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Advanced Solving Strategies
There are actually only 7 techniques that combined will solve any puzzle....
For an in-depth video tutorial teaching you the most advanced Sudoku Secrets Take a look at the Sudoku Video.
Exclusion [Singleton]
Simply put, if there is only one option for a cell, it must be that option.
Likewise, that option is not allowed for other cells in a given constraint(row, column,grid)
In this case, the cell in question (?) can not be a 1,2,3,4,5,6,8 or 9 so it must be a 7.
This alone will solve the easy puzzles.
Uniqueness [Singleton]
The reverse of exclusion, here the cell in question could be any number, but it is the only cell in the grid that could be a 1, therefore it must be the 1 for that grid.
These two techniques will solve most medium & hard puzzles
Exclusion [Doubles]
two options for two spaces affecting others
Here is a variation of the above but for doubles. Namely, you have two spaces with only two options [4 & 5] therefore the rest of the constraint (column, row, grid) must have neither the 4 or the 5.
Exclusion removes options from the other cells (-) in a constraint.
Uniqueness [Doubles]
two options for two spaces affecting self
Again, an other variation of the above uniqueness, here we have two spaces (*) which are the only spaces in which a 2 or a 9 are possible for the constraint (grid) therefore, the remaining numbers 1,3,4,5,6,7,8 must be removed, leaving the ? cell the only one where a 3 is possible.
Uniqueness removes options from the unique cells in question.
Exclusion [Triples]
three options for three spaces affecting others
Variation of the above but for triples. Namely, you have three spaces with only three options [4,5 & 6] therefore the rest of the constraint (column, row, grid) must have neither the 4,5 or the 6.
Be aware that this can show up in a slightly trickier form of three cells, three options such as
[4,5] [4,6] [5,6]. This is harder to recognize than the more repetitious [4,5,6] [4,5,6] [4,5,6]
Exclusion removes options from the other cells (-) in a constraint.
Uniqueness [Triples]
three options for three spaces affecting self
Again, an other variation of the above uniqueness, here we have three spaces (*) which are the only spaces in which a 2,6 or a 9 are possible for the constraint (grid) therefore, the remaining numbers 1,3,4,5,7,8 must be removed, leaving the ? cell the only one where a 3 is possible.
Again, remember that three options for three spaces could also be [2,9] [6,9] [2,6,9].
Uniqueness removes options from the unique cells in question.
Cross Constraints
Row or Column intersecting a Grid
With these 7 techniques you can now solve ANY sudoku puzzle
For an in-depth video tutorial teaching you the most advanced Sudoku Secrets Take a look at the Sudoku Video.
Exclusion [Singleton]
| 1 | 2 | 3 | 4 | 5 | 6 | ? | 8 | 9 |
Likewise, that option is not allowed for other cells in a given constraint(row, column,grid)
In this case, the cell in question (?) can not be a 1,2,3,4,5,6,8 or 9 so it must be a 7.
This alone will solve the easy puzzles.
Uniqueness [Singleton]
| 1 | ||||||||
| 1 | ||||||||
| 8 | ? | |||||||
| 6 | 1 | |||||||
| ? | ||||||||
| 2 | 1 | |||||||
| 42 | ||||||||
These two techniques will solve most medium & hard puzzles
| 1 | 2 | 3 | ? | - | ||||
| * | * | 6 | - | - | - | - | - | - |
| 7 | 8 | 9 | 4 | - | ||||
| - | ||||||||
| - | 4 | |||||||
| - | ||||||||
| 1 | * | 7 | ||||||
| 2 | * | 8 | ||||||
| 3 | 6 | 9 |
Exclusion [Doubles]
two options for two spaces affecting others
Here is a variation of the above but for doubles. Namely, you have two spaces with only two options [4 & 5] therefore the rest of the constraint (column, row, grid) must have neither the 4 or the 5.
Exclusion removes options from the other cells (-) in a constraint.
| ? | * | |||||||
| * | 3 | |||||||
| 6 | 3 | |||||||
| 2 | ||||||||
| 9 | ||||||||
| 2 | ||||||||
| 9 | ||||||||
| 3 |
two options for two spaces affecting self
Again, an other variation of the above uniqueness, here we have two spaces (*) which are the only spaces in which a 2 or a 9 are possible for the constraint (grid) therefore, the remaining numbers 1,3,4,5,6,7,8 must be removed, leaving the ? cell the only one where a 3 is possible.
Uniqueness removes options from the unique cells in question.
| 1 | 2 | 3 | ? | - | ||||
| - | - | - | - | - | - | |||
| 7 | 8 | 9 | 4 | - | ||||
| - | ||||||||
| - | 4 | |||||||
| - | ||||||||
| 1 | 7 | |||||||
| 2 | 8 | |||||||
| 3 | 9 |
three options for three spaces affecting others
Variation of the above but for triples. Namely, you have three spaces with only three options [4,5 & 6] therefore the rest of the constraint (column, row, grid) must have neither the 4,5 or the 6.
