dailysudoku.com

[CT Yankee]

Hi. I'm having trouble with an old sudoku from the Krazydad site. This one's from Super Tough book 50, and it's just labeled #8 so I don't know when it was originally published... But who cares about that, this thing is just plain driving me nuts! Here's the puzzle at the point where I got stuck:

[David Bryant]

Hi, CTYankee! Those Krazydad puzzles are pretty tough, aren't they?

I solved this one with a single "double-implication chain" -- the chains involve seven different cells, as explained below. Maybe you'll think of this as "trial and error". Maybe not. I'll make it as logical as I can.

[CT Yankee]

Thanks for the reply. Your solution is, as you surmised, right on the border of what I consider to be a logic-based solution, but it does work and I sure don't see any other way to complete the puzzle. It's nice to know that I wasn't overlooking something obvious after all... At least, I assume I wasn't overlooking anything - if anyone does know of a more elegant way to solve the puzzle, please post your solution and method. I admit I'm not really familiar with the Almost Locked Sets technique that the solver program recommended, perhaps that's something I should read up on.

It's interesting that both you and the solver both focused on r1c1. Almost the very last thing I did before posting the puzzle was to use that exact cell to eliminate 6 and 7 from r1c4 (a relatively straightforward IC). The very last thing I did was to eliminate 1,9 from r2c3 and also 9 from r2c1. Now, I did that very late at night in a extremely sleep-deprived state. Looked at in the cold light of day, I confess I can't seem to duplicate the logic I used, so if those are among the reductions you couldn't duplicate, they're probably just plain wrong.

The REALLY scary thing is that this puzzle wasn't even taken from krazydad's highest sudoku difficulty level. There's a whole category that's even harder still, I think it's called "Insane", and IMO that's what you have to be to want to try and solve one of them.

[Steve R]

Dave

I am not going to enter into a debate about the meaning of "logic based" other than to say that David’s solution seems excellent to me. Several alternatives are nevertheless available.

If an XY-wing is acceptable, it may be that an XY-chain will also pass muster. In this event, starting from the grid you posted, the elimination of 3 as a candidate for r8c6 by means of r1c6 - 7- r1c1 -9- r8c1 -5- r2c1 – 7- r2c9 -1- r8c9 also solves the puzzle.

Steve

[CT Yankee]

[AZ Matt]

David

Can you give us any insight as to how you "found" the DIC. This is how I determined that the <7> and the <9> were the numbers to be looking at, but I don't think I ever would have discovered the "loop" on the <4> inherent to your DIC.

You can tell there is something going on with the <79> and the <19> because there are 6 cells with those possibilities, and the 4 in boxes 1 and 2 are strongly connected. I looked at the stray <79> and <19> cells to see if there was a "loop," i.e., a number that could affect cells that looped around back to affect cells in boxes 1 or 2, and I see the <7> from the <79> in r4c4 loops around the bottom of box 8; it collects, conveniently a <3> and a <36> locked set in column 5 (boxes 8 and, surprise surprise, 2), and connects again in column 6 -- r9c6 to r1c6.

So this is a beautiful puzzle, and I am certain I am going to solve it, and I struggled mightily (I spent a lot of time trying to "loop" the <3> through box 9 up to box 3, row 3, but I failed).

So I finally work out your chain, and I smack my forehead. I was right there. But the loop on the <4> from r9c6 to r5c5 is so tenuous. It relies on the observation that the <4> can only fit twice in box 8, box 7, and row 6. It's beautiful, but I think I have met my match (with my admittedly inexplicable way of solving). I'll hope if I just would have kept at it (before I resorted to what to my mind is true trial and error -- simply forcing a chain and following it wherever it goes until you spot a contradiction) I would have "gotten it."

Do you have a secret? What do you look for?

[David Bryant]

Hi, Matt! It's always nice to hear from you.

No, I don't think I have a secret. I do have a lot of practice with the "DIC" technique -- someone_somewhere pointed it out on this forum last November, and I've been using it ever since. Here's what I usually look for.

I generally start by looking at the patterns formed by the various missing digits. What I want is a bi-valued cell that will cause a sort of "spiral" to occur when I assign one of the two values in that cell. In other words, if a particular cell has possibilities {a, b} I'm hoping that setting that cell to "a" will determine where all the rest of the "a"s in the puzzle will fit.

I've even started using colors to keep track of this. In my initial analysis of a "DIC" possibility I'll color all the result cells corresponding to "a" blue, and all those corresponding to "b" green. If I can place quite a few "a" and "b" cells and color them this way, it's pretty easy to visualize additional implications of the two base cell assumptions.

Anyway, in this puzzle the "7"s caught my eye because the skeleton of possible "7"s was attractive.

[AZ Matt]

Thanks David. That was helpful for me, and instructive. "Spiral" is a better word than "loop" -- it implies more imagination -- and in the future I will look not only for direct links, but for links that expose hidden and naked sets. The <4> in r9c3 was sitting right in front of me, but I didn't have the imagination to follow its lead. I was right that the interplay of boxes 1, 2, and 8 held the key (or a key) to the puzzle, but it was like the <4> was a secret agent you had to send out on a mission to bring home the needed information.

I know -- geek. Hey, I like to think of Sudoku as more art than science. I'm a literature major, not an engineer...

[CT Yankee]

OK, I’ve been reading some old posts in the General Discussion area and I think I understand some things a bit better now. When I made my comments about logic and trial and error, I had no idea that entire flame wars had already been fought in the sudoku community over the issue. I can see now how I might have offended some people with my casually arrogant assertion that this is what I consider to be logic while that isn’t logic at all. My apologies, this is actually a deep and complex topic and I shouldn’t have just made my pronouncements as if I knew everything there was to know. The truth is that I hadn’t really given the matter much thought. Just reading David’s excellent post above has changed my thinking quite a bit. I now agree completely that looking for and working with long inference chains can be 100% purely logical, as long as you are following a logically thought-out strategy and don’t just pick cells randomly.

David, your method of seeking out the best targets for a forcing chain seems to work quite well. In fact I believe I've stumbled upon a good example grid that works well as a very simple proof-of-concept. This is an old newspaper puzzle, the Universal Syndicate from August 12, that I'd started to work on while on vacation but had put aside upon reaching an impasse. I happened to pick it up again recently, and this time I made a deliberate effort to implement a logical strategy rather than just searching randomly for possible attacks. Almost immediately I realized that there is one truly elegant move available that relies on nothing more advanced than knowledge of strong links, but which cracks the puzzle wide open through the removal of a single candidate. Can you spot it?