Hard Sudoku

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Hard Sudoku

Postby Paulie » Mon Nov 21, 2005 3:10 pm

Hi all,

Stuck on this one. Apparently, some solvers say that there is a naked quad in column 3 but I don't see it. Anyone?

Regards,

Paulie.

Code: Select all
 *-----------*
 |.9.|.54|..2|
 |2..|9.3|...|
 |...|.7.|.8.|
 |---+---+---|
 |48.|5..|.1.|
 |..1|...|4..|
 |.6.|..2|.73|
 |---+---+---|
 |.7.|.6.|...|
 |...|7.5|..1|
 |6..|12.|.4.|
 *-----------*


 *-----------*
 |.9.|654|132|
 |21.|983|7.4|
 |.4.|271|.8.|
 |---+---+---|
 |48.|5..|.1.|
 |..1|8..|4..|
 |.6.|412|873|
 |---+---+---|
 |174|369|..8|
 |...|745|..1|
 |65.|128|.47|
 *-----------*

 
 *-----------------------------------------------------------*
 | 78    9     78    | 6     5     4     | 1     3     2     |
 | 2     1     56    | 9     8     3     | 7     56    4     |
 | 35    4     356   | 2     7     1     | 569   8     569   |
 |-------------------+-------------------+-------------------|
 | 4     8     237   | 5     39    67    | 269   1     69    |
 | 37    23    1     | 8     39    67    | 4     2569  569   |
 | 59    6     59    | 4     1     2     | 8     7     3     |
 |-------------------+-------------------+-------------------|
 | 1     7     4     | 3     6     9     | 25    25    8     |
 | 389   23    2389  | 7     4     5     | 369   69    1     |
 | 6     5     39    | 1     2     8     | 39    4     7     |
 *-----------------------------------------------------------*
[/quote]
Paulie
 
Posts: 10
Joined: 08 August 2005

Postby CathyW » Mon Nov 21, 2005 5:14 pm

Yes, there is a quad in column 3 - look for the cells that only contain 3,5,6 and 9. Then you can eliminate from other cells in column 3, which allows placement of r4c5.

Then there's an x-wing for 9s in boxes 3 and 6.

Hopefully that will lead you to solution.
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Posts: 316
Joined: 20 June 2005

re: trio vs. quartet

Postby Pat » Tue Nov 22, 2005 12:06 pm

Paulie wrote:some solvers say that there is a naked quad in column 3 but I don't see it
Code: Select all
 *-----------*
 |.9.|654|132|
 |21.|983|7.4|
 |.4.|271|.8.|
 |---+---+---|
 |48.|5..|.1.|
 |..1|8..|4..|
 |.6.|412|873|
 |---+---+---|
 |174|369|..8|
 |...|745|..1|
 |65.|128|.47|
 *-----------*

the 2,7,8 trio in c3
eliminates 3 in r4c3.

why would it be easier to find a quartet??

- Pat
Last edited by Pat on Tue Nov 22, 2005 12:13 pm, edited 1 time in total.
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Postby emm » Tue Nov 22, 2005 12:34 pm

A hidden triple vs a naked quad - that's got to be a matter of debate. Personally I think the quad's easier.
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Postby CathyW » Tue Nov 22, 2005 4:45 pm

I agree - in this instance the quad was easier to spot, the triple becoming visible after the eliminations.
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Posts: 316
Joined: 20 June 2005

Postby tso » Tue Nov 22, 2005 5:50 pm

In this case, the naked quad and the hidden triple are two names for exactly the same deduction. Which is simpler to spot is subjective. This illustrates a specific case of a broader point -- that the "next logical step" is ususally subjective. An xy-wing is by consensus more advanced or more difficult to find than a naked pair -- but if you see one while there are still naked pairs available, well, then that's your next logical step. Personally, I often find it much easier to spot even longer forcing chains than uncovering naked quads or hidden anythings, as I can focus only on bi-value cells.

In this case, I might have missed the naked quad and instead found a simple xy-type forcing chain:

r6c3=5 => r2c3=6
r6c3=9 => r9c3=3 => r9c7=9 => r8c8=6 => r2c8=5 => r2c3=6
Therefore, r2c3=6 and the rest is easy.

Who's to say that this isn't just as valid of a "next logical step" as the naked quad/hidden trip?

To some degree, how difficult a specific tactic is perceived is changed by what point you typically attempt to apply it. If you always wait until your bag of tricks is empty to try a specific tactic, you might rate it as the most advanced or difficult tactic while another solver might find that same tactic more of a standard tool to check for earlier on. I have solved many puzzles that supposedly required some combination of x-wings, swordfish, coloring, quads and such, only to find that a single xy-wing, forcing chain or uniqueness brought me to the solution quicker, skipping over all of the "required" tactics. If you find a naked pair, you might as well see if you can make a uniqueness elimination. If you're looking for naked triples, you might as well check for xy-wings at the same time.

The x-wing that CathyW spotted isn't needed as there is a hidden single at r8c8 that accomplishes the same eliminations -- but which is more fun to find? Did CathyW make a mistake by missing the simpler elimination? I don't think so. We are not just rats in the maze following the one and only path to the cheese.
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