a puzzle require many kind of solving techniques

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a puzzle require many kind of solving techniques

Postby Eioru » Sat Aug 19, 2006 1:08 pm

Analysis by Sudoku Explainer:
..97.41..
....62.8.
..4....6.
89..7...2
...2.9...
3...4..56
.5....6..
.3.49....
..73.68..

It has
49 x Hidden Single
1 x Direct Hidden Pair
1 x Naked Single
2 x Direct Hidden Triplet
5 x Pointing
4 x Claiming
2 x Naked Pair
1 x X-Wing
1 x Hidden Pair
1 x XY-Wing
1 x Unique Rectangle type 4
1 x Unique Loop type 4
1 x Aligned Pair Exclusion
1 x Bidirectional Y-Cycle
3 x Forcing Chain

Thanks for pointing out this fault, it's already be corrected.
Total has 15 kind of solving tecnique.
If there is puzzle more than 16, thanks for sharing.
Last edited by Eioru on Sat Aug 19, 2006 10:04 pm, edited 1 time in total.
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Postby ravel » Sat Aug 19, 2006 9:35 pm

I only count 15.

Maybe you should read something before writing the next post.
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Postby underquark » Sat Aug 19, 2006 11:07 pm

Different "kind" of solving technique is open to wide interpretation. A hidden pair is simply a naked septuplet (actually - and usually - less, depending upon how many candidates the cell has). So pairs, triplets and the like are all really the same kind of technique whether they are hidden or naked. You could even argue that a naked triplet is an XY-wing with the stem and branch cells lying in a straight line.
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Postby coloin » Sun Aug 20, 2006 12:28 am

With the exception of unique rectangles/uniqueness - which assumes that the grid is a unique one, I think all solving techniges are "essentially" the same" !

Any technique which generates a clue [or anticlue] ! is the same - if its a wrong clue [and a wrong clue IS a wrong clue] it will generate a constraint or contradiction somewhere furthur along the completion process.

Therefore logically backtracking with a computor is the same as logically "front tracking" with whatever "Fish" technigue you want. If a constraint or contradiction is met then this contributes to the puzzle.

This could be the reason that the method of solving changes sometimes if you solve in a different technique sequence.

Say you guessed a clue in a very hard puzzle, - you perhaps may have a 33% chance of being correct. But should that turn the puzzle into a very easy puzzle and it goes on to solve uniquely - you have solved the puzzle.

Thats how the world champion did it ! [I think] Much to a certain other person's disgust !

Ah........I think I will self refer myself to here - a post on "Complexity, Trial & Error, Backtracking and Guessing"....I may be some time !

PS
I still dont understand how adding a clue can make a puzzle harder !

C
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Postby Eioru » Sun Aug 20, 2006 2:26 am

After that 15 kinds sudoku, I find 19.
..4..91.8
.7.......
5.68...2.
..97.2.6.
....4.2..
7..9.1.3.
6...9..12
..52.76..
2.....9..

48 x Hidden Single
1 x Direct Hidden Pair
2 x Naked Single
5 x Pointing
2 x Claiming
2 x Naked Pair
1 x X-Wing
3 x Hidden Pair
1 x Naked Triplet
2 x XY-Wing
1 x Unique Rectangle type 2
1 x Aligned Pair Exclusion
2 x Bidirectional Y-Cycle
1 x Turbot Fish 1 x Forcing X-Chain
7 x Forcing Chain
1 x Bidirectional Cycle
1 x Cell Forcing Chains
4 x Region Forcing Chains
1 x Dynamic Cell Forcing Chains


This one is rated 9.0 by Sudoku Explainer
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Postby ravel » Sun Aug 20, 2006 8:56 pm

coloin wrote:PS
I still dont understand how adding a clue can make a puzzle harder !

Have you read this thread ? The point is that you must not apply a uniqueness technique (unique rectangle), when you dont know, that a puzzle is unique. We (non purists) know by definition, that a sudoku has exactly one solution, therefore the candidate grid must not contain a deadly uniqueness pattern like
Code: Select all
12    12
--
12    12

because two solutions would be possible:
Code: Select all
1    2
-
2    1
and
Code: Select all
2    1
-
1    2
But if one of these numbers is a given, we cannot make use of it, because a pattern
Code: Select all
1     2
-
2     1
in the solution grid is possible then.
And we cannot know (without much effort), that the puzzle without this additional clue is unique also.
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Postby coloin » Sun Aug 20, 2006 9:11 pm

I had read the thread. I [sort of] understand that you can exlude some clues based on the possibility of an unavoidable set .

- But you dont know which one of the 8 possibilities cant be a 1 or 2
- This must help you in some cases as demonstrated in the thread.

But the puzzles were rated as harder by an analytic program which [I am presuming] doesnt use uniqueness as a solving tool.

So you add a clue to give you two puzzles - by definition it is superfluous. If both puzzles are uniquely solvable - they are from the same grid.

This must give you more information, [at any rate it cant give you less information] therefore the puzzle should be easier - at worst the same.

Im still not sure on this one. I will reread the thread !

Thanks
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Postby fermat » Sun Aug 20, 2006 10:30 pm

Darn near all puzzles can be solved by different methods.

UR frequently saves many steps. (Really many!)

If an added clue removes the UR the puzzle can seem harder, can take more steps.

That is just my opinion, I am not an expert. I do use UR as a shortcut frequently.
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Tougher with one more clue?

Postby keith » Mon Aug 21, 2006 1:29 am

So, let me ask:

If:

1. A puzzle has a unique solution; and
2. We do not use uniqueness techniques to solve:

Can the puzzle be made more difficult by the addition of a clue?

We have seen how the addition of a clue can destroy a UR and make the puzzle more difficult. Does anyone have a thought (if not an actual example) of another instance?

Keith
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Postby Eioru » Sun Aug 27, 2006 10:37 am

this puzzle need 20 kind of technique at least
7..8..1......6......3..9..54..2..7...5.....1...6..8..38..4..2......1......9..7..6

54 x Hidden Single
4 x Naked Single
4 x Pointing
4 x Claiming
4 x Naked Pair
3 x X-Wing
3 x Hidden Pair
1 x Naked Triplet
1 x Swordfish
1 x Hidden Triplet
1 x XYZ-Wing
1 x Unique Rectangle type 4
1 x Bidirectional X-Cycle
2 x Turbot Fish
1 x Forcing X-Chain
2 x Bidirectional Y-Cycle
14 x Forcing Chain
1 x Aligned Triplet Exclusion
1 x Nishio Forcing Chains
4 x Region Forcing Chains
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