Sudoku Puzzles

ouch! surprisingly difficult today despite initial appearances.

Why only 1 color of lights?

6:16 Maen not that bad

Lovely Christmassy tree

15.40

'Merry Christmas'

Have a nice maEn to all.

Nice Tree. Right now I am in Shenzhen, China. It will be the first time celebrating Chinese New Years which is next week. I understand that this celeration is as big as our Christmas celebration back home. Should be an interesting experiance.

Nice Christmas tree. And I confess, I just took the wreath down from the front of my house yesterday. Thought it should go before Valentines's Day, but there are still stragglers in the neighbourhood with their garland and red bows up...perhaps they're frozen in place.

Some of us like Christmas to last a long time-I still have my Nativity sets up, but they blend into their surroundings somewhat. PICTURES of Christmas trees are OK, as long as they're not still actually up in February!

Keyan - Very pretty. Thanks

17:49; tripped and guessed and wobbled on this one. The bright lights sure cheered me up, thanks Keyan.

This one could be very tough....
I will revisit it later - as of now all I have is a depth 8 path.

Good afternoon to all!
Mark: Enjoy the Chinese New Year. I'm sure you'll have a wonderful experience.

Keyan hope you had sunnies on when you took this photo, bright isn't it.

A very enjoyable challenging tough puzzle today. Somehow I managed to finish in 25 min. with one guess which considering my regular time with toughs ... was short of a miracle!! Mark I hope you're taking beautiful pictures of China to share with us.

My brother and his wife used to keep their Christmas tree up until Easter, and then decorate the bare dead branches with Easter eggs.

I do admit my wreath is still up, but my tree has been down for quite some time!

J, from TX (I was too, once), I'm with you. Got spoiled by the last three days.
Today, I would need some higher order of skill than I possess (beyond guessing and retracting a few times) to solve.
I needed this! I was getting spoiled and smug.

Greetings all. looks like another timed exposure.
Very luminous. The puzzles get more and more complicated. Pointing pairs gave up a couple of freebees then it was plotting chains. Sometimes doing potential naked triples in my head just to find the next link. Wasn't pretty or pithy, but I got there

Down by the feast of the three kings (6th January) or the goblins will get you!

Yes, Kate, ours is also always down by the 12th day of Xmas which is 6th of Jan.

My first tough puzzle!

1) Start at 22 filled, Unique Possibilies to (UP) 23.
2) locked 3's at a12 forbid a45 = 3. UP 24
3) locked 6's at b23 forbid b45 = 6. UP 26
4) fc on 5's: i8 == a8 -- a9 == {f9 == i9 -- g7 == g5} -- i5 == i89, forbids i5=5. UP 31
5a) g6=2 == g6=6 --i6=6 == i6=9 -- i1=9 == d1=9 -- d1=7 == More...

Please disregard the lines folowing step 9, they were unneeded and I forgot to delete them.

Hi Dave!
so far, I have perused only as far as step 4 above:
i8 == a8 -- a9 == {f9 == i9 -- g7 == g5} -- i5 == i89

{f9==i9 -- g7 == g5} -- i5 has me confused:
f9--i5 is not a native puzzle condition.
Finally, if I give the chain the mistake check:
Suppose i5=5: I find no More...

Hi Dave!
I have finished studying your proof:
All steps are valid except:
4,5b,6c:
In step 5b I still have i8=8, rendering i5=8 == i2=8 problematic.
In step 6c, I have a similar problem as with 4: It is unclear how:
{b8 == b7 -- g7 == g1} -- i1 works, as g1--i1, but b8 -- i1?
More...

Here is the best proof for this monster that I could come up with:
1) Start at 22 filled - the given puzzle. Unique Possibilities to 23 filled. (UP 23).
2) Locked 3's at a12 forbids a45=3 UP 24
3) Locked 6's at bc3 forbids b45=6 UP 26
4a) Locked 1's at gi1 forbids g3=1
4b) f7=5 == More...

further details:
Step 4b: truncated says:
f7=5 == {g7=1 == i9=5}. Since g7=1, f7=5, i9=5 all forbid g7=5, g7=5 is proven false.

Step 5) A much shorter step, but it has two contained chains!
f5=8**==**{hidden pair 68** at d45} tries to say that: f5=8 == d45=8 and we already have More...

Typical form of a bracketed chain - a chain used as a Boolean:

A*==*{B == .... X*==*Y ..... == C} -- D == E.

Inherent givens not clearly shown:
1) {A,X,Y} is a strong set. (*'s are perhaps a good label for transparency?)
2) B--D and C--D.

Conclusion of chain is: A == More...

More bracketed chain stuff:
Suppose:
A*=={X*==Y* -- C == D}--E==F.
Inherent givens here are:
1){A,X,Y} is a strong set
2) {C,D} is a strong set
3) {E,F} is a strong set
4) X--E and D--E and Y*--C
Conclusion: A*==F


If A*--F is also a given, things get a bit complex again!

I should have written:
conclusion A == F - no need to keep the pesty *.
Sorry!

Thank you Steve.

Thank you for your kind and thorough explanation. I see now what I failed to consider in my compound chains. Namely that if {A == B} -- C, then not only B -- C but also A -- C must be true. Unfortunately, the resulting elimination was by accident true, reinforcing my bad More...

38:56

Took about 45 mts. No guesswork.

This puzzle was a real bear -- too many dead ends! Dec. 5, 2007.

SE=8.5

1.SST to UP=26
2.kraken cell(139)i1 => g7<>5 UP=31
(1)i1-i8=g7
||
(3)i1-(3=2)a1-(246)ahi9=XW(5)ai89
||
(9)i1-(9=6)i6-(6=5)i9
3.kraken column(9)f256 => i6<>9, gi1<>13 STE.
(9-1)f6=(389)f256-(3)a2=a1
||
(9-8)f5=(*68)d45-(7)d5=(7-9)d1=i1
||
(9)f2-d1=i1