The New Sudoku Players' Forum

[Yogi]

3.15........3.....74.216.3..8.637.24...982...27.154.8.....9126.....65..861..23.5.
I thought I spotted this 3Kite in Box 6: r6c37/r57c9 which suggests r7c3 cannot be 3.
But the solved puzzle does put 3 in r7c3. Any ideas?

[keith]

Here is what I have:

Code: Select all

+-------------------------+-------------------------+-------------------------+
| 3       269     1       | 5       47      89      | 46789   479     2679    |
| 589     2569    25689   | 3       47      89      | 1456789 1479    125679  |
| 7       4       589     | 2       1       6       | 589     3       59      |
+-------------------------+-------------------------+-------------------------+
| 159     8       59      | 6       3       7       | 159     2       4       |
| 145     356     3456    | 9       8       2       | 13567   17      13567   |
| 2       7       369     | 1       5       4       | 369     8       369     |
+-------------------------+-------------------------+-------------------------+
| 458     35      34578   | 478     9       1       | 2       6       37      |
| 49      239     23479   | 47      6       5       | 13479   1479    8       |
| 6       1       4789    | 478     2       3       | 479     5       79      |
+-------------------------+-------------------------+-------------------------+


It seems you are missing the possibility of 3 in R6C9. There is no kite here.

Keith

[Leren]

Keith was right about the 3 in r6c9 preventing your 3 kite.

Just to remind you here is the kite exemplar that I used in the other kite thread :

Code: Select all

*-------*-------*-------*
| # k # |       |       |
| k / k | / / / | / K / |
| # k # |       |       |
*-------*-------*-------*
|   /   |       |       |
|   /   |       |       |
|   /   |       |       |
*-------*-------*-------*
|   /   |       |       |
|   K   |       |   K   |
|   /   |       |       |
*-------*-------*-------*

Note the absence of a k in r2c2, the one cell in a potential kite box that must not have a k. In your puzzle, that's a 3 in r6c9. The problem is that if there was a k there then you can't be sure that there is a Weak link to the k's in Row 2, because it might be that the k in r2c2 is the True one. In your puzzle it might be that r6c9 is 3, so you can't be sure that r7c9 is 3.

There was a kite to be flown though as illustrated in this PM.

Code: Select all

*---------------------------------------------------------------------------------*
| 3       269     1        | 5       47      89       | 46789   c479     2679     |
| 589     2569    25689    | 3       47      89       | 1456789 c1479    125679   |
| 7       4      a589      | 2       1       6        |b589    **3**    b59       |
|--------------------------+--------------------------+---------------------------|
| 159     8       59       | 6       3       7        | 159      2       4        |
| 145     356     3456     | 9       8       2        | 13567    17      13567    |
| 2       7       369      | 1       5       4        | 369      8      X369      |
|--------------------------+--------------------------+---------------------------|
| 458     35      34578    | 478     9       1        | 2        6       37       |
| 49      239     2347-9   | 47      6       5        | 13479   d1479    8        |
| 6       1       4789     | 478     2       3        | 479      5       79       |
*---------------------------------------------------------------------------------*

Kite (9) r3c3 = r3c79 - r12c8 = (9) r8c8 => - 9 r8c3. Just to belabor the point note the absence of 9 in the cross-over cell r3c8 which I've labelled (or over-labelled) with *s. I've labelled the offending 3 in your non-kite with an X.

Leren

[Yogi]

OK I think I misunderstood Leren when he earlier said that a box can work as a kitebox if it has up to 8 instances of the candidate that you are looking at. I thought this meant I could string from any of the candidate cells in the potential kitebox as long as there was only one instance of the candidate outside of it. That’s why I ignored the possible 3 at r6c9.
Remember I was combining what Leren had suggested with what Keith had said about potential kiteboxes being what he called type-c, in that they had to have instances of the candidate in more than a single row or column.
Notice that I am using visual, pictorial, almost tactile language to describe this situation, not stuff like abc=k. If you want to communicate effectively then you have to find a way to convert what you are thinking into the language of the person you are talking to. There must be many people who won’t try Sudoku if they get the idea that it’s all algebra. For me it’s more like jigsaws or playing with blocks with a bit of logic thrown in. You pick one up from your supply of unused units, put it in its proper place, and then you have fewer remaining options. Simple. But of course to find the proper place you do have to understand the constraints imposed by the placement rules. That brings us to here:

When I am trying to string into my possible kitebox in a ROW, there must be only ONE instance of my candidate in that ROW within the kitebox (and one outside) and similarly when I am stringing in on a column, there can only be one instance of my candidate in that column within the kitebox. And this would be true no matter how many instances of the candidate there may be in the kitebox.

Is That it?

[Leren]

yogi wrote : When I am trying to string into my possible kitebox in a ROW, there must be only ONE instance of my candidate in that ROW within the kitebox (and one outside) and similarly when I am stringing in on a column, there can only be one instance of my candidate in that column within the kitebox.

Code: Select all

*---------*-------*--------*
| #  k3 # |       |        |
| k1 X k2 | / / / | / Ka / |
| #  k4 # |       |        |
*---------*-------*--------*
|    /    |       |        |
|    /    |       |        |
|    /    |       |        |
*---------*-------*--------*
|    /    |       |        |
|    Kb   |       |   Kc   |
|    /    |       |        |
*---------*-------*--------*

I'll run through this one more time. You can have up to TWO instances of the Kite digit in the Kite box in both the row and column. There is one position in the Kite box that can't have a K and that is at the junction of the row and column Kite strings, which I've now shown as X in the amended Exemplar above. What you are trying to prove is that at least one of Ka and Kb must be True, so Kc must be False and can be eliminated.

So assume Ka is False. Since this is the only k outside of the Kite box in the row, one of k1 and k2 must be True. You don't have to know which one it is, it means that k3 and k4 are both False, so Kb must be True.

You can reverse this argument, start by assuming Kb is False and conclude that Ka must be True.

But imagine what would happen if there was a k in the Kite box at X (call it k5) . If you assume Ka is False, then one of k1, k2 and k5 must be True. You don't know which one it is, but what if it happens to be k5. Since k5 could be True and is also in the Kite column you can't definitely conclude that Kb is True, so the Kite argument collapses.

You can have one or two k's in the Kite box in the row and column and the argument would still work, for example k1 and/or k3 could be missing; k2 and k4 alone would be enough for a valid Kite pattern. Similarly k2 and/or k4 could be missing.

Leren

[keith]

With all due respect, I think you're coming at this backwards.

Please study Havard's classic post:

Strong Links for Beginners

After that, we can get on to grouped strong links, and I think your questions will be answered.

Or, looking at Leren's posts, he may be proposing an Empty Rectangle. Which is quite valid, but it is not a kite or skyscraper.

Keith

[pjb]

A case of barking up the wrong tree. This puzzle is quite hard if one confines oneself to kites or other kinds of chains. However, there is a beautiful swordfish of 9s at r369c379 that solves it in one. I usually check firstly for DPs and fish before embarking on chains.
Phil

[Kozo Kataya]

Wonder why not use [single digit] instead of PM which contain lots of number-digits ( too many information ?).
if table A is given, which candidates can be eliminated is easier process as shown in table B.
For instance, if r46c3 are true, r3c79 and r8c12 are true, which cause candidates c8 are all lost (=contradiction).
So, r4c1 is true in Box4 then [stte].
table C shows [*] must be eliminated without reffering any terms like kite, swordfish etc.

