New methods?

Advanced methods and approaches for solving Sudoku puzzles

New methods?

Postby noggi » Wed Sep 28, 2005 4:58 pm

I read somewhere that Wayne solves all puzzles without candidates.

Has anybody else got any methods of how to solve fiendish puzzles without jotting down candidates?
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Postby Doyle » Wed Sep 28, 2005 5:12 pm

Not really. Wayne's puzzles (he creates them, though I'm sure he solves them also) can all be solved without trial-and-error, or so he says.
Penciling in candidates is another matter entirely. For the more difficult Sudoku, few if any mortals can solve without. Though some can play 50 games of blindfold chess at once, interrupting the games for a night's sleep, then resuming - Najdorf once did this. So maybe Wayne should speak for himself?
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Postby Karyobin » Wed Sep 28, 2005 5:33 pm

Wayne's puzzles can certainly be solved without T & E, that is a fundamental point. And I'd be impressed if anyone can solve Very Hard's (as generated by Wayne's program) in their heads. They normally need X-wings, and X-wings are quite hard to spot without candidates.

In response to the Fiendish question, the only answer is practice. I don't use candidates for any puzzles in a paper, though I used to. Remember: a Fiendish is only comparable to a Hard, and Hards never need X-Wings. You might happen upon one, but you won't have to use it to complete the puzzle.
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Postby tso » Wed Sep 28, 2005 7:05 pm

I can *sometimes* solve the V.Hards without pencil marks, but usually bail in the end and fill *some* of the cells that have only 2 (or 2 or 3) candidates. X-wings can be found without pencil marks -- more fun when that happens.


On the extreme lower end of the spectrum -- Until recently, I did all my puzzle solving on paper. I recently loaded a helper program on my Palm. (Sudoku 1.16 by Andrew Gregory). It has auto-pencilmarks, filtering, etc. I've found it enjoyable to load an EASY or MEDIUM puzzle created in Pappocom or elsewhere and enable auto-pencil marks. A completely different experience. Lots of naked pairs and triples are found this way that would never come up by *normal* solving, as most wouldn't exist after taking care of naked and hidden singles. Only a minute from start to finish.


Then on the extreme upper end of the spectrum -- taking a puzzle I know to be very hard, it's fun to use Simple Sudoku and/or Sadman and/or Sudoku Susser to zip past all the 'normal' logic. I ususally use Simple Sudoku, press F11 until it stalls, then print out the puzzle with pencil marks. A third, completely different solving experience.
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Postby noggi » Wed Sep 28, 2005 7:15 pm

Thanks, guys.
Are you saying that you spot triples and hidden triples without the use of pencils, Karyrobin? And equally carry through the candidate reductions without taking notes? In which case I'm impressed.. (I'm sorry but I'm not quite upto speed on which methods are necessary for the different levels of difficulty).
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Postby noggi » Wed Sep 28, 2005 7:17 pm

Oh and just one more thing: Did you all initially use pencilling in in order to teach yourselves what to look for?
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Postby Karyobin » Thu Sep 29, 2005 7:26 am

Right, easy one first: Yes, originally I pencilled a lot of stuff in, then had to do it less as experience increased.

Harder question, one I had to think about:

noggi wrote:Are you saying that you spot triples and hidden triples without the use of pencils, Karyrobin?


The way you phrase it, it makes it sound quite an acheivement. The thing is, as far as I'm concerned triples and hidden triples are the same thing, i.e. they only get hidden when you pepper the cells with other candidates. I'm still full of cold but I'll try to explain myself:

Imagine looking at a row with, for example, 5 empty cells. You look along it asking yourself, where can a go? Then b, c and so on. At some point it may occur to you: "Hang on - b can only be in cells x and y and so can d! This means I don't have to write b or d in any other cells." Ergo: (pompous or what?) what you actually have in that group of cells is a naked pair and a naked triple. Had you blindly filled in all the candidates before any analysis you would have only a hidden triple, which you might not actually spot, and so on.

You see, in my opinion, much of what is discussed on this site is the same as something else, but viewed from a different angle. Order of approach is crucial, as the correct techniques applied at the correct time in the process can steer you clear of needing the more difficult ones. As a general rule of thumb, go from easy techniques to harder ones. If you start looking to use harder techniques, you are probably going to have to.

