dailysudoku.com

[Marty R.]

[arkietech]

25w-wing in c56 removes a gob of 5's and solves the puzzle

[rmireland]

Hi guys,
I desperately want to get to that Eureka moment, so here is my attempt at starting a Rosetta Stone...
First in english, using Marty's grid, in this puzzle r7c6 must be 5. The key is that r5c5 is either 2 or 5. If the value is 2 then r1c5 is 7 and r1c6 is 2 so the value in r7c6 cannot be 2, so must be 5. If the r5c5 value is 5 then r456c6 cannot be 5 so r7c6 must be 5 since we need a 5 in this column and this is the only remaining possibility.
So I have two paths to represent in one Eureka string. One path might be:
(2)r5c5-(7)r1c5-(2)r1c6=>-2r7c6
The other path might be:
(5)r5c5-(-5)r456c6=>5r7c6
So, how do I combine these into one Eureka string? Like this?
(2=5)r5c5-(7=2)r1c5-(2=7)r1c6- [meanwhile on the other path] (-5)r456c6-=>-2r7c6
Is that close? I have no idea what a = or - mean, other than I remember something about strong and weak links. I'm just pretending like I know.
If it's easier, could someone just show Marty's XY in Eureka? It would be much appreciated.
Rick

[Marty R.]

Hi Rick,

An XY-Wing is actually an XY-Chain, at three cells the shortest XY-Chain possible, so the notation would start not with the pivot cell, but at either end of the chain.

My wing would be notated as follows.

(2=3)r9c4-(3=5)r9c5-(5=2)r5c5=>r4c4<>2

In practical use, if I was describing an XY-Wing as part of a solution, I wouldn't notate it because by saying the three numbers and the pivot cell, the reader can easily see it and I don't think notating it would clarify anything.

If it was slightly more complicated, such as involving a pincer transport, then I would notate it.

Hope that helps.

[rmireland]

Eureka!
I was trying to do too much with this Eureka notation. I thought it was a means to discovery, but instead it's only a method to show what was discovered some other way.
I had mistakenly thought that it would start with the pivot, so I was confused how to show both paths from the pivot to the pincers. I now see that it starts and ends with the pincers (2=3) -(3=5) -(5=2) which for this wing are 2. The 3s pair and the 5s pair. so we have a 2 in r9c4 and a 2 in r5c5, and therefore any cell that "sees" both of these cannot be a 2, so =>r4c4<>2.
Because the string simply starts and ends at the pincers, I can read it in either direction and starting at either end, or in the middle somewhere, like at the pivot.
This particular string is setting values. I will next take some time to explore Eureka strings that eliminate possibilities.
Thanks, Marty and Don. I think I may be getting this, finally.
Rick

[arkietech]

[Marty R.]

[rmireland]

Wow! I am the last guy who should be mediating a Eureka discussion between you two. But I have noticed that you are both using the same ending cells, the only difference being the interim path, which we see all the time. There are often many intermediate paths between two pincer cells.
The difference seems to be that Dan is toggling bi-value cell r5c5, while Marty is keying on the fact that there can be only one 2 in c4. Without any criteria for judging paths, I cannot say that either path is better than the other, but Dan's has the advantage that I can see his logic by starting at the beginning of his string, while I have to analyze more to see Marty's starting point. But until I start speed-reading Eureka, that's not a big difference.
I do have an observation, though, that I can trace Dan's string in either direction, from either end. With Marty's, I cannot start at 5r7c6 and get to -2r4c4 by following his path thru r9c4 (unless I do the X wing to get -2r9c5 first).
Would it make any sense in these strings to indicate the starting point by using italics or underline to denote the key cell or cells?
And finally Marty, are you missing a 2, as in -2r9c4? Is that just a different dialect of Eureka?
Thanks guys. This has been really helpful, at least to me.
Rick

[Marty R.]

[dongrave]

These discussions have been a huge help to me too! The more Eureka examples I see, the clearer it becomes. I have one question. I noticed that Arkitech's solution is almost identical to Rick's solution posted earlier on this page - but there is one subtle difference that seems to make Rick's a 'forcing chain' of either the 'Unit', 'Digit', or 'Cell' sort (which one I'm not sure) instead of a w-wing. How do you represent Rick's 'Digit Forcing Chain' (or whatever type of chain it is) in Eureka? Or is this not the type of solution that one would typically write out in Eureka? Thanks, Don.

[Marty R.]

This is one possible way to notate Rick's "forcing chain."


(5=2)r7c6-r1c6=r1c5-(2=5)r5c5-r456=5r7c6 Contradiction=>r7c6<>2

[dongrave]

Hi Marty, Hey, that's surprisingly simple! I guess I was expecting to see two expressions (one for each path) delimited somehow, and then capped off with symbols for the conclusion. I've been under the impression that these expressions would only be 'correct' if you adhered to some strict set of rules - but now it's appearing to me that maybe it's okay to include embellishments (like adding the word 'Contradiction', or embedding an explanation to a step, etc.) as long as you use some common sense - and as long as others can understand it. Is this true? By the way, the reason I asked specifically about this example is because I only recently discovered these 'multiple path forcing chains' and at the same time I'm trying to understand Eureka better. I can read Eureka expressions that others post but I had no idea how to represent these 'multiple path' solutions. Thanks, Don.

[Marty R.]

Don,

If I were doing a forcing chain I'd use two strings of notation to show a common outcome. But you already mentioned that either way the cell had to be=5. So 2 had to be invalid so I started with that to see when the notation would show the contradiction.

[dongrave]

[dongrave]

I hope Marty's okay! He's normally right on top of removing those unrelated posts by Nina. Hey Marty, are you okay? We all hope so! (except maybe Nina.) Let us know if you're alright![/list]