Code: Select all

  table A                                table B                              table C
 *---------+---------+---------*       *---------+---------+---------*       *---------+---------+---------*
 |    9    |       9 | 9  9  9 |       |    9    |       9 |         |       |    9    |       9 | *  9  * |
 | 9  9  9 |       9 | 9  9  9 |       | 9  9    |       9 |         |       | *  9  * |       9 | *  9  * |
 |       9 |         | 9     9 |       |         |         |*9    *9 |       |       9 |         | 9     9 |       
 |---------+---------+---------|       |---------+---------+---------|       |---------+---------+---------|
 | 9     9 |         | 9       |       |      *9 |         | 9       |       | 9     * |         | *       |     
 |         | 9       |         |       |         | 9       |         |       |         | 9       |         |
 |       9 |         | 9     9 |       |      *9 |         | 9     9 |       |       * |         | 9     9 |
 |---------+---------+---------|       |---------+---------+---------|       |---------+---------+---------|
 |         |    9    |         |       |         |    9    |         |       |         |    9    |         |
 | 9  9  9 |         | 9  9    |       |*9 *9    |         |         |       | *  9  * |         | *  9    |
 |       9 |         | 9     9 |       |         |         | 9     9 |       |       9 |         | 9     9 |
 *---------+---------+---------*       *---------+---------+---------*       *---------+---------+---------*


Please teach me what DPs means ?
Regards kozo

[Leren]

DP stands for Deadly Pattern and refers to any candidate pattern that would prevent a valid solution from being reached. It usually refers to Uniqueness patterns, of which there are many kinds. This is a big topic covered by many threads on this site.

The best place to start on this site is here under the heading Uniqueness Tests.

You might also like to try other sites here and here, which are more concise and suitable for a relatively painless introduction to this large topic.

Also, your table method looks like Pattern Overlay, or Templating, which you can see described here and here.

Leren

[Yogi]

Thanx again, guys. It seems that I missed the crucial point that the Kite will not work if the intersecting cell common to your two strings contains the candidate you are trying to eliminate. Leren's charts are illuminating. So I think my original rules for kite hunting are generally accurate as long as they include this proviso, and what I stated in my last post in this thread was not right. I might add that I am not disagreeing with firstly identifying strings and then looking for kiteboxes if that suits you. I have simply found that I have difficuly with that approach.

Yogi

[Kozo Kataya]

Also, your table method looks like Pattern Overlay, or Templating, which you can see described ...

It's not like Pattern Overlay or Templating. A process is as follows.

[single digit] related techniques, such as fish, empty rectangle, kite etc., are all derived from the simple reasoning.
Which you might say Uniqueness or Intersection (in Hodoku).

Take a part of [single digit] as table A-1. A-2 shows, if a mini-column in Box2 has void at neighboring mini-columns,
candidates at other mini-colums in Box2 must be eliminated. marked void [ / ] and elimination [ * ]
Then next step, as in A-3, in Box3 only one mini-column has candidates and other two are void.
So, candidates in neighboring mini-columns (in Box1) must be eliminated.
This is a very simple technique, anyone knows Because of Sudoku-rule = the singularity.

Code: Select all

     A-1                 A-2                 A-3
   |    9    |         | /  9    |         |    *    |
   |    9  9 |   Box1  | /  9  9 |         |    *  9 |
   |       9 |         | /     9 |         |       9 |
   *---------*         *---------*         *---------*
   |    9    |         |    *    |         |         |
   | 9  9  9 |   Box2  | 9  *  * |         | 9       |
   | 9     9 |         | 9     * |         | 9       |
   *---------*         *---------*         *---------*
   |    9    |         | /  9    |         | /  9  / |
   |    9    |   Box3  | /  9    |         | /  9  / |
   |         |         | /       |         | /     / |       


Applying this process to puzzle B, B1 [single digit] at the biginninig
Then next B2 and the ending B3 step by step. marked [ * ] as elimination at a step
B = [......3.186..........2.........4.76...1.............8..7....64.5..1.3......5.....]

