dailysudoku.com

[keith]

Here is a good example of some of the stuff I have been talking about.

I found it in a book of puzzles I bought at a dollar store.

[immpy]

Hello all, not sure what others found when trying to solve this one. But I was able to use BASICS only to solve it. Yet, it was rated too hard by the Draw/Play in its initial state. I used a few prelim pencil marks, but they were steadily erased as the dominoes continued to fall. No advanced moves necessary. Be mindful that I look at puzzles just a bit differently of late, using strong links to eliminate early on some would-be candidates that no longer apply because of the strong links. If I spot them!! LOL I surely don't always see everything. LOL

Here is how I ended up....

[immpy]

Keith, at a point later in the puzzle, there was a potential BUG+1 that looked like it may develop, but following through on the basics washed the BUG away, leaving only basics.

Maybe this is what you meant by your example??

cheers...immp

[immpy]

If you are interested, check out my post for Top Shelf Hard Puzzle. It seems similar somehow to my experience with this puzzle, in that a puzzle rated above Very Hard was managed to be solved by basics only.

http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=8428&start=0&postdays=0&postorder=asc&highlight=&sid=6d746eaff04d1bef06ae3c3c3672c98f
That particular puzzle was rated "unfair" by my software, and yet I solved it first try with BASICS only. Helmut's helper ran aground, I couldn't replicate my path....my software found all kinds of wings, chains, etc. to solve it....but I DID IT WITH BASICS.....very puzzling indeed.

Ajo Dimonios referred to backdoors in this instance....maybe that has something to do with it....

Any enlightenment here is greatly appreciated.....

cheers...immp

[keith]

immpy,

I think you made a fortuitous solving mistake. I first solved this by pencil and paper, then checked my work using Sudoku Susser.

Here is my after basics grid:

[Marty R.]

[keith]

Marty,

Your "after basics" is the same as mine. It is good they agree.

Now, take a look at the Nataraj diagram for "2", and you will see what I am driving at at this point.

Keith

[immpy]

Helmut's helper was stymied by the puzzle from a previous post that I referred to. I didn't use it on this one.

cheers...immp

[immpy]

Indeed Keith, strong links on 2 can be used to begin making some needed eliminations. I see the example crystal clear. I must be doing some of these eliminations along my route without realizing it. I simply never get so lucky as to have a fortuitous solving mistake. LOL

Excellent example to drive home the point. Beautiful!

[keith]

immpy,

In addition to the swordfish on 2 in the after basics grid posted above, this needs at least one XY-wing. I don't buy your claim of inadvertent basics.

Anyway, here is the end game:

[immpy]

Interestingly all 3 of the BUG+3 cells have 5 as the potential DP breaker, and even more interesting, in ALL cells the 5 is indeed TRUE!

If anyone cares, I plugged this puzzle into the HoDoKu program. It allows for a search for a "backdoor" to any puzzle. It found two backdoors:

r1c7<>8
r2c5<>8

I don't understand what that means (if anything), and I am completely in the dark when it comes to the term "backdoor". I had no idea anything like this existed in some puzzles. Most importantly, what do they (backdoors) mean to someone trying to solve an extremely hard puzzle?

cheers all...imp

Thank again to Keith for posting this interesting puzzle.

[immpy]

I found something interesting today, an article on legal moves and backdoors, etc. Very good reading. Check it out if you have time.

https://sourceforge.net/p/hodoku/discussion/907402/thread/7d21e2ac/?limit=25#24dd

Basically, the author was wondering if moves he was making were illegal somehow. Because he was sometimes finding (as I have now found twice) that some very difficult puzzles are sometimes being solved very easily, i.e. with basics only.

I am quoting the author here:

" And yes, the side effects of
eliminations can be confusing."

The first case (eliminating a candidate makes the puzzle easier) is simple
enough to understand: Every puzzle has one or more cells, that, when set,
reduce the puzzle to singles (the "backdoors"). The solver searches for steps
in a predefined order. A human solver solves more intuitive. If an
elimination, that is not part of the computer solution, triggers a backdoor,
the puzzle becomes very easy indeed."

And again I quote the author of the post:


"Determining if an elimination is "legal" or not is not as easy as it sounds
and I doubt it can be done altogether, especially when you take into account,
that players sometimes execute more than one step at once. The only real
"ultimate" check is, wether an eliminated candidate was part of the solution
or not, as you mentioned above."

I maintain that I solved this example puzzle with BASICS ONLY because I did in fact do so. I have no reason to lie about this fact. Whether or not I was fortuitous, lucky, or even stupid or mistake prone makes no difference. The end result is that my solved puzzle matched the author's (Keith) solved puzzle. And that is the bottom line. If a mistake would have been made, the results would not match, or the puzzle would be rendered unsolvable or invalid. I do now (more than ever) execute multiple steps at one time without thinking about it consciously. My path is almost impossible to replicate unless I would jot down every move as I made it. I am indeed a pencil and paper solver, and I therefore believe I am much more intuitive than a computer program.

Hope I shed some light.....

cheers...immp

[keith]

immpy,

Sorry, I don't buy it. You say you solved this puzzle by basics only, but you are not prepared to say exactly how?

Yes, we would expect you to explain every step.

