Tough Sudoku

a bit grey isn't it? not the sort of day that shouts 'Let's go to the beach!'

So

assuming 'strong sets' means a strong link in a chain (CR=x == CR=y),

'sets 14, depth 6' means that your proof has 14 different steps/chains/observations/whathaveyou, and that the longest or most complicated one required following the chain or argument through 6 levels of complication?

Do I understand correctly that a level of complication includes a strong link, or do I count both strong and weak links?

Finally (whew!) in your explanation you say ''Strong' sets being a set in wh

you say ''Strong' sets being a set in which at least one of the possibilities listed must be true'. Isn't it one and ONLY one must be true, ie, A implies not B AND B implies not A?

oops - above I mean CR to be variables each representing a cell, perhaps the same, perhaps not, depending on the link.

I'm not arguing with your logic, I just want to be sure I understand it. I find your proofs to be very helpful.

Christina and Tammy, I've read the other resources on this site, and after s

Christina and Tammy, I've read the other resources on this site, and after study think I understand them pretty well. I often think there are probably answers somewhere in the archives to the questions I have, but barely have time to keep up day to day, much less sort through all the conversations for esoteric logic. I love the idea of a link for FAQ's.

David, In case Steve doesn't see your question, abc6=2 is shorthand for a6=2 or b6=2 or c6=2. In his proof, where he has abc6=2==h6=2, he is using GB's forbidding chain notation and means to say that of the two propositions, {a6=2 or b6=2 or c6=2} and {h6=2} at least one must be true (in this case, only one CAN be true). Thus the two propositions are strongly linked, as indicated by the ==.

Strictly speaking, no, a strong set is the same as the logical or statement. One must be true, but both might be. Often, it is the case that exactly one is true. This information, though, is often unimportant in the proof. Weak links are not counted, as they are generally obvious without even looking at the grid.

larryville: The definition of A==B is that 'at least one' of A and B must be true. It is sometimes the case that the relationship A==D inferred by the oscillating chain A==B--C==D actually results in both A and D being true. That possibility must be taken into account; otherwise you will be tempted to pick up a lot of false bystanders (false eliminations) along the chain.

The equivalent logical statements used are:
A == B means A OR B ( A union B)
A -- B means (notA) OR (notB) (also, not(A AND B))

HI DJ! Thanks for helping, as I am fairly poor at explaining things without the crutch of, well, symbols and such.

Of course, local A==B relationships (A and B refer to cells in the same row, column or square) are of the 'only one is correct' type. The A==D relationship referred to above is usually a 'nonlocal' strong link.

Hi, yourself, Steve. Thanks for the solution involving the 24's. I completely missed it before I left this morning.

The reason, I think, for using strong and weak links rather than if then implications, is that once one establishes a chain using only or statements, order is not important. Implications, on the other hand, do not 'go both ways'.

I just about missed it myself, getting caught up in an unusual configuration this morning - if one were to look at the SS stuck point, there are many opportunities for eliminations based upon a rare, but interesting, pentagonal relationship in pairs 24. ( For example, b6=4 is forbidden since it would yield a 24 pentagon, in which all of the members of the pentagon can be shown empty.

/Sorry, I mean b6=7. Sorry!

13:55

By golly, you're right. And I was actually trying to make a remote pairs connection with 24's. I shouldn't start these things so early, but they help wake up my mind for the rest of the day.

14:40 Seemed too easy for a tough. Looks like an Australian beach - either around Sydney or Perth (probably the latter). Any nominations as to which beach?

8:54

DJ - BTW - the elimination of 24 at b4 is a remote pairish elimination. 24 at b1 vs 24 at abc6.

completed! thanks!

you guys are weird

D a m n !
Got to 13:23, nearly finished and then accidently reset the puzzle. Dont have the heart to start again.

why am I having such a hard time with the TOUGH?I almost always bomb out the first two or three times. Any suggestions?

May 2, 2007.

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mlqb tcqgn rhmek hlwvnxeo hflvjp vqbdoguew pqmurgje http://www.aowlvh.wdihmgyb.com

SE=7.6

17:47.