Sudoku Puzzles

Good photo fi - beautiful blue sky

Thanks to all who submitted vomit synonyms! Daughter Rebecca scored 100% on her oral presentation – prof. said it was the best presentation of all! Rebecca says big thanks to all, and especially those who suggested ‘chunder’, which is her personal favorite. ☺

I’m a little delayed in posting More...

Good Maen. Rather rugged looking.

9.21 not too tough!

6:19 Maen

It does look rugged for a beach. Australia looks like it would be a beautiful place to visit.

to Debby from MI: Can't you picture any Michigan beaches that look almost like this? I think I can!

8:05 I was there once, in Australia, and I loved to be there... down under!!! Great people, lovely country

Karen - We have a lot of Rocks in Michigan. (My husband has done a lot of our landscapiing with rocks.) Those are pretty big rocks in the picture. You could probably find some big rocks along the Great Lakes. (Especially where there has been some erosion.)

4:27

Terrific photo. Have a great day/night, everyone.

Over an hour to solve.

a tough one:

1) Start with 22
2) UP 25
3) Locked: b987=6, de6=1, ghi6=8, def5=4, g987=5, h321=3, ab9=7
=> ~(c87=6, ef4=1, bde6=8, (de6, ef4)=4, g32=5, i1=3, abc8=7)
4) e9=9 == a9=9 -- c7=9 == HP: c32=69 -- c2=7 == e2=7
=> ~e9=7, UP 31
5) a9=9 == e9=9 -- e4=9 == HP: More...

i dont know how one can solve it less than 10 minutes..remarkable if u could do it really!!well initially i thought it was a straight forward one but,later as i progressed found too many possiblities and it was not easy deciding the correct candidate..think i must've taken a full half an hr plus to solve this..fi's pic is always a delight to watch..
cheers

Black...black...black...ah...ah...ah...good!

4:03

Good afternoon to all! Is that a cat sitting on the rock in the middle Fi? Sneaking one in and trying to fool everybody? Oh, and by the way, another great picture Fi!

m Aen all

In step 3 of Pat's solution it says that there are locked 7's in ab9. I do not think this is true because there is a 7 in e9. Don't know if I've made a mistake or if this has an impact on the proof, but thought I'd ask.

typo - that lock occurs after the chain elimination
step 4 ~e9=7.

Possible proof of tough sudoku of 10 24 06:

1) Start at 22 filled - the given puzzle. Unique Possibilities to 25 filled. (UP 25).
2a) Locked 6's at c23 forbids c78=6
2b) e9=9 == a9=9 -- a3=9 == {hidden pair 69 at c23} -- c2=7 == e2=7 forbids c78=6 and forbids e9=7 depth 4
2c) More...

Possible replacement for step 8: BUG using odd even theorem of remaining possibilities forces c3=9. UP 81

Hmm b4 the bug,need the xwing on 1's, then up 59, then the BUG, UP 81. Sorry.

Pat's proof and mine are very similar - to UP 37. Paths appear a bit divergent after that.

TO G:
I posted a reply to your question yesterday late on that page. Continuation of same:
cellx=# == celly=## is not an if then type statement. It is merely a logical OR statement.
On the other hand, using the logical ORs and NORs:
cellx=# -- celly=## == cellz=### does More...

Hi PAT from Milwaukee,

Could you please clarify the abbreviations used in your proof (NT, NP, HP)? Thank you!

N = Naked
T = Triple
H = Hidden
P = Pair
NT = almost naked triple
HP = almost naked pair etc.
always one degree of freedom, ie one more
candidate than number of cells in set.

note: a depth 4 proof exists for this sudoku,
but it requires lots of chipping away with
depth 4 chains.

SE=8.3