To make it easier for you to explain, what is your next move?

[immpy]

Keith, here's the rub. You are correct when you ask, what is your next move? But that assumes that I am exactly HERE when it's time for the next move. Without you looking over my shoulder as I solved, I can't tell you where I was, but I would think many of my 2s were already solved by now...again I have no proof, because I cannot replicate my path; I simply don't write down every move as I make it. Assuming then that I arrived here, you are correct in also assuming basics will not solve it from HERE. I only looked quickly, but I don't think they will.....again FROM THIS POINT!!

All I am saying is that I now have solved two super hard puzzles with basics only. The first time it happened I was confused and amazed....not only at my accomplishment, but that others who tried did not find it to be that easy. Marty was the first person who got me questioning myself, when he found the puzzle much harder than my results indicated. I then ran it through Helmut's Helper as a self check....and after it did it's basics, it found a few (no more than three) advanced moves, and then the program displayed the message "I'm sorry, this puzzle is beyond this helper's capabilities"...or something along those lines. I was truly puzzled now. I then ran the same puzzle through my program which it was created on, which was HoDoKu....and it was able to solve it, but it found XY-wings, flightless XY-Wings with extensions, etc. and I think it culminated in a long chain of a sort. I am incapable of finding chains, and I simply don't even try to find them. Even as I followed the path of the program's use of this chain, I still could not grasp the execution of it. I suck at chains. So how DID I solve it?? I asked the community, and Ajo Dimonios referred to "backdoors" of which the noted puzzle supposedly had 25 of these. And I again asked this community....What does it all mean?? What are backdoors?? Any help is greatly appreciated.

Your puzzle "A Nice Example" is the second one I have been able to solve with basics only, and I think it is a super hard puzzle, much harder than most, requiring several moves to complete.

If it happens once (the solving by basics)...OKAY, maybe I got lucky somehow. When it happens twice, something is going on here. What is it?

I just wanted to inform you, or anyone reading this, that it has happened to others as well, I no longer feel alone when it comes to this. I am assuming you checked out the link I included in an earlier post on this topic. The author of that post stated that the exact same thing has happened to him/her several times with a quite difficult puzzle. I can only think that it may have something to do with these "backdoors". And that was the explanation given....unlocking one of these backdoors can render a very difficult puzzle to a much easier state. It also states that what we do in our "basics" mode of solving could also very well make a particular puzzle even harder than it was....we may eliminate a candidate that removes the chance of an XY-Wing, UR, X-Wing, strong link, etc. There are two sides to this conundrum!!

I, as stated earlier, like to think that we (as human pencil and paper solvers) are much more intuitive than a computer program. And I believe this is true. You have said it yourself, if I remember correctly...."We, as pencil and paper human solvers have a slight advantage, because almost all Sudoku puzzles are created by a program of some kind.

I am also certainly not trying to hide anything, I have no reason to. I just honestly relate my experience, and that is all I can do. I love solving Sudokus....so if I seem like I am not prepared to tell you how I did it
....I think I just did tell you....or at least I tried to tell you from what knowledge I have just recently been made aware of.

My question to you now is, has this not ever happened to you before?? A quite difficult puzzle which solved almost too easily for belief??

Keith, and everyone...have a good day.......
immp

[keith]

immpy,

Solving a Sudoku with basics is not path dependent. Either the puzzle is solvable with basics, or it is not. If it is not, everyone will reach the same "after basics" grid.

So, if a puzzle requires advanced moves, and you claim to have solved it with basics only, you have made a lucky mistake. There is no other explanation, such as it was a full moon on Ground Hog Day. Or, you just happened to be more "intuitive" yesterday.

If you want to pursue this, I ask that you solve the puzzle again, and tell us how you get beyond the "after basics" grids posted above.

I am only aware of one case where Sudoku solutions are path dependent. That involves UR eliminations, where one UR may obscure another.

By the way, a "back door" is a case where solving a single cell will reduce the rest of the solution to basics only. Some people use software to find back doors so they can then be triumphant about finding one-step solutions.

In this case, R1C3 = 2 is a back door.

Keith

[immpy]

Keith, thank you for taking the time to respond and enlighten. As a solver who is always looking to learn something from each new experience, your knowledge is respected and greatly appreciated by me, and others as well, I am sure. Had you not taken the time to reply and share, I'd still be in the dark. Thanks again.

Upon trying again to solve the puzzle, several times in fact, I can get only as far as the latest grid with possibly a few candidates missing, but not any that reduce it to singles.

LOL, with many puzzles, most of the time I'm just plain happy to have solved the damn thing.
I am not going to pursue this puzzle any longer....

cheers...immp

[Ajò Dimonios]

Hi everyone


This sudoku has 22 “backdoors” (R1C3=2,R1C5=5,R2C1=5,R2C2=6,R2C7=4,R3C1=3,R3C2=4,R3C4=2,R3C9=5,R5C1=2,R5C2=3,R5C9=7,R6C3=6,R6C7=2.R7C4=5,R7C7=7,R7C9=2,R8C1=6,R8C3=5,R8C9=4,R9C5=2 and R9C7=5). Each of these candidates, if inserted, solves the puzzle but does not demonstrate the uniqueness of the solution.

Ciao a Tutti
Paolo