Be aware that this can show up in a slightly trickier form of three cells, three options such as
[4,5] [4,6] [5,6]. This is harder to recognize than the more repetitious [4,5,6] [4,5,6] [4,5,6]
Exclusion removes options from the other cells (-) in a constraint.
| ? | * | |||||||
| * | 3 | |||||||
| * | 3 | |||||||
| 2 | ||||||||
| 9 | ||||||||
| 6 | ||||||||
| 2 | ||||||||
| 9 | ||||||||
| 3 | 6 |
three options for three spaces affecting self
Again, an other variation of the above uniqueness, here we have three spaces (*) which are the only spaces in which a 2,6 or a 9 are possible for the constraint (grid) therefore, the remaining numbers 1,3,4,5,7,8 must be removed, leaving the ? cell the only one where a 3 is possible.
Again, remember that three options for three spaces could also be [2,9] [6,9] [2,6,9].
Uniqueness removes options from the unique cells in question.
| * | ^ | ^ | | | | | | |
| * | ^ | ^ | | | | | | |
| * | ^ | ^ | | | | | | |
| 1 | | | | | | | | |
| 2 | | | | | | | | |
| | | | | 8 | | | | |
| 4 | | | | | | | | |
| 5 | | | | | | | | |
| | | | | | | | 8 | |
Row or Column intersecting a Grid
^ = not an 8
This is an interesting issue where a grid is intersected by either a row or a column. In this case, the 8 must appear with in the intersection (*'s) of the cross constraints, and therefore must not occur in the non-shared cells of the two constraints (^) With these 7 techniques you can now solve ANY sudoku puzzle
Latest page update: made by Anonymous, Mar 9 2008, 8:43 PM EDT
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About This Update
Fixed the uniqueness table
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Fixed the uniqueness table
- anonymous
2 words added
5 words deleted
view changes
- complete history)
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| Started By | Thread Subject | Replies | Last Post | |
|---|---|---|---|---|
| Anonymous | Hmmm... | 1 | Jun 7 2008, 10:30 PM EDT by Anonymous | |
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Thread started: Dec 5 2007, 5:26 PM EST
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There is this one puzzle that I have been trying to solve, but can't solve it for crap. It's so insanely hard, even when it seems like you have it right, then you realize at the last minute that you messed up something. It's stressing me out.. I wish I could post it, but I'm not sure how. And don't let the fact that a lot of the numbers are there fool you. I figured it would be easy because of that, but it's not. I will try to figure a way to put it on here.
In other news, my favorite game is Kakuro. It is like Sudoku, except, not only can the numbers not repeat themselves, but they also have to add up to the small numbers in the corners of all the rows and columns. I find that one easier than sudoku, and they don't even start you off with numbers at all.
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| sudoku_maniac | not true | 1 | May 28 2008, 11:57 PM EDT by Anonymous | |
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Thread started: May 9 2008, 8:32 PM EDT
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there are lot of puzzles that you can't solve with these 7 techniques. try evil puzzles from http://www.sudoku-solver.net/ . I bet you won't be able to solve many of them with these 7 techniques alone.
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| Anonymous | shendoku | 0 | Oct 17 2007, 7:14 PM EDT by Anonymous | |
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Thread started: Oct 17 2007, 7:14 PM EDT
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If you want to try out something new in sudoku, try shendoku, using the sudoku rules but playing two people, one against the other, like battleshipps. They have a free version to download at http://www.shendoku.com/sample.pdf . Anything else they are bringing out or they are working on you can find at www.shendoku.com or at they´r blog www.shendoku.blogspot.com . Have fun, I am. I specially like one slogan I heard about Shendoku: SUDOKU is like masturbation (on your own)…. SHENDOKU is like sex (it takes two).
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| Anonymous | not really true :-) | 0 | Aug 27 2007, 3:43 PM EDT by Anonymous | |
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Thread started: Aug 27 2007, 3:43 PM EDT
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Agree with the first comment that it is not true that all these will enable you to solve ANY sudoku puzzle. If it is that simple, I guess many sudoku players wouldn't be as frustrated. The most-advanced sudoku puzzles require a bit more extensive experience and at times even process-and-rollback, etc.
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| Anonymous | Not True | 0 | Mar 13 2007, 1:42 AM EDT by Anonymous | |
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Thread started: Mar 13 2007, 1:42 AM EDT
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These techniques will solve all the puzzles I classify as Novice & Player, but will not solve any of the puzzles I classify as Expert. For examples go to my Website <A>www.sudoku-help.com/mX</A> and select any of the Expert puzzles. See also the Tutorials on the techniques needed to Solve ther Expert puzzles.
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