## May be a silly question but....

Advanced methods and approaches for solving Sudoku puzzles

### May be a silly question but....

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.
skgolfer

Posts: 3
Joined: 23 December 2008

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.
ab

Posts: 451
Joined: 06 September 2005

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 |'------------------'----------------'-----------------`
skgolfer

Posts: 3
Joined: 23 December 2008

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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Once upon a time I was a teenager who was active on here 2007-2011
999_Springs

Posts: 367
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

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.

Luke
2015 Supporter

Posts: 435
Joined: 06 August 2006
Location: Southern Northern California

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.
skgolfer

Posts: 3
Joined: 23 December 2008