I can honestly say that I rarely come across Hidden Triples, especially in puzzles in the paper. I sit, look, think and to an extent try to 'see' candidates in my mind's eye. And because I know that Fiendish won't require X-wings, and that I've done them before, I know that I can do it. The rest is just patience.
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Postby noggi » Thu Sep 29, 2005 8:57 am

Thanks again for the reply. I am quite up to speed. I should have been clearer in stating that what I don't know is how they define the levels of difficulty in the papers with regards to what methods are needed..

I really just wanted to know if anyone uses completely other methods than those generally described in the forum.

46# ### ###
#1# #98 7##
### ### ##8

### ##1 5##
57# ### #96
##6 4## ###

7## ### ###
##2 98# #1#
### ### #23

Can you have a look at this - which shouldn't be too hard, and give me an idea of how you go about it, and at what time, if any, you used pencil marks?

Sorry about your cold. My head is filled with cotton wool due to stinking cold at this end, so we might at least communicate on a similar level..
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Postby Karyobin » Thu Sep 29, 2005 11:12 am

Interestingly, Wayne's rated it as Very Hard and Angus's didn't like all the #'s. Taking Wayne's grading therefore, I went straight into using candidates.

So, I typed it into Angus's, asked for candidates and wandered through until it was finished. I expected an X-wing to crop up, because they generally do when Wayne's says they are V. Hard, but one didn't. There was an occurence of a Hidden Pair, but this illustrates precisely what I'm talking about. Had I marked the candidates in by hand, I would have noticed this pair, and it therefore wouldn't be hidden. Like Angus's, most programs throw up every possible candidate for a cell, and leave the user to search for the pairs/triples etc. - hidden or not.

But I strongly doubt I would have had the stamina to go through this one without candidates. In my experience the only paper which prints puzzles this hard (not that hard I know, but hard enough if you're Joe Public and don't know the tricks) is the Sunday Times. Their Superior sometimes requires some quite advanced tricks.

Weirdly, I've found that I'm solving less and less sudoku these days. As tso said in a different post (and I'm paraphrasing - a lot!), sudoku fall into two camps: ones that can be done with a pencil and a deal of thought and others that need seriously advanced filtering techniques. I'm not interested in the latter because let's face it, it's a puzzle (sacrilege, I know) and I've done so many of the former that, well, I'm up for something else now.

Maybe I'll try my hand at trying to solve cryptic crosswords again.
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Postby emm » Thu Sep 29, 2005 11:37 am

I agree. Most people will probably work their way up the ladder of difficulty to the point of saturation. At the moment I’m into the vhards using solvers for the menial stuff while sadly I ignore the daily newspaper puzzles I used to fight to get my hands on. I don’t know yet if there’s another step on the ladder - maybe I'll try solving without pencil marks!
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Postby Doyle » Thu Sep 29, 2005 1:07 pm

Karyobin wrote:Weirdly, I've found that I'm solving less and less sudoku these days.


Not so weird, though a bit sad perhaps. It's the climb up the learning curve that's fun, the plateaus can be boring. (That, plus the realization that some are better, even much better, than I.) My Rubik's cube, and the notebook devoted to it, are on the back shelf, though I ocassionally pull them out, and try to recreate the keen enjoyment. (No web sites in those days, that would have been something!)
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Postby Katprof » Thu Sep 29, 2005 1:41 pm

Karyobin wrote:There was an occurence of a Hidden Pair, but this illustrates precisely what I'm talking about. Had I marked the candidates in by hand, I would have noticed this pair, and it therefore wouldn't be hidden. Like Angus's, most programs throw up every possible candidate for a cell, and leave the user to search for the pairs/triples etc. - hidden or not.
.


Thanks for pointing this out -- I think it's a key point. When I stopped devising ways to solve Sudoku on my own, and got online to read about others' techniques, it was very confusing at first because I didn't always understand the issues they were describing. Then I realized they were dealing with a board with every possible candidate filled in already, whereas I had been marking in selectively, so some of the things that were considered tricky issues were things I was able to see right away from my selective marks.

I think that if your focus is on how to solve puzzles with ever-increasing-speed, rather than puzzles on the outer limits of logical possibility, then the issues to be discussing here are different strategies for marking (or not marking) the grid, and different tricks for recognizing patterns more quickly. And I think that as long as you have your own last best time to compete against, you won't get bored! (or at least, not as bored as quickly).

best,
KP
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