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5 September Difficult for Me

 
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jabejochke



Joined: 16 Mar 2006
Posts: 21
Location: Reading

PostPosted: Wed Sep 06, 2006 2:49 pm    Post subject: 5 September Difficult for Me Reply with quote

I found this puzzle very difficult. After completely profiling by row, I had identified only four values. In the end I could only solve using multiple unique rectangles with same base: 35 pair in row 7, columns 4 and 6.

Since there have been no comments, there probably was a much quicker solution path than I took. Any insights as to other solution paths would be appreciated. Thanks!

The layout at the point that I followed the unique rectangle path is shown below:

Code:
248    23568  23568  2568   258    9      457    5678   1     
489    568    5689   1568   158    7      459    2      3     
289    7      1      2358   4      2358   6      589    89
6      9      2358   12358  123578 12358  37     378    4     
178    1358   4      358    35789  358    2      36789  6789
278    238    238    4      23789  6      379    1      5
129    12     7      35     6      35     8      4      29 
5      4      268    9      128    128    137    367    267   
3      1268   2689   7      128    4      159    569    269   
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Wed Sep 06, 2006 4:12 pm    Post subject: Hidden triplet in column 5 Reply with quote

Hi, Jack!

I thought this puzzle was kind of cute.

-- Because of the {3, 5} pair in row 7 (which you've already identified) and also because the "3" in row 3 must lie in r3c4 or r3c6, you can identify the "hidden triplet" {3, 7, 9) in c5r456 right off the bat. Alternatively, you can see the "naked quad" {1, 2, 5, 8} in c5r1289 and identify the triplet that way.

-- Once you find the triplet you'll see the {5, 8} pair in r5c46, which lets you make quite a few eliminations.

Finally, the {3, 5} in row 7 and the {5, 8} in row 5 make an X-Wing on "5", allowing you to set r3c8 = 5 ... the rest should be straightforward. dcb
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Thu Sep 07, 2006 1:39 am    Post subject: Reply with quote

If puzzles had names, this one could be called "Box/line, box/box interaction (locked candidates 1, locked candidates 2) to the rescue".

Entering the singles didn't seem to have much of an affect, but all the exclusions from the box/line, box/box interactions made things quite apparent. One box/line interaction on 1's, two box/line & one box/box on 3's results in a naked pair in row & box 5. Once those exclusions are made, three more singles can be entered. Now a box/box interaction on 5, which makes the same exclusions as the X-wing mentioned by David Bryant and allows the same placement in r3c8, which indeed makes the rest of the puzzle straightforward.


Last edited by TKiel on Thu Sep 07, 2006 9:58 pm; edited 1 time in total
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Marty R.



Joined: 12 Feb 2006
Posts: 5175
Location: Rochester, NY, USA

PostPosted: Thu Sep 07, 2006 5:05 pm    Post subject: Reply with quote

I think maybe what Tracy calls "box/box" and "box/line" interactions, I call "locked candidates." I don't recall which I used in this puzzle, but they're normally used in just about every puzzle I do.

In this particular one, over and above the locked candidates and pairs, triples, etc., I used a Type 1 rectangle on 69 to finish it off.
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keith



Joined: 19 Sep 2005
Posts: 3182
Location: near Detroit, Michigan, USA

PostPosted: Thu Sep 07, 2006 9:24 pm    Post subject: My solution Reply with quote

In the grid posted by jabejochke there is a minor error: R1C8 cannot have the candidate <6>.

I spotted the <35> pair in R7B8 almost immediately, without pencil marks (yet). As I now usually do, I then went looking for a UR, and put candidates in R3. Type 3 or Type 4, your choice. The result is that R3C8 is <5>. From then on it is pretty straightforward.

But, Tracy is correct. This can be solved with "basic" methods only (no UR's or X-wings), but that is a lot more difficult than what I outlined above.

Marty, In the posted grid there is a line-box interaction. The <1> in R7 must lie in Box 7. So, R9C2 cannot be <1>. You can tell us if that is a locked candidate.

