Need help solving these

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Need help solving these

Postby wolobofe » Fri Aug 05, 2016 11:31 am

Is there anyone out there who can complete the attached partially-solved Sudoku puzzles, without using guesswork? If there is a method of doing so, I would be grateful if an explanation could be provided!!
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wolobofe
 
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Re: Need help solving these

Postby JasonLion » Fri Aug 05, 2016 2:02 pm

The first one, 3d.gif 906T age 26, has a BUG+1. If R4C5 was not 8 the puzzle would have two solutions. Therefore R4C5 must be 8. Singles from there to the end.
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Re: Need help solving these

Postby Sudtyro2 » Fri Aug 05, 2016 7:59 pm

I'll give the second puzzle (900T) a try ...
Code: Select all
+--------------+--------------+--------------+
|  378   1   2 |    4  38   9 |    5 378   6 |
|  378   4   6 | b358   2  58 |  c37   1   9 |
|  358  58   9 |    6   7   1 |    2  38   4 |
+--------------+--------------+--------------+
|    9   3  15 |    7  15   6 |    8   4   2 |
|   28  28  17 |    9  13   4 |    6 357 357e|
|    4   6  57 | ah38 358   2 |  d37   9   1 |
+--------------+--------------+--------------+
|   25   9   4 |  g58   6   7 |    1 235 358f|
|    1   7   3 |    2   9  58 |    4   6  58 |
|    6  25   8 |    1   4   3 |    9 257  57 |
+--------------+--------------+--------------+

The above grid was taken directly from Andrew Stuart's online solver after inputting your givens for 900T. This Forum's normal starting grid results after applying the "basics," which comprise the first six steps in this solver (or others available). In doing that, one additional basic elimination is -5r6c4 from the box/line reduction step, and that digit has been removed from your grid.

At this point, one tries to find one advanced step after which the puzzle solves completely with "singles to the end (stte)." This can be done by hand or by using, say, a solver's (Discontinuous Loop) Alternating Inference Chain, as this solver did:
3r6c4 = 3r2c4 - 3r2c7 = 3r6c7 - 3r5c9 = (3-8)r7c9 = 8r7c4 - (8=3)r6c4 => +3r6c4.
The chain starts and ends with a strong link to 3r6c4, and that places the digit for an stte solution.

Hope this helps to get you started.

SteveC
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Re: Need help solving these

Postby Leren » Fri Aug 05, 2016 9:46 pm

Here are the three puzzle solved cell statuses in line format (which is more convenient for others to use) :

...61.45.1.48.567.9653472816.1...3943794615284.2..371621..36.45.932.4167.461...32
.124.95.6.46.2..19..96712.493.7.6842...9.46..46...2.91.94.671..17329.46.6.81439..
4..8931...9.124.3..136..94.95....67163..1.4.514..6..93.84..631...1.8..6..692.1...

The solution to the first puzzle was correctly described by Jason.

The simplest solution I could find for the second puzzle (ignoring basics as described by SteveC) takes two (non-basic) moves :

Code: Select all
*--------------------------------------------------------------*
| 378   1     2      | 4     38    9      | 5     378   6      |
| 78-3  4     6      |*358   2     58     |*37    1     9      |
| 358   58    9      | 6     7     1      | 2     38    4      |
|--------------------+--------------------+--------------------|
| 9     3     15     | 7     15    6      | 8     4     2      |
| 28    28    17     | 9     13    4      | 6     357   357    |
| 4     6     57     |*38    58-3  2      |*37    9     1      |
|--------------------+--------------------+--------------------|
| 25    9     4      | 58    6     7      | 1     235   358    |
| 1     7     3      | 2     9     58     | 4     6     58     |
| 6     25    8      | 1     4     3      | 9     257   57     |
*--------------------------------------------------------------*

There is an XWing in 3's c47 r26 (the cells marked * in the diagram), which removes the 3's in r2c1 and r6c5. I assume you are familiar with X Wings.

