Beldon 9 107

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Beldon 9 107

Postby ArkieTech » Mon Nov 20, 2006 2:38 am

Here is a puzzle I got from a Beldon book #9 the puzzle is 107 and verified v Hard with Poppacom. I worked it down to this point.:(

Code: Select all
 2 . 4 | 5 1 8 | . 3 9
 9 3 1 | 6 7 4 | 8 2 5
 8 5 . | 9 2 3 | 1 . 4
-------+-------+------
 . 8 . | . 3 5 | 9 . .
 5 . 2 | 4 9 1 | 3 . .
 . 9 3 | . 8 6 | . 5 .
-------+-------+------
 7 2 . | 3 . 9 | . 1 .
 3 4 . | 1 6 2 | 5 . 7
 6 1 . | 8 . 7 | 2 . 3





2         67        4         5         1         8         67        3         9         
9         3         1         6         7         4         8         2         5         
8         5         67        9         2         3         1         67        4         
14        8         67        27        3         5         9         467       12       
5         67        2         4         9         1         3         678       68       
14        9         3         27        8         6         47        5         12       
7         2         58        3         45        9         46        1         68       
3         4         89        1         6         2         5         89        7         
6         1         59        8         45        7         2         49        3         



Help?:(
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Postby udosuk » Mon Nov 20, 2006 2:52 am

There is an x-wing on 6 but not very useful... The critical move is a turbot fish on 7:
Code: Select all
 *--------------------------------------------------*
 | 2   *67   4    | 5    1    8    |*67   3    9    |
 | 9    3    1    | 6    7    4    | 8    2    5    |
 | 8    5    67   | 9    2    3    | 1   -67   4    |
 |----------------+----------------+----------------|
 | 14   8    67   | 27   3    5    | 9    467  12   |
 | 5   *67   2    | 4    9    1    | 3   *678  68   |
 | 14   9    3    | 27   8    6    | 47   5    12   |
 |----------------+----------------+----------------|
 | 7    2    58   | 3    45   9    | 46   1    68   |
 | 3    4    89   | 1    6    2    | 5    89   7    |
 | 6    1    59   | 8    45   7    | 2    49   3    |
 *--------------------------------------------------*

r3c8=7 would force two 7s on c2, therefore r3c8<>7.

It'd be nice to post the original puzzle to see if it requires other techniques...:idea:
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Postby daj95376 » Mon Nov 20, 2006 3:01 am

Code: Select all
# X-Wing   on <6>    => [r5c8]<>6
# XY-Wing  on [r5c8] => [r4c8]<>6 (Singles follow)

# -or-

# XYZ-Wing on [r5c8] => [r4c8]<>6 (Singles follow)
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Postby ArkieTech » Mon Nov 20, 2006 6:25 am

Thanks,:D

Here is the original puzzle.

Code: Select all

 2 . 4 | . . 8 | . . 9
 9 . 1 | . 7 . | . . .
 . 5 . | 9 . . | . . 4
-------+-------+------
 . 8 . | . 3 . | 9 . .
 . . 2 | 4 . 1 | 3 . .
 . . 3 | . 8 . | . 5 .
-------+-------+------
 7 . . | . . 9 | . 1 .
 . . . | . 6 . | 5 . 7
 6 . . | 8 . . | 2 . 3


2         367       4         1356      15        8         167       367       9         
9         36        1         2356      7         23456     68        2368      2568     
38        5         678       9         12        236       1678      23678     4         
145       8         567       2567      3         2567      9         2467      126       
5         679       2         4         59        1         3         678       68       
14        14679     3         267       8         267       1467      5         126       
7         234       58        235       245       9         468       1         68       
1348      12349     89        123       6         234       5         489       7         
6         149       59        8         145       457       2         49        3         



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Postby re'born » Mon Nov 20, 2006 10:46 am

udosuk wrote:There is an x-wing on 6 but not very useful... The critical move is a turbot fish on 7:

r3c8=7 would force two 7s on c2, therefore r3c8<>7.


Here is an alternative that is sometimes easier to spot, especially for an intermediate player:

Code: Select all
 *--------------------------------------------------*
 | 2    67   4    | 5    1    8    | 67   3    9    |
 | 9    3    1    | 6    7    4    | 8    2    5    |
 | 8    5   *67   | 9    2    3    | 1   *67   4    |
 |----------------+----------------+----------------|
 | 14   8   *67   | 27   3    5    | 9    467  12   |
 | 5   *67   2    | 4    9    1    | 3   -678  68   |
 | 14   9    3    | 27   8    6    | 47   5    12   |
 |----------------+----------------+----------------|
 | 7    2    58   | 3    45   9    | 46   1    68   |
 | 3    4    89   | 1    6    2    | 5    89   7    |
 | 6    1    59   | 8    45   7    | 2    49   3    |
 *--------------------------------------------------*


The technique is remote naked pairs. It implies that r5c8 <> [67], i.e., that r5c8 = 8.

Note that in this puzzle, the result is no better than the turbot fish above. In general, I think the best bang for your buck would be to color the 7's and deduce at once that r1c2, r3c8, r4c34, r5c8, r6c7 <> 7. But, like I said, in this puzzle, you only need the one exclusion to do the work of them all.
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Another way to see it

Postby Carcul » Mon Nov 20, 2006 11:47 am

Code: Select all
 *--------------------------------------------------*
 | 2    67   4    | 5    1    8    | 67   3    9    |
 | 9    3    1    | 6    7    4    | 8    2    5    |
 | 8    5    67   | 9    2    3    | 1    67   4    |
 |----------------+----------------+----------------|
 | 14   8    67   | 27   3    5    | 9    467  12   |
 | 5    67   2    | 4    9    1    | 3    678  68   |
 | 14   9    3    | 27   8    6    | 47   5    12   |
 |----------------+----------------+----------------|
 | 7    2    58   | 3    45   9    | 46   1    68   |
 | 3    4    89   | 1    6    2    | 5    89   7    |
 | 6    1    59   | 8    45   7    | 2    49   3    |
 *--------------------------------------------------*

{ATILA(6,7): r5c8|r3c8|r3c3|r4c3|r5c2}, => r5c8=8.

