| Professor
| | Joined: 28 Feb 2008 | | Posts: 6 | | : | | Location: Earth |
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 Posted: Wed Apr 02, 2008 4:45 am Post subject: Neero-farabi |
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1. Abstract
This method is fairly straightforward. After applying basic techniques, I go directly to apply this method. Almost always the Sudoku breaks. It is assumed that pencil marks are present. In the solution procedure, background of unsolved cells are filled with various colors to assume the cell's value. If you do not get solution during "Pass 1", go for "Pass 2". Each pass will require three different colors.
This post will be updated from time to time. Few questions are still pending. You are invited to work on those questions. Questions are inserted in { } brackets where appropriate.
2. Name
This method is named as "Neero-farabi". {pronunciation: knee-row far'e bee}
3. Cell Distribution
All unsolved cells fall into one of the three categories, i.e. bivalue, trivalue and multivalue cells.
4. Scope
This method is applied when sufficient bivalue cells are on the board. {"Sufficient" needs more explanation yet}
5. Color Choice
Any six colors are enough to apply this method. I prefer to use: VIBGYOR colors. These are borrowed from rainbow: the V(iolate), I(ndigo), B(lue), G(reen), Y(ellow), O(range) and R(ed). First three colors, VIB, are used during pass 1 and last three colors, YOR, for pass 2. This drops need of green color which acts as boundary between pass 1 and pass 2.
6. Color indication
Every unsolved cell will have more than one digit. One of the digit will definitely be maximum. Similarly one the digit will definitely be minimum.
| Code: |
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........Color Indication...........|.....Pass 1.......|........Pass 2.......|..........R E M A R K S.............|
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........Maximum value..............|....Violate.......|...... Yellow........|...Bivalue, Trivalue & Multivalue...|
........Intermediate value.........|....Indigo........|...... Orange........|...Trivalue only....................|
........Minimum value..............|....Blue..........|...... Red...........|...Bivalue, Trivalue & Multivalue...|
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7. Example
Here is an example of color application for a cell. Let a trivalue cell consists of 2/3/7. Violate, Indigo or Blue will be applied for choosing 7, 3 or 2 respectively during pass 1. Yellow, Orange or red will be applied for choosing 7, 3 or 2 respectively during pass 2.
8. Pass 1
You will play with violate, indigo and blue colors during this pass. Choose any bivalue cell as "starting cell". Arbitrarily assume any value of the cell as solution and change the background color of the cell as violate/blue depending on your choice in the bivalue cell. Now work onto solution further. You will encounter one of the following three situations:
8.1 Correct. If majority {what is "majority"? needs explanation. I have judged when 80% of the unsolved cells are colored gives us majority} of the cells are filled without any violation, gives us solution. Stop here. You have found the solution.
8.2 Wrong. Finding any kind of violation, indicates that your choice at "starting cell" was wrong. Insert correct value in the "starting cell". Take a note that the situation does not prove that all chosen values in various cells are wrong. Working with wrong choice in the "starting cell" may lead on the right track somewhere. As few cells are wrong, therefore, again one detracks and go on choosing wrong values.It can not be known when one climbed on right track and when he/she was detracked.
8.3 Stuck. You can not move further and you do not know whether your choices are correct or otherwise. Now go to section "9. Pass 2".
9. Pass 2
During pass 2 you will be applying yellow, orange and red colors. Now revert the choice at the "starting cell". Either violate color will change into red or blue will change into yellow colors. Generally, the moving path is different from pass 1 path. During this pass whenever you meet a cell of pass 1, act as follows:
9.1 Bivalue. If the value during pass 1 and pass 2 are same. It is solution of the cell.
9.1 Trivalue. If the value during pass 1 and pass 2 are same. It is solution of the cell. In case it is different, you can eliminate the third value.
9.3 Multivalue. If the value during pass 1 and pass 2 are same. It is solution of the cell. In case it is different, you can eliminate the remaining values.
Enjoy! |
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