dailysudoku.com

[Asellus]

[Marty R.]

[Asellus]

Congratulations on your first W-wing!

Where was your initial X-wing located, if you recall ('cause I can't see one)?

I'm still wobbly with URs and have to look up Type numbers... but, mine was Type 1 (and Type 6 in that an X-wing was superimposed). And, my ALS was also an XY-chain, which is easier to see as such.

I don't know what the "DB puzzles" are. This one was from a newspaper and 5 stars was the maximum.

While one wasn't involved in this case, I find it interesting that so many people say they find XY-wings hard to spot. For me, they are the easiest... easier even than X-wings. Lucky me, I guess! I only learned that they could be expanded into XY-chains in the past week or so from reading this board. Gotta practice that more!

[Mogulmeister]

There was an X-wing on 7's in columns 6 and 7 .

[Marty R.]

Asellus,

The first X-Wing I noticed was on 7. Then a Type 4 rectangle on 25. There was a Type 1, I think on 13, that I didn't use. Then another X-Wing on 5, followed by the W-Wing. I didn't notice a Type 6. I am weak on XY Chains and even weaker on ALS's.

DB is the initials of a puzzle maker, David Bodycombe, whose six-star puzzles are often published by Keith on Saturdays, including today. I believe DB's Friday puzzles are five stars, which is why I thought yours was one of his.

[Mogulmeister]

I wonder if the David on this board is the same DB ?

[keith]

[lkmckin]

I eventually resorted to a UR, which I consider cheating, and still didn't solve this B%$#. Here's my progress. Any help?

[Asellus]

lkmckin,

Since I started this, I'll respond! First, it is possible to get to the position you show without having used a UR.

The most obvious next step is the X-Wing on 7 mentioned in earlier posts. It is located at Rows 2 and 8 and Columns 6 and 7.

After that, all postings have indicated requiring the need of at least one UR. So, "cheating" may be obligatory!

After the X-Wing, I used an XY-Chain: R7C9>R8C7>R8C6>R8C4 to eliminate <9> from R7C4.

This leaves a Type 1 UR that has only a single extra digit. So, if that's "cheating," then it is probably the puzzle creator who cheated!

(This UR is also an X-Wing on 2 which makes it also, I believe, a Type 6 with <2>s mandatory in the diagonal bivalue cells.)

[lkmckin]

Asellus,

Thanks for the help. I was over 2 hrs into this mess.

I had found all the x-wings, and I used the UR to eliminate 5 from R7C4, R7C6, and R8C3, since R7C4 or C6 must be 2. However, since I didn't find the XY chain, I couldn't progress.

I had thought that UR's were never necessary, and philosophically don't like them, but maybe I was wrong after all.

[Asellus]

lkmckin,

OK... I like a challenge: find a solution without a UR. I did. But first...

You might be interested to note that the XY-Chain is also Almost Locked Sets (ALS), which is how I first saw it in fact. (This will come in handy again in a moment!) The strong link is on 3 and shared common is 9 resulting, of course, in the same elimination. Without proving so, I suspect that any ALS that includes only bivalue cells is an XY-Chain.

Also, the debate about "deadly pattern" based solutions is interesting. For me, any invalid solution is acceptable as a logical basis. I'm not picky about the flavor. I just like whatever gets me to the valid solution.

Now, the non-UR solution:

From where we left off, there is an XY-Wing with pivot R8C6 that eliminates <3> from R2C3.

That results in a 37 Naked Pair in C7.

Next is an ALS:
ALS1 is R7C1, R7C2, R8C3
ALS2 is R8C7
Strong link on 3; Shared common is 7.
Eliminates <7> from R7C8.

Now, a simple color wrap on 7: R9C5 > R8C6 > R8C7 > R9C8
Eliminates 7 from R9C2 and the solution follows immediately.

So, maybe you can survive without URs after all!

[Mogulmeister]

Hi Asellus,

I am a little confused by your ALS (see below)



As I understand ALS eliminations, you need a restricted common candidate which can only exist in one set or the other but not both upon resolution. When you have met that criteria you can then look for the shared common.

As I see it, you have 3 as your locked common which is also in r7c12 - this means that as far as your two ALS are concerned 3 can be in both sets after resolution.

Perhasp I'm missing something.........

[Mogulmeister]

As you said, the xy chain is also an ALS (set A pink, set B green) with the restricted common being 7 (r8c67) which will be in A or B but not both.

The shared common which is the 9 (orange) in r7c4 is eliminated as it can see 9 in both sets.

[Asellus]

Ooops! My apologies. That's not an ALS. I got lucky.

However, in reviewing what I did, I discovered that the "non-ALS luck out" step isn't necessary to arrive at a solution without a UR (which was my goal).

First, the starting point is after elimination of <9> in R7C4 using the XY-Chain discussed earlier (which actually is an ALS this time!). This reveals the XY-Wing mentioned earlier:

[Mogulmeister]

It works as would another triple in box 7 of {3,5,7) however, how did you lose the 9 that had existed before in r8c3 ? This is crucial to your triple (and mine!).

[Asellus]

There were only two nines in column 4.

[Mogulmeister]

We're talking about c3 though where there were 3 9's (see my diagrams above).

[Mogulmeister]

its OK I've seen it - the 9 in r8c3 is eliminated as a result of the XY chain which gets rid of one of the 9's in c4 making r8c4 a 9. Your diagram didn't show the values in the solved squares and mine shows the state of play prior to the XY execution !!