The New Sudoku Players' Forum

[kiyoshige]

Here is the start and what I've narrowed it down to...

Code: Select all

 *-----------------------------------------------------------------------------*
 |         9               |                         |                         |
 |         4               |         1               |         6               |
 | 6                       | 5       7       3       |                         |
 |-------------------------+-------------------------+-------------------------|
 | 5                       |                         |                 7       |
 | 1               4       |         6               | 3               9       |
 | 2                       |                         |                 8       |
 |-------------------------+-------------------------+-------------------------|
 |                         | 2       3       8       |                 6       |
 |         6               |         9               |         1               |
 |                         |                         |         3               |
 *-----------------------------------------------------------------------------*

 *-----------------------------------------------------------------------------*
 | 378     9       123578  | 46      28      46      | 257     78      1235    |
 | 378     4       23578   | 89      1       29      | 257     6       235     |
 | 6       12      128     | 5       7       3       | 249     89      124     |
 |-------------------------+-------------------------+-------------------------|
 | 5       38      69      | 13489   28      1249    | 16      24      7       |
 | 1       78      4       | 78      6       25      | 3       25      9       |
 | 2       37      69      | 1379    45      179     | 16      45      8       |
 |-------------------------+-------------------------+-------------------------|
 | 479     15      157     | 2       3       8       | 4579    79      6       |
 | 3478    6       2378    | 47      9       457     | 2458    1       245     |
 | 789     25      78      | 16      45      16      | 789     3       245     |
 *-----------------------------------------------------------------------------*


Ok, using Mike's notation I'll try to explain the ALS...

Code: Select all

+-------------------+------------------+-----------------+
|   378   9  123578 |     46  28    46 |   257  78  1235 |
|   378   4   23578 |     89   1    29 |   257   6   235 |
|     6  12     128 |      5   7     3 |   249  89   124 |
+-------------------+------------------+-----------------+
|     5  38      69 | -13489 *28  1249 |    16  24     7 |
|     1  78       4 |    *78   6   *25 |     3  25     9 |
|     2  37      69 |   1379 *45   179 |    16  45     8 |
+-------------------+------------------+-----------------+
|   479  15     157 |      2   3     8 |  4579  79     6 |
|  3478   6    2378 |    #47   9   457 |  2458   1   245 |
|   789  25      78 |     16 -45    16 |   789   3   245 |
+-------------------+------------------+-----------------+

Suppose r6c5 is 5.
Then r9c5 is 4.
But r5c6 is 2, r4c5 is 8, r5c4 is 7 and then r8c4 is 4.
Since r9c5 and r8c4 cannot both be 4, r6c5 cannot be 5!!!

When "n" numbers can be in "n" spots they are said to be "locked".
However when "n+1" numbers can be in "n" spots, they are "almost locked."
(78, 28, 45 and 25 are the "almost locked" 5 numbers in the 4 spots in the middle).

A better explanation is found at:
http://forum.enjoysudoku.com/viewtopic.php?t=2510

[tarek]

A couple of box line eliminations.......

Can't see anything else simple, this looks like a complex one......

I'll give it a try with my solver later to see if I've missed something...


I checked it with the solver, it solvedwith a 5 node ALS-xy rule as the most complex technique needed.

Any better offer ???!!!

tarek

[daj95376]

Code: Select all

.9........4..1..6.6..573...5.......71.4.6.3.92.......8...238..6.6..9..1........3.

# basic techniques get me here
 *-----------------------------------------------------------------------------*
 | 378     9       123578  | 46      28      46      | 257     78      1235    |
 | 378     4       23578   | 89      1       29      | 257     6       235     |
 | 6       12      128     | 5       7       3       | 249     89      124     |
 |-------------------------+-------------------------+-------------------------|
 | 5       38      69      | 13489   28      1249    | 16      24      7       |
 | 1       78      4       | 78      6       25      | 3       25      9       |
 | 2       37      69      | 1379    45      179     | 16      45      8       |
 |-------------------------+-------------------------+-------------------------|
 | 479     15      17      | 2       3       8       | 4579    79      6       |
 | 348     6       238     | 47      9       457     | 2458    1       245     |
 | 789     25      78      | 16      45      16      | 789     3       245     |
 *-----------------------------------------------------------------------------*


An XY-Chain to get over the hump.

