dailysudoku.com

[rikko]

Hi, new to this forum, Not sure if this is the right place to ask, but anyway, I am able to do the majority of "hard" puzzles solved without relying on a 'hint', but probably only less than half of the ones marked as "very hard". However, this one (number 47, marked "hard") was in our local newspaper a few days ago, and it is a doozy - I am totally stuck!! I think it should be marked as "very hard indeed"!! and I can't resolve even one square using logic? (I obviously need some help with my logic). Has anyone else had problems with 47 too? (do I need to type it out here?). I'd rather not use a "hint" unless I could see the logic behind it...

- - - - 3 - - 6 -
- 5 - 4 - 1 7 3 -
- - - 6 - 7 - - -
2 - - - - 9 1 - -
- - 7 - - - 9 - -
- - 1 8 - - - - 4
- - - 9 - 6 - - -
- 8 9 7 - 3 - 1 -
- 6 - - 2 - - - -

Thanks,

[David Bryant]

Hi, Rikko! Welcome to the forum. This is the right place to ask questions about "other" puzzles.

You need to think in terms of candidate profiles to solve this one. I'd suggest that the first number you can set is r6c2 = 9. Let me explain.

Concentrate on column 2, and on the middle left 3x3 box. By direct enumeration you can see that the only possible values at r4c2 are {3, 4} -- you have {1, 2, 7} in the middle left box, {5, 6, 8} in column 2, and a "9" in row 4. r5c2 is exactly the same because there's also a "9" in row 5. We can concude, then, that the pair of digits {3, 4} lies in r4c2 & r5c2, in some order.

Now look at r6c2. The only possibilities are {3, 9} -- you have {1, 2, 7} in the middle left 3x3 box, {5, 6, 8} in column 2, and a "4" in row 6. But there can't be a "3" in r6c2 because of the pair we just located. The only possible value in r6c2, then, must be the "9". dcb

[TKiel]

Rikko,

IMO a puzzle like this is a good reason to use a helper software program, because there are no cells that can be solved by direct exclusion. I use a program that lists the candidates for each cell, after the starting grid has been entered. (I know some people think of this as cheating.) With that feature it is easy to see that there is a naked pair at r4c2 & r5c2 (3,4) and that the only candidates for r6c2 are (3,9), which allows for the exclusion of 3 and the placement of the 9 in that cell, as outlined by David in his post above. Actually, this whole puzzle has 3 naked pairs that, once those exclusions are made from other cells, allows one to solve the puzzle with nothing but singles, which doesn't seem to qualify as hard by anyones definition.

The question, in my mind, is how long does one want to spend figuring out candidate lists for each cell, until one finds the cells that allow some exclusions or placements that advance the puzzle? Truly hard puzzles don't allow placement of values in very many cells by direct inspection, so some kind of candidate list for each cell must be maintained, whether on the computer screen, on the paper or in your head. I can't/don't want to do it in my head and got tired of using up a whole eraser and having the paper look like bird cage liner material when I was done, so I use the software, which allows me to concentrate on solving the puzzle, not on making and maintaining candidate lists.

David,

I'm not sure what you mean by 'candidate profile'.

[David Bryant]

[TKiel]

David,

That's what I thought but I wanted to check to make sure. Thanks.

The auto log-in still doesn't work, so I'm just logging in manually.

[Marty R.]

Tracy,

I've been engaged in this insanity for about two months now, and I'm strictly a paper, pencil and eraser guy. I never cared for doing puzzles on the computer. It's so much more comfortable for me to sit on a couch, fully support my back and have the paper on a clipboard. Maybe someday I'll try the computer thing.

But I must admit, filling in cells with candidates is time-consuming, mistake-prone, drudgery and real "grunt" work. So is erasing the whole thing after I've backed myself into a corner with a duplicate number.

I don't think computer help is "cheating." After all, we're just entertaining ourselves, not engaged in competition where we've pledged to not use any electronic aids. Same with crosswords. I'll use dictionaries, almanacs, atlases, etc., again, just because I'm trying to entertain myself.

Rikko,

This is solvable using hidden singles, naked pairs and triples and locked candidates. It took me three times because twice I got backed into a corner with duplicate numbers due to mechanical errors. But no fancy, arcane techniques are needed.

[rikko]

Thank you all for your kind assistance. I think I can see some light to get me going now!
Cheers,

[alanr555]

[Marty R.]

Alan,

Thank you very much for taking the time to write that reply. I am definitely interested in learning how to solve puzzles with less drudgery. At this point, I have been able to solve what I think are some difficult puzzles, such as the one introduced in this thread, by basic techniques such as hidden singles, naked pairs, triples and quads and locked candidates. I rarely, if ever, find an X-Wing, swordfish, XY-Wing or unique rectangle. The only advanced technique, if it is even considered advanced, that I’ve been able to use with any degree of regularity is forcing chains. Not coincidentally, these chains employ more mechanics than logic. I’m weak on binary logic and related areas.

What I do is start out by filling in whatever cells I can by techniques called “cross-hatching” and “slicing and dicing.” This solves very few cells in the more difficult puzzles. Then it’s writing the missing numbers for rows and columns outside the grid, which I did not know was called “derivation of missing profiles”). Then it’s filling in all cells with their candidates, which I didn’t know was called “derivation of candidate profiles.” Then it’s on to the techniques described in my first paragraph.

Unfortunately, I do not know what “mandatory pairs” are or how they would be used. Of course, I could easily determine embedded pairs/triples from the missing profiles, but wouldn’t know what to do with them.

Thanks again for your time and information. If you or others would like to amplify on the mandatory pairs and embedded pair/triples, that would be much appreciated.

[alanr555]

[Marty R.]

Alan, once again, thank you for the explanation. I've printed it out so I can study and try to digest it somewhere more comfortable than a computer chair.

[Marty R.]

Alan, just to provide a little feedback: I now am using the mandatory pairs. Some puzzles they're of little help, others, a fair amount. Sometimes they yield naked pairs early in the process and can solve cells more easily and earlier than they would otherwise. Of course the drudgery of "Candidate profile derivation" hasn't disappeared, but can be a little less time-consuming.

I doubt that I am using mandatory pairs to its fullest potential, but it's definitely a helpful addition to the arsenal of techniques.