May be a silly question but....

Advanced methods and approaches for solving Sudoku puzzles

May be a silly question but....

Postby skgolfer » Wed Dec 24, 2008 2:21 am

Hi

I am new to this board. Have been solving these puzzles for a long time. Recently though in one particular book, I have run into a slew of puzzles that I can't seem to solve logically and always have to do some guess work. Is this typical, I thought the point was that there was always a logical answer. Just wondering if this is an illogical thought? Thanks.
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Postby ab » Wed Dec 24, 2008 11:35 am

many public sources for sudoku publish puzzles that can be solved using a very limited set of techniques. typically singles, locked candidates and pairs, occasionally triples and x-wings and sometimes quads, swordfish, jellyfish and xy-wings. if you look through this section of the forum you'll see that there are many other solving techniques.

it's hard to comment on the puzzles that have foxed you without seeing some examples. but they can probably be solved by techniques explained here.
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Postby skgolfer » Thu Dec 25, 2008 3:10 am

Here is the puzzle and where I got to before I felt I needed to guess (apologies for the table):


Code: Select all
.------------------.---------------.-----------------.
| 5     24   124   | 8    6     7   | 9     3     12 |
| 128    7   128   | 9    3    15   | 6     4    125 |
| 6      9    3    | 14   2    145  | 8    17    157 |
:--------------------+--------------+----------------:
| 7     58   189   | 3    4     2   | 15     6   189 |
| 23   235    29   | 6    1     8   | 257   279    4 |
| 1248   6   1248  | 7    5     9   | 12    128    3 |
:------------------+----------------+----------------:
| 2389 238    6    | 12   7    13   |   4    5   189 |
| 2348   1    5    | 24   9     6   |  23   278   78 |
| 2349 234    7    | 5    8   134   | 123   129    6 |
'------------------'----------------'-----------------
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Postby 999_Springs » Thu Dec 25, 2008 7:37 am

From your candidate grid you seem to have only one place for 7 in column 7. Then you have a bunch of singles and an XY-wing.

But perhaps you may not have eliminated 7 from r8c7 and left it out accidentally, so you can eliminate 7 from r8c7 like this:
7-r8c7=3=r8c1=4=r8c4-4-r3c4=4=r3c6=5=r3c9=7=r8c9-7-r8c7 => r8c7<>7.
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Postby Luke » Thu Dec 25, 2008 1:49 pm

I think 999_Springs correctly determined your position with the added 7. Here's a very short solution path using some basic strategies:
Code: Select all
.------------------.---------------.-----------------.
| 5     24   124   | 8    6     7   | 9     3   #12  |
| 128    7   128   | 9    3    15   | 6     4   #125 |
| 6      9    3    |*14   2    145  | 8   #17   #157 |
:--------------------+--------------+----------------:
| 7     58   189   | 3    4     2   | 15     6   189 |
| 23   235    29   | 6    1     8   | 257   279    4 |
| 1248   6   1248  | 7    5     9   | 12    128    3 |
:------------------+----------------+----------------:
| 2389 238    6    |*12   7    13   |   4    5  -189 |
| 2348   1    5    | 24   9     6   | 237   278   78 |
| 2349 234    7    | 5    8  -134   | 123   129    6 |
'------------------'----------------'-----------------

Empty rectangle (above).
Then a short discontinuous nice loop: [r8c7]=3=[r8c1]=4=[r8c4]-4-[r9c6]-3-[r9c7]=3=[r8c7]==>[r8c7]=3.
This will get you to here:
Code: Select all
 *--------------------------------------------------*
 | 5    24   124  | 8    6    7    | 9    3    12   |
 | 12   7    8    | 9    3    15   | 6    4    125  |
 | 6    9    3    | 14   2    145  | 8    17   157  |
 |----------------+----------------+----------------|
 | 7    8    19   | 3    4    2    | 5    6    19   |
 | 3    5    29   | 6    1    8    | 7    29   4    |
 | 124  6    124  | 7    5    9    | 12   8    3    |
 |----------------+----------------+----------------|
 | 89   23   6    | 12   7    13   | 4    5    89   |
 | 248  1    5    | 24   9    6    | 3    27   78   |
 | 249  234  7    | 5    8    34   | 12   129  6    |
 *--------------------------------------------------*

X-wing on 1 [r14c39], and a XY-wing: 17[r3c8], 27[r8c8], 12[r9c7].
Singles, and nary a guess.
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Postby skgolfer » Fri Dec 26, 2008 4:18 am

Thanks, funny how sometimes you can work through these things and just not see some of the obvious moves no matter how much you stare at it.
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