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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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 Posted: Wed Dec 26, 2007 6:22 pm Post subject: Pincer coloring |
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This writeup assumes the reader is familiar with XY-Wings and simple coloring. Basic moves bring one to this position.
| Code: | ----------------------------------------------------------
|234 6 7 |8 29A 49 |34 1 5 |
|349 5 349 |7 1 6 |2 48 348 |
|8 1 24 |25C 3 45 |7 9 6 |
----------------------------------------------------------
|269 4 29 |3 68 1 |5 28 7 |
|259 3 8 |4-59X 59B 7 |6 24 1 |
|56 7 1 |456 68 2 |49 3 489 |
----------------------------------------------------------
|7 9 35 |26 4 8 |1 56 23 |
|34 8 6 |1 259 59 |349 7 2349 |
|1 2 45 |69 7 3 |8 56 49 |
---------------------------------------------------------- |
Note the XY-Wing on 29-59-25 in boxes 2 and 5, with the cells marked by ABC. The pincers are 5 in cells B and C and take out the 5 in the cell marked X. However, this move does nothing.
Here is the grid after that move.
| Code: | ----------------------------------------------------------
|234 6 7 |8 29A 49 |34 1 5 |
|349 5 349 |7 1 6 |2 48 348 |
|8 1 24 |25C 3 45D |7 9 6 |
----------------------------------------------------------
|269 4 29 |3 68 1 |5 28 7 |
|259 3 8 |49 59B 7 |6 24 1 |
|56 7 1 |456 68 2 |49 3 489 |
----------------------------------------------------------
|7 9 35 |26 4 8 |1 56 23 |
|34 8 6 |1 2-59X 59E |349 7 2349 |
|1 2 45 |69 7 3 |8 56 49 |
---------------------------------------------------------- |
Keep in mind that with pincers, at least one or the other must be true, so any cell seeing both must be false. Note that row 3, box 2 and column 5 have strong links (only two occurrences) on 5. Make a three-cell coloring chain on 5 in cells C, D and E. If C=5, then D ≠ 5 and E must = 5. Therefore, if C is a pincer, then E must be one also. Substituting E for C, E and the other original pincer B take out the 5 from cell X and the puzzle is solved.
The W-Wing on 59 in boxes 5 and 8 yields the same result and perhaps other techniques are available as well.
Pincer coloring can be used with W-Wings and other pincer situations. It is a very valuable technique to have in one's arsenal.
Last edited by Marty R. on Sat Dec 29, 2007 10:32 pm; edited 1 time in total |
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alanr555
Joined: 01 Aug 2005
Posts: 198
Location: Bideford Devon EX39
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| Posted: Thu Dec 27, 2007 5:44 am Post subject: Re: Pincer coloring |
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| Marty R. wrote: |
Pincer coloring can be used with W-Wings and other pincer situations. It is a very valuable technique to have in one's arsenal. |
Logically, this is true - but the psychological element appears to be
discounted.
Often, I can see that there "ought" to be a relationship based on an
apparent pattern that the human eye can perceive. However, there
have been times when I have acted on such a perception - only to
have the puzzle collapse into error-dom when it becomes apparent
that the "pattern is illusory. By that time, all the good work using
Mandatory pairs etc has been lost and the only prospect is to start
again from the beginning - or a recognised "save point".
Thus it comes down to confidence - based on a sound understanding
of the principles and, particularly, an ability to recognise when a
supposed pattern is NOT useful.
In the past, I used to play the Minesweeper game on the computer
and with that game, there are patterns to be recognised. On many
occasions I have rushed into premature action and had the whole
game "blow up" on me. It is worse with minesweeper as there is a
continually advancing timer applying psychological pressure. With
Sudoku there is no equivalent time pressure but just as some people
fail exams because they cannot hack the time management in the
examination room it is also possible to be beset by "panic" when doing
Sudoku with concern for the clock.
The moral is to dispense with ANY form of time pressure and just
allow the experience to make its own progress.
The universe is filled with something called ENTROPY. Essentially, this
means that things get more chaotic in the sense that the living of life
erodes order. To demonstrate that, one could try living a "normal" life
in a show house for even as short a time as twenty four hours!
An initial Sudoku grid is a thing of beauty. After it has been solved, it
is quite often covered by a variety of "pencil marks" and scrawlings
used to reach the solution. Value has been added in that a solution
has been obtained - but at the cost of removing "pristine-ness". To
some this can be psychologically distressing.
Easy or Medium puzzles can be done in many cases without pencil
marks and so it is possible to write the solutions carefully. Even if
one erases the pencil marks (and I use a non-erasable pen) there
is still a sense of having spoiled what was presented. Tragically, it is
not easy to solve Hard or VH without marks and so one should heed
the old adage about needing to break eggs to make omelettes.
I know that there are six types of Unique Rectangles but I could not
enumerate them or recognise other than the most basic pattern.
Maybe there is a role for the Sudoku coach - in the same way that
sports people in other events have found such support useful - but
would that not also deny the essential spirit of the activity? |
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