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Guest · Posted: Sat Mar 25, 2006 6:34 pm Post subject: DB Saturday puzzle (March 25)

I posted this once, but it seems to have disappeared. A good one.

David Bryant · Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

Marty R. · Posted: Sun Mar 26, 2006 10:49 pm Post subject:

keith · Posted: Mon Mar 27, 2006 3:26 am Post subject:

I found a solution using unique rectangles, XY-wings, and three Double Implication Chains (a first for me). I'll post a solution after I have studied it further.

David, I agree this is about the most difficult DB puzzle to date. There was another one of a similar difficulty in December 2005.

Best wishes,

Keith

someone_somewhere · Joined: 07 Aug 2005 Posts: 275 Location: Munich

Hi,
Some comments about using the DIC (Double Implication Chains):
- it depends on your starting Alpha star.
- it depends about how many stars you are willing to follow (how deep you are ready to go). If I start with letter A than I can mark with "a" all that will be excluded, with "B" all that ones that are forced to be, with "b" all the ones excluded by B, with "C" all the ones forced, with "c" all excluded and so on ... with every level some remaining digits from the candidate table are marked as stars with a BIG or SMALL letter. Thorectic I could continue with this till I get a contradiction or I get a star excluded, or I it can happen that I am getting NOWHERE any more. In this last case, I will have to strat with a next ALPHA star.

Starting from this observation, I can be lucky or not in which case I will have to work more.
Now lets prove what I have stated - with this example.

case I.
from the following position I am ready to go any as deep as level "c" from a ALPHA star.

keith · Posted: Tue Mar 28, 2006 12:59 am Post subject: Double meanings

Someone,

Thank you very much for the detailed explanation. Now, I undersatnd your Double Implication Chains (DIC) and Constellations. (I think!)

As I see it, your technique involves choosing a value in a square (that has only two possibilities?) and then following the dual implications of values that other squares can and cannot have.

There is another "Dual Implication" technique. This is to start from a square that has only two possible values, and then to track the implications of each value.

For example, look at R6C8 = <68> as the Alpha square. (It is a confusing coincidence that this square has the same possibilities as its row and column numbers!)

Then R6C8 = <6>, R4C7 = <9>, and R5C9 = <3>.

And, R6C8 = <8>, R7C8 = <6>, and R7C9 = <3>.

So, no matter the value of R6C8, there is a <3> in C9, and R9C9 is not <3>.

There are a number of such eliminations which can be made in this puzzle. I am still studying it.

---------------
Someone and David,

I am not so sure about the proposed double star technique (as stated and as I understand it). If you start with the same value in two related squares, that is already a contradiction. If you start with the same value in two unrelated squares and then reach a contradiction, what can you conclude?

Best wishes,

Keith

David Bryant · Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

someone_somewhere · Joined: 07 Aug 2005 Posts: 275 Location: Munich

Hi David,

That is exact what I had in mind, and that you have suggested in one of the last emails.

Instead of starting from an ALPHA star with 2 digits, we could also start from a "double" star. So it is quite easy to find such double stars.
I have to look in the candidate table on rows, on columns and in the boxes and than I can start the DIC from them.

This is real an real enhancement to the DIC that I have used till now!
Thank you David for all your pacience to expain it so clear. Of course that everyone should start using it in order to find out that there are a couple of nice cases that where not explained (by intention).

see u,