Best wishes,

Keith
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Thu Sep 07, 2006 9:57 pm    Post subject: Reply with quote

Marty R. wrote:
I think maybe what Tracy calls "box/box" and "box/line" interactions, I call "locked candidates.


Correct. Box/line interactions are locked candidates 1 (exclusions in a row or column) and box/box are locked candidates 2 (exclusions within the same box). I previously referred to them as locked candidates (because that is what they were called in SS), but have since been made aware that most people refer to them as box/line, box/box. In the interest of common terminology, I switched. These are the easiest exclusions to find, after naked singles, IMO.
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Marty R.



Joined: 12 Feb 2006
Posts: 5175
Location: Rochester, NY, USA

PostPosted: Fri Sep 08, 2006 12:47 am    Post subject: Reply with quote

Quote:
Marty, In the posted grid there is a line-box interaction. The <1> in R7 must lie in Box 7. So, R9C2 cannot be <1>. You can tell us if that is a locked candidate.


Yes Keith, it is.

Quote:
I previously referred to them as locked candidates (because that is what they were called in SS), but have since been made aware that most people refer to them as box/line, box/box.


I call them locked candidates because that is the term for the technique that I first learned when I was a newbie scouring web sites and old habits are hard to break. I did not realize that most people call them something else.

I probably learned them from AngusJ, whose definitions are below. So which is box/box and which is box/line?
------------------------------------------------------------------------------------------------
Locked Candidates 1:
Sometimes a candidate within a box is restricted to one row or column. Since one of these cells must contain that specific candidate, the candidate can safely be excluded from the remaining cells in that row or column outside of the box.

Locked Candidates 2:
Sometimes a candidate within a row or column is restricted to one box. Since one of these cells must contain that specific candidate, the candidate can safely be excluded from the remaining cells in the box.
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Fri Sep 08, 2006 1:31 am    Post subject: Reply with quote

Marty R. wrote:
I call them locked candidates because that is the term for the technique that I first learned when I was a newbie scouring web sites and old habits are hard to break. I did not realize that most people call them something else.

I probably learned them from AngusJ...


I did too.

Marty R. wrote:
...whose definitions are below. So which is box/box and which is box/line?
------------------------------------------------------------------------------------------------
Locked Candidates 1:
Sometimes a candidate within a box is restricted to one row or column. Since one of these cells must contain that specific candidate, the candidate can safely be excluded from the remaining cells in that row or column (row or column = line)outside of the box.

Locked Candidates 2:
Sometimes a candidate within a row or column is restricted to one box. Since one of these cells must contain that specific candidate, the candidate can safely be excluded from the remaining cells in the box.
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Marty R.



Joined: 12 Feb 2006
Posts: 5175
Location: Rochester, NY, USA

PostPosted: Fri Sep 08, 2006 3:40 am    Post subject: Reply with quote

Well, I'll try, maybe it's possible to teach an old dog new tricks. I wonder how long it will take for me to learn the distinction between box/box and box/line. Question
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Fri Sep 08, 2006 9:58 am    Post subject: Reply with quote

Up until a few weeks ago I didn't even realize there two names, but I still used them both.

For box/line (locked candidates 1) you're looking for a box that has the candidates confined to a single row or column. Candidates in a box locked in a line.

For box/box (locked candidates 2) you're looking for a line that has the candidates confined to a single box. Candidates in a line locked in a box.
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Marty R.



Joined: 12 Feb 2006
Posts: 5175
Location: Rochester, NY, USA

PostPosted: Fri Sep 08, 2006 3:42 pm    Post subject: Reply with quote

The distinction is fuzzy, as both involve a box and a line. For me, one term, "box/line", would suffice. In fact, not only would it suffice, it would probably be clearer and less confusing to the masses, which includes moi.
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Fri Sep 08, 2006 11:27 pm    Post subject: Reply with quote

I agree. I don't think it was until the most recent version of SS that a distinction was made, but I could be wrong. Maybe it's from the same people that decided all the UR's needed to be a different type. The term 'locked candidates' seems to make more intuative sense, because they are either locked in a certain box or locked in a certain line and it wouldn't be hard to figure out which applied.
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