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Postby RW » Mon Nov 20, 2006 3:11 pm

Code: Select all
 *--------------------------------------------------*
 | 2    67   4    | 5    1    8    | 67   3    9    |
 | 9    3    1    | 6    7    4    | 8    2    5    |
 | 8    5    67   | 9    2    3    | 1    67   4    |
 |----------------+----------------+----------------|
 | 14   8    67   | 27   3    5    | 9    46+7 12   |
 | 5    67   2    | 4    9    1    | 3    78+6 68   |
 | 14   9    3    | 27   8    6    | 47   5    12   |
 |----------------+----------------+----------------|
 | 7    2    58   | 3    45   9    | 46   1    68   |
 | 3    4    89   | 1    6    2    | 5    89   7    |
 | 6    1    59   | 8    45   7    | 2    49   3    |
 *--------------------------------------------------*

BUG+2: r4c8<>6, r5c8<>7

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Postby daj95376 » Mon Nov 20, 2006 6:25 pm

rep'nA wrote:I think the best bang for your buck would be to color the 7's and deduce at once that r1c2, r3c8, r4c34, r5c8, r6c7 <> 7. But, like I said, in this puzzle, you only need the one exclusion to do the work of them all.

Nice catch on the Remote Naked Pairs. However, if we're making recommendations, then I favor the XYZ-Wing because it's simple and leads to a cascade of Singles to solve the puzzle.
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Postby re'born » Mon Nov 20, 2006 6:55 pm

daj95376 wrote:
rep'nA wrote:I think the best bang for your buck would be to color the 7's and deduce at once that r1c2, r3c8, r4c34, r5c8, r6c7 <> 7. But, like I said, in this puzzle, you only need the one exclusion to do the work of them all.

Nice catch on the Remote Naked Pairs. However, if we're making recommendations, then I favor the XYZ-Wing because it's simple and leads to a cascade of Singles to solve the puzzle.


I guess it is a matter of personal taste. Remote naked pairs has always been, for me, one of the easiest techniques to apply and it took me less than 10 seconds to spot it in this puzzle, whereas an XYZ-wing I have to look for consciously. Of course, which of these techniques is easier for a beginning to intermediate player to learn, I'm not sure. I've long since forgotten in which order I learned them (though it should correspond to their appearance in the manual for Sudoku Susser, my first solver program). Perhaps some of the more recently added members to the forum can share their experiences with learning these techniques.

For the human solving with pencilmarks, I also prefer my elimination as, after it, all of the deductions are naked singles while after yours, there is one hidden single first. This is not terribly relevant unless one is competing for time (which few of us here do), but there is little else for me to complain about when I am trying to split hairs.:)
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Postby daj95376 » Mon Nov 20, 2006 7:37 pm

Wait a second. We're mixing apples and oranges.

I commended your spotting the Remote Naked Pair and using it. I still do! I also agree that there are several ways to approach this puzzle, and personal preference/experience should dictate which is best for any individual.

However, my next comment was my disagreeing with your recommendation to use coloring on <7> as the best bang for your buck. My XYZ-Wing involved three primary cells, one elimination cell, and a cascade of Singles to solve the puzzle. To me, that sounds like a lot of bang for your buck!

I don't recall anyone saying that we were only talking about techniques applied by hand. You added that late in the discussions.
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Postby re'born » Tue Nov 21, 2006 12:21 am

daj95376 wrote:Wait a second. We're mixing apples and oranges.

I commended your spotting the Remote Naked Pair and using it. I still do! I also agree that there are several ways to approach this puzzle, and personal preference/experience should dictate which is best for any individual.

However, my next comment was my disagreeing with your recommendation to use coloring on <7> as the best bang for your buck.


daj,

Sorry, but I read your response and not what you quoted from my post. Mea culpa.

My XYZ-Wing involved three primary cells, one elimination cell, and a cascade of Singles to solve the puzzle. To me, that sounds like a lot of bang for your buck!


No doubt. It is still a matter of taste, of course, especially for this puzzle. If the standard is "fewest primary cells needed to make a puzzle busting elimination", I cannot top your XYZ-wing. If the standard is "easy to spot and makes a puzzle busting elimination", then it depends on your Sudoku upbringing I suppose. If, however, the standard is "most eliminations with one easy to spot technique", the coloring on 7's is the best that I have found so far.

I don't recall anyone saying that we were only talking about techniques applied by hand. You added that late in the discussions.


I didn't suggest that we were 'only' talking about techniques applied by hand. I merely noted that situation as a special case in a failed attempt at humor. The idea that one solution should be preferred over another because the cascade of singles of one starts with a hidden single is almost absurd.

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Postby udosuk » Tue Nov 21, 2006 2:30 am

I agree that what seems the easiest move to you is determined by your "Sudoku upbringing"... For me, it's Simple Sudoku, which has a nice feature of filtering candidates of a single digit out... When I filtered the 7s out, the turbot fish stood out, which immediately let me determine all the 7s in the grid and it's all naked singles afterwards... The "colors" move basically has the same effect...

If solving on paper, I think remote pairs are definitely easier to spot than xyz-wings etc... But then again I'm no expert in that area...
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