Code: Select all

  B1                                B2                               B3
*---------+---------+---------*   *---------+---------+---------*   *---------+---------+---------*
|         |         |       1 |   |         |         |       1 |   |         |         |       1 |
|         |    1  1 |         |   |         |    1  1 |         |   |         |    1  * |         |
| 1  1    |    1  1 |         |   | 1  1    |    *  * |         |   | *  1    |         |         |
|---------+---------+---------|   |---------+---------+---------|   |---------+---------+---------|
|         |       1 |         |   |         |       1 |         |   |         |       1 |         |
|       1 |         |         |   |       1 |         |         |   |       1 |         |         |
|         |    1  1 | 1       |   |         |    *  * | 1       |   |         |         | 1       |
|---------+---------+---------|   |---------+---------+---------|   |---------+---------+---------|
| 1       |         |         |   | 1       |         |         |   | 1       |         |         |
|         | 1       |         |   |         | 1       |         |   |         | 1       |         |
| 1  1    |         | 1  1    |   | *  *    |         | *  1    |   |         |         |    1    |
*---------+---------+---------*   *---------+---------+---------*   *---------+---------+---------*


Another example [ finned mutant ? ] According to a text ( quoted from Hodoku ?), 8r1c7 to be eliminated.
So, 8r2c9 is true then 8r2c4 and 8r4c9 are to be eliminated, also 8r3c1, because Box2 has 8r3c46 (mini-row).
With 2 steps of the above mentioned, it is easily recognizable that a case [ if r3c1 = 8 ] shows contradiction.

Code: Select all

 Candidate '8': finned mutant bbbb\rrcc                         [single digit]                  if r3c1 is true > no 8 in Box 3,6
 *-----------------------------------------------------------*  *-----------------------------*  *-----------------------------*
 |*4689 *689  *489   | 1     3     7     |-489   5     2     |  | 8  8  8 |         |*8       |  |         |         |         |   
 | 2    /1    /3     | 489   5     6     | 7     49   #489   |  |         |*8       |       8 |  |         | 8       |         |   
 |*489  /5    /7     | 489   2     48    | 6     1     3     |  |*8       | 8     8 |         |  |*8       |         |         |   
 |-------------------+-------------------+-------------------|  |---------+---------+---------|  |---------+---------+---------|   
 | 5     3    *89    | 7     1     2     |*489   469  *689   |  |       8 |         | 8    *8 |  |       8 |         |         |   
 |*89   /4    /1     | 3     6     89    | 2    /7    /5     |  | 8       |       8 |         |  |         |       8 |         |   
 | 7    /2    /6     | 5     48    489   |*89   /3    /1     |  |         |    8  8 | 8       |  |         |         |         |   
 |-------------------+-------------------+-------------------|  |---------+---------+---------|  |---------+---------+---------|
 | 1     6789  2     | 468   478   5     | 3     469   4679  |  |    8    | 8  8    |         |  |    8    |    8    |         |   
 | 46    67    5     | 2     9     3     | 1     8     467   |  |         |         |    8    |  |         |         |    8    |   
 | 3     6789  489   | 468   478   1     | 5     2     4679  |  |    8  8 | 8  8    |         |  |    8    |    8    |         |   
 *-----------------------------------------------------------*  *-----------------------------*  *-----------------------------*


Wonder, which is easy to get elimination [ * ], PM or [single digit] ?
Regards kozo

[Pat]

which is easy to get elimination,
PM or [single digit] ?

looking at "pencilmarks" ( all possibilities in each cell ),
it is indeed difficult to see just one digit

say you're interested in the 7,
it is easier if the software highlights just the 7s

but
this only happens when you choose 7 and
ask the software to highlight


and how did i know to focus on 7 ??

what happens is, i request a highlight of 1s,
find nothing interesting, so i move on to highlight 3s,
then 5s, and eventually i'll get to the 7s

the real experts
can just look at "pencilmarks"
and mentally highlight each digit---

~ Pat

[Kozo Kataya]

and how did i know to focus on 7 ??
what happens is, i request a highlight of 1s,
find nothing interesting, so i move on to highlight 3s,
then 5s, and eventually i'll get to the 7s

[ How focus ? ] i think it's depends on smaller number of clues or digits to be surveyed firstly.
For example , in the above mutant( ? ), digit 4, 8 and 9 have only one clue.
[single-digit]4 has 1, 8 has 4, 9 has 5 cells to be eliminated respectively.
in case of [ Why Did This Kite Not Fly ], digit 9 has only 2 clues which is the smallest and has 12 false.

Regards kozo