The New Sudoku Players' Forum

[PhatFingers]

I've found a very simple, [but not] logical technique that I haven't seen elsewhere, that can gain ground even on difficult puzzles. I'm calling it "Clipped-Wing", as it's a close cousin of the X-Wing technique, but with fewer cells.

For any given strip (row, column, or box), if only two cells have a candidate number A in common, and only two cells have a candidate number B in common, and one of those cells has both A and B in common, then you can eliminate any other candidate besides A or B from that intersecting cell.

In the example below, the strip is represented by the fifth row. Within that row, there are only two cells with {3} as a candidate (R5C5, R5C9), and two cells with {6} as a candidate (R5C5, R5C7), and one of those cells (R5C5) is common to both sets. That intersecting cell contains {1356} as candidates, and the candidates {15} can be eliminated from that cell.

Code: Select all

 *-----------*
 |..1|...|5..|
 |7..|.41|2.6|
 |..9|...|3.1|
 |---+---+---|
 |..6|..7|..4|
 |..4|8.9|.2.|
 |3..|4..|...|
 |---+---+---|
 |...|...|4.7|
 |.4.|1.2|...|
 |8..|5.4|9.2|
 *-----------*


{246}    {2368}   {1}      {23679}  {23689}  {368}    {5}      {47}     {89}     
{7}      {358}    {358}    {39}     {4}      {1}      {2}      {89}     {6}     
{246}    {268}    {9}      {267}    {2568}   {568}    {3}      {47}     {1}     
{1259}   {12589}  {6}      {23}     {1235}   {7}      {18}     {3589}   {4}     
{15}     {157}    {4}      {8}      {1356}   {9}      {167}    {2}      {35}     
{3}      {125789} {2578}   {4}      {1256}   {56}     {1678}   {5689}   {589}   
{12569}  {123569} {235}    {369}    {3689}   {368}    {4}      {13568}  {7}     
{569}    {4}      {357}    {1}      {36789}  {2}      {68}     {3568}   {358}   
{8}      {1367}   {37}     {5}      {367}    {4}      {9}      {136}    {2}     


John Pile (aka PhatFingers)
Sacramento, CA

[Jeff]

Hi PhatFingers, That's pretty cool. Could you provide a proof?

[Carcul]

Hi PhatFingers.

This is very interesting, but I think you are not the first person that makes this kind of "conclusion". Can you provide a proof of that? Because I cannot see why "1,5" can be eliminated from r5c5. I would be very interested to see a proof of this.

Regards, Carcul

[angusj]

I've found a very simple

Sorry, nice try but it doesn't hold water (or should I say it doesn't fly ).
Eg: using the same puzzle and same candidate position, try using your technique in row 8 (with candidates 7 & 9).

[Geraldao]

I agree with Carcul. I don't see what prevents you from putting 1 (or 5) in R5C5, 6 in R5C7 and 3 in R5C9.

I'm looking for nice tips for solving hard sudokus. I already have a few ones. I began a few months ago and am really fund of if (I'm not sure that expression exists, sorry for the mistakes, I'm from France and didn't speak english for long ).

Here, sudoku is spreading everywhere !!! Very nice !

Geraldao

[Carcul]

Hi PhatFingers.

Where did you get the puzzle that you have posted above? Its not very easy to reach the solution, with some quite advanced nice loops to be required (at least for me).

Regards, Carcul

[PhatFingers]

Excellent, angusj,

Thanks for your elegant illustration-- clearly I was mistaken. I fell into a classic trap and just didn't recognize it. For it to work, there must be an additional loop somewhere tying the two pairs together.

Carcul -- I found the puzzle on this board some time ago... don't recall who made the original post. It was one of the first puzzles I found where I couldn't solve it using SS, even with hints.

PhatFingers

[PhatFingers]

Carcul -- Any chance you could show me any applicable techniques for finding those loops? Despite my error, I'm still interested in finding a solution... other than finding a mutually exclusive pair, clicking on one of them, and listening for Simple S to either go "bonk" or accept it (or performing a manual equivalent of that T&E technique).

[Carcul]

Hi PhatFingers.

Do you me to post the solution or to indicate you some tips?

For now, here go some good links. Try this link , this one , this one , and this one .
Here is a thread where I have posted 6 exercises for applying some loops.

Regards, Carcul

[bennys]

Here is a tip

Code: Select all

+----------------------+----------------------+----------------------+
 | 246    2368   1      | 23679  23689  368    | 5      47     89     |
 | 7      358    358    | 39     4      1      | 2     *89     6      |
 | 246    268    9      | 267    2568   568    | 3      47     1      |
 +----------------------+----------------------+----------------------+
 | 1259   12589  6      | 23     1235   7      | 18    *3589   4      |
 | 15     157    4      | 8      1356   9      | 167    2     %35     |
 | 3      125789 2578   | 4      1256  ^56     | 1678  *5689   589    |
 +----------------------+----------------------+----------------------+
 | 12569  123569 235    | 369    3689   368    | 4      13568  7      |
 | 569    4      357    | 1      36789  2      | 68     3568   358    |
 | 8      1367   37     | 5      367    4      | 9      136    2      |
 +----------------------+----------------------+----------------------+

[PhatFingers]

Thanks, Carcul. Very good explanations, by the way. I've been spending a lot of time slicing and dicing Sudoko into little charts on a spreadsheet, trying to understand how things work, when reading the forums would have been a better use of my time! This technique of using "nice loops" seems so much more robust and elegant a technique for solving. Looked like hairy scary voodoo magic the first time I saw it, but all the illustrations and examples are overwhelming my initial fears .

Bennys-- I think I'll need to read a bit in the forums before I understand your tip. Not sure what the symbols '*', '%', and '^' represent.

[bennys]

They don't represent anything
just that if r6c9=5 then the %cell will be 3 and the ^cell will be 6
and all that will eliminate 5 3 and 6 from the * cells and you will have tree cells that will have only 89 as candidates and that impossible.

[ronk]

Code: Select all

 246   2368  1     | 23679 23689 368   | 5     47    89
 7     358   358   | 39    4     1     | 2    *89    6
 246   268   9     | 267   2568  568   | 3     47    1
-------------------+-------------------+----------------
 1259  12589 6     | 23    1235  7     | 18   *3589  4
 15    157   4     | 8     1356  9     | 167   2    %35
 3     1257892578  | 4     1256 ^56    | 1678 *5689  589
-------------------+-------------------+----------------
 12569 123569235   | 369   3689  368   | 4     13568 7
 569   4     357   | 1     36789 2     | 68    3568  358
 8     1367  37    | 5     367   4     | 9     136   2

if r6c9=5 then the %cell will be 3 and the ^cell will be 6
and all that will eliminate 5 3 and 6 from the * cells and you will have three cells that will have only 89 as candidates and that impossible

I didn't recognize it at first, but that's an example of your 2 ALS 2 restricted common rule:

Code: Select all

If A have degrees of freedom of 2
and B and C are ALS
with
x restricted common to A and B
y restricted common to A and C
and z common to A B C
then you can't have z in a cell that can see all the z candidates in A B C

A = {r2c8, r4c8, r6c8}, B = {r5c9}, C = {r6c6}
x = 3, y = 6, z = 5
which implies r6c9<>5

... but looking at it from the viewpoint of "if r6c9=5, then ... contradiction" is definitely easier to understand.