Code: Select all
*--------------------------------------------------------------*
| 378   1     2      | 4    a38    9      | 5     37-8  6      |
| 78    4     6      |b358   2     58     |c37    1     9      |
| 358   58    9      | 6     7     1      | 2    d38    4      |
|--------------------+--------------------+--------------------|
| 9     3     15     | 7     15    6      | 8     4     2      |
| 28    28    17     | 9     13    4      | 6     357   357    |
| 4     6     57     | 38    58    2      | 37    9     1      |
|--------------------+--------------------+--------------------|
| 25    9     4      | 58    6     7      | 1     235   358    |
| 1     7     3      | 2     9     58     | 4     6     58     |
| 6     25    8      | 1     4     3      | 9     257   57     |
*--------------------------------------------------------------*

This is followed immediately by a W Wing : (8=3) r1c5 - r2c4 = r2c7 - (3=8) (the cells marked a-b-c-d in the diagram) which removes the 8 from r1c8 (the W Wing shows that at least one of cells a or d must be 8, so r1c8 can't be 8).

The puzzle solves in singles from there. If you are unfamiliar with W Wings you can find them described here.

The third puzzle takes 3 non-basic moves :

Code: Select all
*--------------------------------------------------------------*
| 4     27    56     | 8     9     3      | 1     25    67-2   |
| 78    9     56     | 1     2     4      | 578   3     678    |
|*28    1     3      | 6     57    57     | 9     4    *28     |
|--------------------+--------------------+--------------------|
| 9     5     28     | 34    34    28     | 6     7     1      |
| 6     3     278    | 79    1     2789   | 4     28    5      |
| 1     4     278    | 57    6     2578   | 28    9     3      |
|--------------------+--------------------+--------------------|
|*257   8     4      | 579   57    6      | 3     1    *279    |
| 357-2 27    1      | 34    8     579    | 257   6     479-2  |
| 357   6     9      | 2     34    1      | 578   58    478    |
*--------------------------------------------------------------*

The is an X Wing in 2's r37 c19 (cells marked *) which removes the 2's from r1c9, r8c1 and r8c9.

Code: Select all
*--------------------------------------------------------------*
| 4     27    56     | 8     9     3      | 1     25   a67     |
|c78    9     56     | 1     2     4      | 58-7  3    b678    |
| 28    1     3      | 6     57    57     | 9     4     28     |
|--------------------+--------------------+--------------------|
| 9     5     28     | 34    34    28     | 6     7     1      |
| 6     3     278    | 79    1     2789   | 4     28    5      |
| 1     4     278    | 57    6     2578   | 28    9     3      |
|--------------------+--------------------+--------------------|
| 257   8     4      | 579   57    6      | 3     1     279    |
| 357   27    1      | 34    8     579    | 257   6     479    |
| 357   6     9      | 2     34    1      | 578   58    478    |
*--------------------------------------------------------------*

The next move is called an XYZ wing. The logic is, that if all the 7's in cells a, b and c were false, cell b would be empty, so one of cells a, b and c must be 7.

Since r2c7 can see all three of these cells, it can't be 7. You can find a description of XYZ Wings here.

Code: Select all
*--------------------------------------------------------------*
| 4     27    56     | 8     9     3      | 1     2-5   67     |
| 78    9     56     | 1     2     4      |a58    3     67     |
| 28    1     3      | 6     57    57     | 9     4    b28     |
|--------------------+--------------------+--------------------|
| 9     5     28     | 34    34    28     | 6     7     1      |
| 6     3     278    | 79    1     2789   | 4     28    5      |
| 1     4     278    | 57    6     2578   | 28    9     3      |
|--------------------+--------------------+--------------------|
| 257   8     4      | 579   57    6      | 3     1     29     |
| 357   27    1      | 34    8     579    | 27-5  6     49     |
| 357   6     9      | 2     34    1      | 78-5 d58   c48     |
*--------------------------------------------------------------*

Following some more basics there is a W Wing (5=8) r2c7 - r3c9 = r9c9 - (8=5) r9c8 in cells a-b-c-d, which shows that at least one of cells a and d must be 5, so 5 can be removed from r1c8, r8c7 and r9c7.

The puzzle solves in singles from there. Let me know if you need any further explanation of all this.

Leren
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Re: Need help solving these

Postby wolobofe » Sat Aug 06, 2016 4:59 am

Thanks for these replies...much appreciated. Everyone I've asked thus far has been clueless.
Looks like I've got some homework to do, to investigate these solutions!!!
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