Code: Select all

[r2c6]=2                                                                => [r5c6]<>2
[r2c6]=9,[r2c4]=8,[r5c4]=7,[r8c4]=4,[r9c5]=5,[r6c5]=4,[r6c8]=5,[r5c8]=2 => [r5c6]<>2


[Mike Barker]

Another option is a kind of pretty generalized VWXYZ-wing (or an ALS xz-rule for purists) which immediately reduces the puzzle to singles:

Code: Select all

+-------------------+------------------+-----------------+
|   378   9  123578 |     46  28    46 |   257  78  1235 |
|   378   4   23578 |     89   1    29 |   257   6   235 |
|     6  12     128 |      5   7     3 |   249  89   124 |
+-------------------+------------------+-----------------+
|     5  38      69 | -13489 *28  1249 |    16  24     7 |
|     1  78       4 |    *78   6   *25 |     3  25     9 |
|     2  37      69 |   1379 *45   179 |    16  45     8 |
+-------------------+------------------+-----------------+
|   479  15     157 |      2   3     8 |  4579  79     6 |
|  3478   6    2378 |    #47   9   457 |  2458   1   245 |
|   789  25      78 |     16 -45    16 |   789   3   245 |
+-------------------+------------------+-----------------+

[simleung]

I'm pretty new to this forum, but I've been Sudoku's for some time and loving it. I think I'm pretty good (other than the occasional sloppiness), but after poking through this forum I see that I'm in kindergarten compared to you folks!

I tried looking up this ALS xz rule and VWXYZ-wing, and I've read about it and I STILL don't get it . Can someone explain this strategy to me using this example above? Maybe I'll understand it if I see a real-life example.

Thanks!

[Mike Barker]

Simleung, you're familiar with naked pairs, which are two cells containing two candidates, naked triples, etc. These are locked sets - every candidate in the cells must appear in one of the cells. Almost Locked Sets (ALS) are similar, but they contain one extra candidate, for example, three candidates in two cells. By themselves they are pretty useless, but if two or more ALS can be combined then they can act like a locked set. In the above example of the VWXYZ-wing, which is a form of an ALS xz-rule, there are two ALS: {r8c4}={4,7} and {r5c46, r46c5}={2,4,5,7,8}. In the first case there is 1 cell with 2 candidates and in the second there are 4 cells with 5 candidates. The magic happens because there is a candidate, called the restricted common, in both sets such that all the cells which contain the candidate in one set can see all the cells which contain the candidate in the other set. In the example, the restriced common is "7" since it occurs only in r8c4 and r4c4 and these cells can see each other.

With a restriced common instead of there being two extra candidates, one in each ALS, there is only one because the restriced common can only occur in one of the ALS. Now if another cell contains a candidate, other than the restriced common, which eliminates all occurances of the candidate from the two ALS then there won't be enough candidates left to fill the cells making up the two ALS. This is impossible (given there is a solution to the puzzle) and so the candidate can be eliminated. In the example, if r4c4 is "4" then the first ALS, r8c4, must be 7 and the 4 cells of the second ALS can only contain {2,5,8} which is impossible. Therefore, "4" can be elimitated from r4c4.

ALS can also be "doubly linked", that is they contain two restricted common candidates. In this case, the mutual exclusion rule applies. Any candidate in a cell which is not part of the ALSs, which is not one of the restriced common candidates, and which eliminates all occurances of the candidate from either of the ALS can be eliminated.

[simleung]

I think I get it. After the explanation, I think it makes sense. I'm not sure if I'll be able to easily recognize one of these situations, but at least now I get it. Thanks much!!!!