dailysudoku.com

garytorborg · Joined: 19 Jan 2011 Posts: 28

I tried the techniques that I know so far, but I still have WAY too many candidates in this messy puzzle. After "basics," I am at this position:

Marty R. · Posted: Tue Feb 22, 2011 10:18 pm Post subject:

There are a few basics remaining, none of which do any good that I can see.

R7c3<>1 due to locked candidates
R4c2<>8 due to 8 being solved in that row
R3c6<>4 due to locked candidates
R4c8<>6 due to locked candidates

There's an XYZ Wing, r5c2<>1

garytorborg · Joined: 19 Jan 2011 Posts: 28

keith · Posted: Wed Feb 23, 2011 12:14 am Post subject:

After basics:

Marty R. · Posted: Wed Feb 23, 2011 1:19 am Post subject:

daj95376 · Joined: 23 Aug 2008 Posts: 3854

You've tackled a puzzle that's far outside the techniques you use.

It's possible that a deadly pattern exists that'll crack the puzzle. That's beyond what my solver can handle. However, my solver found two chains that open it up for many steps.

garytorborg · Joined: 19 Jan 2011 Posts: 28

Thanks, everyone. Whew! I'm going to have to brush up on my chains as a technique for solving tough puzzles like this one.

Koala · Joined: 15 Mar 2011 Posts: 8

Gary Torborg
I totally agree with your point stated in the other discussion “I disagree that any puzzles have no solution other than guessing”. At this discussion, I don’t think daj95376’s technique will satisfy you. To me it is a kind of forcing net . I think a method I used in another puzzle posted in sudokuxtra forum to solve this puzzle perhaps can satisfy you better. I am looking forward to hearing comments from all of you, especially from Keith and Marty.
The puzzle :

Koala · Joined: 15 Mar 2011 Posts: 8

Gary Torborg
(Continued)

The logic : r3c7=4 => r9c7<4>r2c9=78,
r3c7=4 =>r3c1=6=>r1c3=157=>(a naked triple 157 in box 1)=>r2c2=39=>(a naked pair 39 in row2)=>r2c4=78=>(a naked pair 78 in row2)=>r2c3=5=>r7c3=4
=>r9c1<>4 and r9c2<>4.
The result: r3c7<>4 and the puzzle can then be solved by singles.

Koala · Joined: 15 Mar 2011 Posts: 8

Gary Torborg

daj95376 · Joined: 23 Aug 2008 Posts: 3854

It took a bit of deciphering, but I did manage to create a close clone to Koala's solution.

keith · Posted: Sun Mar 27, 2011 5:14 am Post subject:

Very nice.

Koala · Joined: 15 Mar 2011 Posts: 8

Daj95376 and Keith
Thank you so much for giving me an immediate and helpful response. First, Daj95376 is so nice and clever to let me know a better way to get r3c7<>4. Please take a look at my story behind the work and give me your comments again.
Secondly, Keith has enough reasons to suspect my work being a justification of a backdoor found. I must confess that this is not my first version of the work, it did come afterwards, but not the way you think. My story is that I did this in 3 steps (shown in the following) and then I found it can be condensed in one step.

YZ-method (1)

Asellus · Posted: Sun Mar 27, 2011 6:45 pm Post subject:

There is a bit too much "if this is true then that happens" in this YZ-method concept for my taste. It seems to me that this is replicating (multi)coloring with transports. If so, I prefer the coloring because it is more mechanical without requiring strings of if-then statements. Let's look at this same thing using coloring, starting with the weak inference <5>s in those c3 bivalues, which I will color "a" and "b":

Koala · Joined: 15 Mar 2011 Posts: 8

Hi Asellus

Asellus · Posted: Mon Mar 28, 2011 11:24 pm Post subject:

Hi Koala,

These are old and endless debates. Where one comes down in them regarding solving practices is pretty much a personal choice.

Yes, "if-then" reasoning underlies all logical techniques. But that doesn't mean that I am performing "if-then"s in my head when I use a solving technique. I can use an XY-Wing or X-Wing or the like by recognizing the pattern. It is true that to understand how it works (why it is valid) I have to have done some "if-then" thinking initially. But I don't redo that reasoning any longer after I have been convinced. I apply the method mechanically. It is the same with coloring and multi-coloring: I apply rules mechanically without making assumptions or doing any "if-then" thinking.

All coloring (and most anything else in sudoku) can be expressed as alternate implication chains (AICs), which are what I call the things you have notated. "Forcing Net" is a more general term. I do not consider AICs to be forcing because, again, they can be constructed and used without making any truth assumptions or performing any "if-then" thinking. I merely need to know how to recognize weak and strong implication instances within the grid and note occasions where they link up end-to-end in alternating fashion that leads to a loop discontinuity (contradiction).

