Tough Sudoku for 10/November/2006

comet like

Wow. Impressive cliff.

12:16 Maen

No more stalling--time to get to work. Have a great day/night, everyone!

wow..what a gradient!!the puzzle isnt that tough,managed to finish it w/o mistake and any difficulty by say 20 minutes...(well either the puzzles are getting a bit straightforward or me have developed some abnormalities for its third consecutive day i have completed the tough with such an ease!!)
cheers

4:01

Make a nice morning stroll for the ape on the picture we had the other day.

Great picture, Utah...! 1:32:19 tough today

Good afternoon to all! A nice shot. How many Utah pictures have been submitted? Seems like that's all we see lately.

And I really don't mind seeing them. Great pictures, but a change would be nice Gath!

Apologies. The comments above are much more negative then I meant them to be. I enjoy everyone's photo submmisions, but if at all possible, I would like to see the pictures that are presented mixed up a little to give us some variety GATH. Sort of like seeing cats and dogs eveyday when we get 15 or 20 shots from the same place running.

15:40. From wrinkles on the dog to wrinkles on the rock, a story behind every wrinkle - loved this pic, shld make a challenging jigsaw.

C. Greg: I think Gath just submits them in the order received so a lot of people must like Utah. None of the photos today are from me, and unfortunately I have a few more coming from Utah. I also submitted a few from my recent trip to Napa.

Does anybody else see the face in the cliff????

I am finding this puzzle particulary resistent to a nice proof.

Great rock going to do the jigsaw

Yes, Kerry, I definitely see a face. If you use your amagination you can even see a lower body and the face has a whisker.

Another great shot from Utah. I love the travel pictures. Makes me a great armchair tourist.

Nice puzzle.

Either I am particulary addled today, or today's puzzle is extraordinarily difficult to prove. Hopefully the latter is true. This puzzle shall temporarily ( I hope ) reside in the unproven case file.

Top right hand corner Kerry?

This cliff looks like a smiling CHESHIRE CAT!

Yes, Rosemary. Are you THE Rosemary from Southhead?

Steve,
I haven't had much time to look at this one, but from what I can see it's a real monster.

I look at cliffs that are made from the same rock formations out of my home windows every day. I see the face on the left side about 2/3rds the way up. cliffs like these are always changing with light angles and shadows. This is a great pic. I enjoy the travel and pet pics.

Took me a while. But got it in the end :)

Steve, where are you when we need you? That was one hard tough!

8:46 and for the second day I have finished the 4 of them, for this I am pleased. Nice photos of UTAH. Night All. xxxx

Hi STEVE,
after UP use technique (rule of pairs in bock on the same row or column), i don't know this is new technique or not => d9=1 then solve it.

Hi ttt: I would love a deeper explanation, as this puzzle is very tough - I do not see what you have found....

Hi Steve,

Rule of pairs :
row 1: a1 a2 a3 /- - -/- - -/
row 2: a4 a5 a6 /- - -/- - -/
row 3: a7 a8 a9 /- - -/- - -/
always have pair (a1,a2) or (a1,a3) or (a2,a3) on row 2&3 - continue for numbers in block 1 on row 2&3 => numbers on row or column in each block have at leats 1 the same pair in other block on row or column (sorry, very difficult for me to exlain more clear in Engligh but i'm sure you know what i meant).

on this puzzle : after UP, locked block 2 - column 4 : only pair 12 or 69 is possible. if pair 69 => only pair 15 is possible, a lot simple eliminated => impossible (have not 1's on column 3 or two 1's on column 7...) => pair 12 : d9=1 then solve it.
after study more i think this way look like GUESSING, but it reduce a lot step. i'm not sure this rule useful or not but i try to study more again...!

Took over 3 hours. Had to chip away.

Really tough one for me. The proof by gurus will be more elegant, but i have a very ugly one.

1.Start 22. UP 25.
2.Naked pair 39 de6=39;
3.Locked 6s at bc9 => UP 27 (d8=f1=6);
4.Locked 7s at ef2 => naked pair 79 at gh1=79
5.if c9=2 => a2=2 and we have a naked 1347 at b2, e2,f2,i2. So c2=6 and c2=9 which is impossible. => a8=2.
6.This step is nasty and there is probably a better way of doing this. But after this step you easily cruise to the end. If a5=9 => c1=4, a1=5, b1=8, b3=2. Triplet 345 at ghi3 causes d3=1. That makes e4=4 and e4=8. So a5=5.
7.if g4=7 =>g1=9, h1=7, i6=5 and h6=h8=1. SO g4 <>7 and b4=7.
8.Locked 8 on bc6 eliminates 8 in f6.
9.if a1=4 => d1=3, d1=4 and it means that the column d does not have any 8s. So a1=3.
10.if c9=6=>b3=6. It is easy to see that if b2=1 => c6=4 or if b2=4=> c6=1. So cells c1,c2,c3 can’t have 1s and 4s, which is impossible. So b9=c3=6 and UP b7=3;
11.if e7=5 => g4=5 and we have g1=79,g6=17,g7=179 and g8=17, which is impossible So e7 <>5 and f9=5. UP 81.

Hi sergio!
Thanks for posting a proof to this one. I cannot quite follow step 5. I also do not see all of step 6. If you could 'fill in the blanks' - all the intermediate steps you took to get to your conclusions, it would be helpful to me.

Hi Sergio,
your proof step 5 : c2=6 and c2=9 which is impossibe => a8=2, typo...? in block 7 : 6's only in b3 & c3

Below is just a taste of what I think it takes to logically unravel this one:

Possible start to a proof of tough sudoku of 11 10 06.
1) Start at 22 filled - the given puzzle. Unique Possibilities to 27 filled. (UP 27).
2a) Hidden pair 39 at de6 forbids hi6=3,c6=9,d6=48,e6=58
2b) Hidden pair 79 at gh1 forbids i2=7,ac1=9,g1=345,h1=35
2c) Locked 5's at ab1 forbids b3=5
2d) c5=8 == c5=9 -- c2=9 == a2=9 -- a2=2 == a8=2 -- h8=2 ==={g4=1 == h6=1 -- h8=1 == h8=7 -- h1=7 ==g1=7} -- h4=7 ==b4=7 forbids b4=8 depth 7
2e) {g4=1 == h6=1 -- b6=1 == b6=7 -- b4=7 == g4=7} == ({pair 48 at ac6} -- c5=8 == gi5=8} forbids g4=8 depth 5
Note: basically this step says that c6=1478 all forbid g4=8, as the following is established as a strong set: (g4=17 == gi5=8}
The chain seperates c6 into two pieces: c6=17 == c6=48. The first chain uses c6=17, the second chain uses c6=48
2f) Locked 8's at de4 forbids f6=8 UP 28

Both steps, 2d and 2e, are using simultaneous chains that are linked through normally not very 'strong' cells. This does not invalidate them, but instead makes them far more interesting.

SE=9.0

25:53