Are there puzzles that require advanced techniques?

Everything about Sudoku that doesn't fit in one of the other sections

Postby jraggio » Fri Jun 30, 2006 10:16 pm

tso wrote:
jraggio wrote:I am actually still struggling with why r1c9 and r4c9 do not form a hidden pair.

Code: Select all
+-------------+-------------+-------------+
| 478 789 5   | 6   3   89  | 1   2   47  |
| 48  1   2   | 7   5   89  | 49  6   3   |
| 67  679 3   | 1   2   4   | 79  5   8   |
+-------------+-------------+-------------+
| 3   67  1   | 8   46  2   | 5   9   467 |
| 678 2   4   | 9   1   5   | 78  3   67  |
| 5   68  9   | 3   46  7   | 48  1   2   |
+-------------+-------------+-------------+
| 2   3   7   | 4   9   1   | 6   8   5   |
| 9   5   8   | 2   7   6   | 3   4   1   |
| 1   4   6   | 5   8   3   | 2   7   9   |
+-------------+-------------+-------------+


A naked pair is two cell each of which have the same two candidates. Cells r1c9 and r4c9 have *three* candidates between them. You are correct that the three cells r145c9 form a naked triple in column 9. No two of those three cells are a naked pair. You may be conflating naked pairs with *hidden* pairs.

In this row, the first two cells are a naked pair. You can exclude the 1's and 2's from the rest of the row:
Code: Select all
Before: [12][12][12345][12678] ...
After: [12][12][xx345][xx678] ...

In this row, the digits 1 and 2 appear ONLY in the first two cells. You can exclude all other candidates from these first two cells:
Code: Select all
Before: [12345][124567][<>1,2][<>1,2][<>1,2][<>1,2][<>1,2][<>1,2][<>1,2]
After:[12x][12xx][<>1,2][<>1,2][<>1,2][<>1,2][<>1,2][<>1,2][<>1,2]



Thanks again for your time. To clarify, does "[<>1,2]" mean anything but 1 or 2?

Thanks,
John
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Postby tso » Sat Jul 01, 2006 5:18 am

[quote="jraggio]To clarify, does "[<>1,2]" mean anything but 1 or 2?
[/quote]

Yes. "<>" means "is not equal to"
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Postby RW » Sat Jul 01, 2006 7:58 am

jraggio wrote:I'd like to clarify my original statement of hoping that it is not the case that you need to learn the advanced techniques to solve even the hardest puzzles. What I meant to say was that I hope that I would be able to solve a very hard puzzle without learning what an x wing or jellyfish was, but rather apply some of that logic without knowing the official tactic.


That is very possible. Most techniques rely on patterns with n cells that let you make an elimination. Common for ALL non-uniquenessbased techniques is that if the eliminated number was true, then there would be a contradiction within the n cells. Some patterns have been found common or easy for the human eye to spot and these are defined as techniques. There are also several easy patterns that haven't been defined as techniques, but can be used to solve puzzles anyway. If you can see the contradiction caused by a certain implication, then you don't need to know wether it is a xp-wing or mr Frankenfish's nephew.

Personally I had solved puzzles for a few months before I ever read anything about techniques, and so far I have found very few new techniques that I wouldn't have discovered by myself in those few months. I may not have defined them as clearly in my head as some are defined on this forum, but I had used them. An x-wing for example is logically so simple that I was very suprised when I found out that some people called it an "advanced technique". To summarize: just think logically and you already know most of the techniques out there.

RW
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Postby jraggio » Sat Jul 01, 2006 3:06 pm

RW wrote:
jraggio wrote:I'd like to clarify my original statement of hoping that it is not the case that you need to learn the advanced techniques to solve even the hardest puzzles. What I meant to say was that I hope that I would be able to solve a very hard puzzle without learning what an x wing or jellyfish was, but rather apply some of that logic without knowing the official tactic.


That is very possible. Most techniques rely on patterns with n cells that let you make an elimination. Common for ALL non-uniquenessbased techniques is that if the eliminated number was true, then there would be a contradiction within the n cells. Some patterns have been found common or easy for the human eye to spot and these are defined as techniques. There are also several easy patterns that haven't been defined as techniques, but can be used to solve puzzles anyway. If you can see the contradiction caused by a certain implication, then you don't need to know wether it is a xp-wing or mr Frankenfish's nephew.

Personally I had solved puzzles for a few months before I ever read anything about techniques, and so far I have found very few new techniques that I wouldn't have discovered by myself in those few months. I may not have defined them as clearly in my head as some are defined on this forum, but I had used them. An x-wing for example is logically so simple that I was very suprised when I found out that some people called it an "advanced technique". To summarize: just think logically and you already know most of the techniques out there.

RW


RW, Thanks for the reply. I think you captured the essenceof my original question. I appreciate all the help I've been getting and enjoyed the conversation. Your reply is encouraging. I'm glad to hear that logic can survive any lack of the defined techniques. I wanted to make sure that I didn't get into a position where I needed to relearn differential equations to solve these things.

Thanks,
John
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