Sudoku Puzzles

Marti,
How did you get rid of the 2 in a1 or i9 or the 3 in a9 to make a9=2 a unique placement?

Sundance - the chain is a wrap-around chain, hence one can make all those eliminations.

HI Steve from US. It takes me about 20 steps to get the contradiction at e7. Is that about how long it took you?

There are lots of solutions of depth 9 to 12 that I found, just decided to publish one of less max depth. Whether this is easier or not, I have no clue.

i agree with you lil, the explanations are more puzzling than the puzzle!

Thanks, Steve. I see it now.

OK, Steve. Now I'm up to 13, but I don't get the weak link 'i9=45--h7=4'. If i9 is 4 or 5, how does that prevent h7=4? Can't i9=5, h7=4? What am I missing now? I can get there if I use the assumed locked 45's in Ci and make more eliminations, but I don't think that is what you did. Please help (again).

After my step 10, it is perhaps easier to do a proof by contradiction to forbid f5=9 at depth 8 using almost locked sets 58,589 at gi8, 23,53,2345 at ahi9, 45,459 at e5,i5 strong link h46=5 == h79=5.

GRRR - I mean of course forbid g5=9.

Since I am only the 45 -- 4 is ok since I am really looking to eliminate the 5. should be written (45) -- 5 or 4--4.... ok?

In other words, whether i9 is 4 or 5, we still will have no 5 at h9

step 13 rewritten for clarity:
c9=5 == c9=3 -- AI9=3 == a9=2 -- i9=23 == i9=45 (note 19=5-- h9=5, while i9=4 -- h7=4 == h7=3 -- h6=3 == h6=5 forbids h9=5.

13)This step another way(perhaps more clear): consider the ALS 23 53 4523 at a9,c9,h9. Note h7=4 -- h9=5 at depth 3. h6=5==h6=3--h7=3==h7=4 forbids h9=5. (total depth of step is 5)

The giraffe is awesome! Good maeN to all.

Alternative proof:
1) Start at 23 filled. Unique Possibilities to 27.
2) Locked 8's forbid 8 at ACGI 5. UP to 28.
3) Locked 9's forbid df5=9.
4) a4=8 == a4=3 -- a9=3 == a9=2 -- i9=2 == g7=2 -- g7=8 == bc7=8 forbids a8=8. UP to 31.
5) Danger multi chaining here!
a) g8=9 == More...

5) Danger multi chaining here!
a) g8=9 == (g8=58 using i8=58) -- c8=58, i89=5, gh7=5. (depth 3)
b) c8=58 == c8=7 -- c9=7.
c) h79=5 == h46=5 -- i5=5 == i5=4 -- c5=4,i9=4.
d) i9=45 (note a) == (i9=23 using a9=23) -- c9=73 (note b) (depth 3)
e) c9=73 == c9=5 -- c5=45(see c) == c5=9 forbids g5=9.
depth of step 11.
8) UP 81
Sets 17, depth 11.

OK. I get it now. Essentially, the chain split at the point i9=45. If i9=5, obviously h9<>5, and if i9=4, you follow the rest of the chain. Thanks again. This one was well beyond me. I suppose I could have done one of those depth 20 of so proofs, but that seems to me more like guessing. Then, what's the point.

12:42

I like your comment :)

However I'm grateful to all the people who post their solutions; keep up the good work and thanks !

People who post amazing times make me smile so you too keep it up!

I give up. No problem to 28 filled, but no matter what I tried after that, I couldn't come up with further solutions. Thanks to all of you who came up with explanations but I've just lost the plot. Might try again when my head clears.

Congratulations, Steve on a masterful solution. You must have had a snow day. What a stroke finding that wrap-around fc.

What is a 'wrap around' and how does this help.

I am a newbie at tough and the explanations are just as hard.

30:05 Good maEn! Happy Saint Paddy's Day!

David: Suppose you have the fc chain A==B--C==D (with as many alternating weak-strong links as there happen to be in between) and suppose A--D (a real weak link, i.e., it should be possible for both A and D to be false.) Then you can replace all weak links in the chain with strong links (it's fun to prove this) and use them to make further eliminations.

20+... one mistake, but no guesses! still struggling with the whole x-wing concept...

Steve,
Thanks for the solution. What tricks do you use to figure out where to start, like in steps 6, 10-13?

that one was a killer!

18:27

8.15 good quick tough puzzle
Happy St Patricks Day one and all
what a gorgeous giraffe

Hi Dave!
Two months ago, on this site, I asked the same question a number of times. To date, I have never seen the question answered. The reason, I suppose, is that there is no good short answer. 'Focal points' of strong links are generally the areas in which I search. Experience trims the choices. I am still searching for the true answer to your question.

1:02:24 Finally

July 2, 2007.

SE=7.3