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jabejochke · Joined: 16 Mar 2006 Posts: 21 Location: Reading

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:

David Bryant · Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

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

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

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.

Marty R. · Posted: Thu Sep 07, 2006 5:05 pm Post subject:

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.

keith · Posted: Thu Sep 07, 2006 9:24 pm Post subject: My solution

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

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

Marty R. · Posted: Fri Sep 08, 2006 12:47 am Post subject:

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

Marty R. · Posted: Fri Sep 08, 2006 3:40 am Post subject:

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

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

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.

Marty R. · Posted: Fri Sep 08, 2006 3:42 pm Post subject:

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.

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

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.