Not everyone thinks of AICs in this way and so it creates confusion with forcing methods, in my opinion. If people are making true/false assumptions and then doing "if-thens" around the grid in order to discover their AICs, that's fine. But it's not how I do it.

As I said, it's an old debate and a matter of personal preference. However, I do believe that there is a more or less clear divide between basic forcing approaches and those that involve the application of mechanical rules. I prefer to stay on the latter side of the divide, myself.

PS: Years ago I raised objections similar to yours in response to Myth Jellies. Clearly my thinking has evolved since because I now agree with him.

Koala · Joined: 15 Mar 2011 Posts: 8

Hi Asellus,

Thank you so much for your helpful response! First, I agree that once a device is set up with logic we need not mention “if-then” anymore. Secondly, this is the first time I learn the transports skill from you (it is great). I didn’t understand at the first reading so I mistook it as some kind of forcing. Sorry! In the past, I took (multi)coloring as a pair of conjugate groups with two different colors. You may get some candidates eliminated, or one group disappeared, or nothing happen at all. I feel that the transporting to coloring is far more fruitful than the fins to the fishes. Anyway, thanks a lot! Now I wish to let you know about the YZ method. When I did the VH, I began by looking for X-Wing, fishes, XY- wing and so on. Someday I found myself just like a child looking for the hidden rabbits in a picture. It is no fun anymore! I started with considering naked pairs. Everybody loves it I suppose. It is so natural to eliminate some candidates just because they make a conflict in these two cells. Now, if instead of a naked pair we have, for example, 23 and 25 in different cells in one unit, is it possible to eliminate some candidates just because they make a conflict in these two cells? YZ method is to find candidates that eliminate 3 and 5 separately first and then to see if we are able to find the one which can do both. I did this for quite some time and enjoyed myself. I applied YZ method to do the “tough one” and posted. Someone took it as a justification of a backdoor stuff, someone took it as a replication of something. So I am not going to post controversial things anymore. BACK TO VH FAMILY! If you would be so kind to have a look at the work I did for the 2011-3-27 VH posted I should appreciate very much!

Best regards,

Koala

Asellus · Posted: Tue Mar 29, 2011 9:41 am Post subject:

Koala,

Don't worry about posting new ideas that may be "controversial." That's how one learns. Plus, you never know if some new idea may turn out to lead others to discover something useful.

I looked at the 2011-3-27 posting. There are 3 different ways apparent to me for how that same elimination can be derived with standard mechanical rules.

First, an XY-Chain: (5=6)r1c2-(6=9)r1c8-(9=4)r3c8-(4=5)r2c9

Second, as simple coloring. The weak inferences in the XY-Chain above are all conjugate pairs so coloring would propagate along the chain and reveal those pincer <5>s as well. (Multi-coloring and transports are not necessary here.)

Third, as an ALS or XZ technique. The r1c2 bivalue is one ALS. The other is the 3-cell 4569 ALS in box 3. The <6>s in row 1 are shared exclusive and the <5>s are shared common:
(5=6)r1c2 - ALSr13c8|r2c9[(6)r1c8=(5)r2c9]

In general, your "Yellow Zone" method is exploiting the strong inference that exists within the YX and XZ 2-cell ALS: Y=Z. The <X>s have a weak inference and if they are a conjugate pair (as in the 2011-3-27 puzzle) then you can form a single color cluster. Otherwise, you can form two color clusters, one from Y and one from Z with the X-X weak inference serving to "bridge" the two clusters (as in the example above in this thread). Note that any candidate thus "trapped" and eliminated by the coloring produces a contradiction that would result in both Y and Z being false, the desired result of your method but without any truth assumptions or "if-then"s. Seen in this way, there is no reason to limit oneself to a 2-cell ALS composed of two bivalues. Any strong inference in any ALS is a potential germ of such a method.

As for those fish fins, they can be transported too, you know. (I believe that is an example of what some call Kraken Fish... but don't quote me on that!)

Koala · Joined: 15 Mar 2011 Posts: 8

Asellus

I am so happy to learn so many things from you. I just wonder our posts may be off the topic “tough one” and will be banned anytime. I don’t know in what way I can get in touch with you again. I believe I understand all (you are marvelous!) you stated (took quite some time I must confess) but the following :

“the Otherwise, you can form two color clusters, one from Y and one from Z with the X-X weak inference serving to "bridge" the two clusters (as in the example above in this thread). Note that any candidate thus "trapped" and eliminated by the coloring produces a contradiction that would result in both Y and Z being false,”

If you don’t mind could you let me have more details on what you said above under the topic 27March VH?

Thank you

Koala