dailysudoku.com

shoeless · Joined: 03 Aug 2007 Posts: 13

Looked through the forum to see if this one had come up before, but there seems to be a big gap from about 10/06 to 5/07. Question

Anyway, I'm stuck on this one...

nataraj · Posted: Wed Aug 08, 2007 3:43 pm Post subject:

shoeless, you saved my day!

no new sudokus for 5 days, what a drag...

in your position,

shoeless · Joined: 03 Aug 2007 Posts: 13

nataraj,

Thanks for the tip on the naked quad. Other than eliminating a few candidates on r6, it didn't really get me over the hump. When you say "business in 2", do you mean box 2? If so, I'm still not seeing any of the wings there. Confused

nataraj · Posted: Wed Aug 08, 2007 6:54 pm Post subject:

actually, removing candidates from row 6 isn't so bad. especially the 3 in c9.

now all '3's in c9 are in box 3.

by "business in '2'" I meant the cells with candidate 2. When I don't see an x-wing or swordfish immediately I start to do quick sketches of the board with all cells containig '1', another sketch of the '2's and so on. It sounds much more tedious than it is. 4 quick lines like this:

nataraj · Posted: Wed Aug 08, 2007 7:34 pm Post subject:

the "business in 2" is an x-wing in rows 1 and 8 (removing 2 from cols 4 and 9)

removing '7' from r5c4 is more difficult.
on my drawing it looks like this

Asellus · Posted: Wed Aug 08, 2007 9:29 pm Post subject:

I believe that <7> elimination example is sometimes called a "Kite" or "2-String Kite" or "Turbot Fish," and may have other names. It is also an example of a more general method called "Color Wing." More generally still, it is a Alternate Implication Chain (AIC). Nataraj explains the logic well.

(I, too, have drawn those simple dot grids.)

cgordon · Joined: 04 May 2007 Posts: 769 Location: ontario, canada

I'm not interested in this puzzle guys - just hangin around for the next VH Day. But I should mention that I made up an Excel spreadsheet to do the "pencil work" stuff and show the candidate numbers that are available in each cell. I can also click to see X's for where the individual numbers are: this helps identify the patterns.
This isn't cheating eh! It's just a tool to take out the mundane and tedious groundwork before the battle.

shoeless · Joined: 03 Aug 2007 Posts: 13

I agree, nataraj's explanation of the logic was clear and made sense. It's always easy to see that stuff when someone points it out, but recognizing those patterns in the first place....that's where I have problems.

Anyway, I took your advice, tried making several grid drawings showing strong and weak links. I guess I'm still just too new at this stuff because the patterns don't jump out at me. Correct me if i'm wrong, but it seems like you need an odd number of "hops" as you progress around the chains in order to eliminate a candidate from a cell (if that makes sense). Using your example,
starting at r5c4, I'd hop to r1c4 -> r1c9 -> r2c8 -> r5c8 -> ending back at r1c4 for a total of 5 hops. Since each hop is a yes/no kind of logic, the odd yes/no's eliminate the candidate. Anyway, all I see is even hops...make sense?

After 2 days of fiddling with this puzzle on and off, I'm about ready to throw in the towel... Sad

TKiel · Joined: 22 Feb 2006 Posts: 292 Location: Kalamazoo, MI

shoeless · Joined: 03 Aug 2007 Posts: 13

nataraj · Posted: Thu Aug 09, 2007 7:02 pm Post subject:

shoeless,
Look at box 4 and notice how all the 8's are on row 6 (gets rid of 8 in r6c4).
Then (with 79 as candidates in r6c4) there is an xy wing (pivot r5c6) 79-57-59 eliminating 9 from r4c6 and r8c4.

Once you have eliminated 9 from r2c4 (happens a few steps later), there is an XYZ wing in box 3:

47 in r2c4 and 247 in r2c7 point the gun, 27 in r1c9 pulls the trigger, and 7 in r2c8 drops dead. The shape looks like a gun backfiring:

shoeless · Joined: 03 Aug 2007 Posts: 13

nataraj,

Thanks! I caught the 8's on row 6 shortly after I made my post. It was the 79-57-59 xy wing that was eluding me. It fell into place once you pointed that out. In general, how do you spot those on your grid drawings? As I understood you before, I made a grid drawing for each digit. Do you overlay them somehow to see the xy wings? Thanks for all your help on this one.

nataraj · Posted: Thu Aug 09, 2007 7:47 pm Post subject:

glad I could help.

The xy(whatever variety) and the drawings are diffent approaches.

The drawings show ALL occurrences of ONE number, like all sevens, no matter how many other candidates are in the cell. The links work on purely yes/no relationships ("if 7 is in cell a, then NOT in B,C,D")

I have not yet found a similar graphic approach to xy-relationships.
Tried to connect cells with lines once, but that became very messy.

XY-chains/wings work with bi-value cells (cell A is either 5 or 7) and take the form "if not A then B".

Since bi-value cells are easy to see and usually there aren't that many of them, it is just a question of taking them one by one and see if a wing exists.

cheers

TKiel · Joined: 22 Feb 2006 Posts: 292 Location: Kalamazoo, MI

There are programs that can be used to help one solve sudoku. Many of them have settings that can be adjusted to be of more or less help, depending on the requirements of the user. The one I use is called Simple Sudoku (available here ) and is free. In my opinion they are invaluable in helping to solve puzzles, such as this one, that require more advanced techniques, which can be extremely difficult to spot. SS can filter on each digit individually (useful for searching for strongly linked cells) or on bi-value cells (useful for searching for XY-wings/chains). Or one can use it for nothing but maintenance (keeping the pencil marks up-to-date). It really is up to the user. And I know that there are many others out there that will do much the same thing.