor enhancement:

As the first thing I do is to untick all of the Tough Strategies, Diabolical Strategies, Evil Strategies, and Trial and Error boxes, I would really appreaciate a tick box for each of these strategies that would toggle between switching them off/on.

Thanks and keep up the great work!

Paul McIlfatrick

Andrew Stuart writes:

That's a good suggestion. I also want to add a checkbox to remove all strategies that assume uniqueness - Unique Reactangles, Empty Rectangles and BUG.

## Tuesday 22-Aug-2006

## ... by: Larry Murphy, San Francisco

## Sunday 20-Aug-2006

## ... by: Vijay, Michigan

Load Sudoku: CLICK TO LOAD1. for the sudoku (see above)

When I click solution count, it correctly gives me three possible solutions. However, if I click step at a time, it resolves to only one solution (In the BUG step it incorrectly eliminates candidates in H3)

2. In the advanced strategies, when it resolves a square, and I click "<<", to go back, and then "take step" to replay, it skips past, ie does not re-resolve it.

If your sudoku has more than one solution then the following strategies will create errors or misbehave:

Unique Rectangles, BUG, Empty Rectangles

These three rely on the sudoku being unique. They are called uniqueness arguments. You need to uncheck them. Even then, the solver will only give you one of the possible solutions.

On the Back button this is a known bug which I'm working to solve.

Thanks for the feedback

## Saturday 19-Aug-2006

## ... by: Arthur Lurvey, Tucson, AZ, USA

Load Sudoku: CLICK TO LOADI use the following strategy to help eliminate possibilities.

Looking at the 2,3 chain located at I8, E8, D9, D5, it is possible to eliminate the 2,3 at I5 as follows. The 2,3 at I5 can be reached by both an even and odd number of steps starting at I8 (odd=I8-->I5; Even=I8-->E8-->D9-->D5-->I5; count number of arrows to determine even/odd). Since there is both an even and odd path, the 2,3 can be eliminated from I5. This can be "proved" by assuming that I5=2or3 and "solving" the puzzle to a contradiction.

This may well be a special case of one of the coloring or chain methods, but what is different is the notion of following even and odd number steps from a starting position to show that a possibility can be eliminated.

Note that you do not have to both numbers of the pair-chain in the taget cell where you are trying to eliminate them from. Just one of the numbers will do. For instance, if I5 only had a 2 or 3 (but not both) as a possibility, that single number could still be eliminated using the same logic.

Note the solver uses other strategies to solve this puzzle. The puzzle orginated from Michael Mepham, dtd 8/18/06 in the AZ Daily Star.

#8 is examined regardless of whether the checkbox is checked or not.

## Friday 18-Aug-2006

## ... by: Chris Riesbeck, Chicago IL

Great site. Best collection of strategies and most useful helper/teacher I've seen.

## Tuesday 15-Aug-2006

## ... by: Ben, Burlington, VT, USA

Load Sudoku: CLICK TO LOADThanks so much for the wonderful site.

Ben

## Sunday 13-Aug-2006

## ... by: Michael, UK

Load Sudoku: CLICK TO LOADPS That should read :- "Removes 3 from R1C6 because of R21C76 and two strong links on 5" What does this mean? I can't find any explanation in your documentation.

I'll be posting docs on this strategy very soon.

## Sunday 13-Aug-2006

## ... by: Ashley Hayman, Manchester, UK

Load Sudoku: CLICK TO LOADAIC Rule 2, on 5 (Alternating Inference Chain, length 10):

3[r1c3]=3[r1c8]-3[r8c8]=3[r8c7]-3[r2c7]=5[r2c7]-5[r2c9]=5[r7c9]-5[r7c1]=5[r3c1]-

- Chain ends R1C3 cannot be 5 and R3C1 cannot be 3

I am confused by the narrative and the notation. Isn't the starting point 5[r1c3], not 3[r1c3]? And why conclude that R3C1 cannot be 3, when 3 was never a possibility?

To me a better way of understanding it is this: If R1C3=5, then R1C8=3 and then R1C6=1. Then R1C5 is stranded as 4 or 5, with nowhere else for the other 4 or 5 to go. So R1C3 can not be 5. There is no need to go all the way round the board to reach that conclusion.

- Chain ends R1C3 cannot be 5 and R3C1 cannot be 3

The easy part of the claim is

R3C1 cannot be 3 if R1C3 is 3

R1C3 cannot be 5 is R3C1 is 5

The AIC links these two candidates and it works in both directions. Starting from R1C3, if R1C3 is NOT 3, then R3C1 will be 5, therefore 5 cannot exist in R1C3 (whether 3 is or is not there, 5 cannot be there).

It's not important that there is no 3 in R3C1 but the logic is the same. Starting from R3C1, if R3C1 is NOT 3, then R1C3 will be 3, therefore 3 cannot exist in R3C1 (whether 5 is or is not there, 3 cannot be there).

You're second method is perfectly valid and is shorter. Searching for an AIC, especially with Almost Locked Sets embedded in them - which is your method, can take a long time so in this strategy I return the FIRST solution I find which is rarely the SHORTEST. I would like to find all candidate eliminations and return the shortest but it could take a while. The next update will go a small way to addressing this issue.

I think it's a little unfair of publishers to publish sudoku's requiring AICs since they are a long way from human-solvable using pencil and paper except for the most dedicated.

## Friday 11-Aug-2006

## ... by: Thomas, Germany

the "Take Step" Button is good, so see step-by-step which solution works.

how about a button, which does all strategies on an on, so long untin the sudoku is done or no strategie works ?

this will help, if i need a "fast" solution and don´t want to press the Enter-Button again an again, or click 100-time on the Button...

Greetings from rainy Germany...

Thomas...

## Friday 11-Aug-2006

## ... by: Thomas, Germany

Load Sudoku: CLICK TO LOADbut i have problems to read the "infos" under the sudoku...

this is not a "bug" but a "thing to make better perhaps":

the sudoku is listet in Colums 1-9 and rows from A to J.

in the beginning "#6 Pointing Pairs" works: and the sudoku says:

"POINTING PAIR: 9s at C2/C3 points to C4, removing 9

POINTING PAIR: 9s at C2/C3 points to C6, removing 9"

but later for example "#28 almost locked sets" brings some information:

"ALS/ALS: [r1c1|r9c1] and [r6c1|r6c3|r6c7], 3 is restricted common, other common candidate 5 can be removed from R4C1 "

R means row and C means column. OK. but why don´t write: A1, J1 and F1, F3 and F7 ?

Later on with "#33" the same; "BOWMAN BINGO: R4C6 cannot be 3 because R5C2 and R6C1 are both 3 "

BUT: again: Thank you for your time investet in this site !!!

it gave me much, an i´ve learnd much about sudoku !!!

Greetings, Thomas...

## Tuesday 8-Aug-2006

## ... by: Paul McIlfatrick, Northern Ireland

I reALY like the changes you have made with v1.32 allowing various strategies to be selected/unslected when solving a Sudoku.

Suggestion for a minor enhancement:

As the first thing I do is to untick all of the Tough Strategies, Diabolical Strategies, Evil Strategies, and Trial and Error boxes, I would really appreaciate a tick box for each of these strategies that would toggle between switching them off/on.

Thanks and keep up the great work!

Paul McIlfatrick