Sudoku Puzzles

Another day, another sudoku

Oh the roar of airplanes! I have a son who is an airplane mechanic. He has his license now for airframe and powerplant. He loves his work.

5:24 Maen

6:01

Here's a first attempt at a proof. I'm sure one with shorter chains can be found:

1) Start 22, unique possibilities to (UP) 26.
2) c9=9 == hi9=49 -- hi9=2 == e9=2 -- e8=2 == e8=1 -- e1=1 == b1=1 -- b9=1 == b9=6 -- a9=6 == a9=3 forbids c9=3.
3) e1=8 == f3=8 -- f4=8 == c4=8 -- c8=8 == More...

Fun puzzle and great picture.

16:39

I see we are recycling old pictures again. This one has been used too many times,

I uploaded some the other day. We will have to see how long it takes before wee see them.

France or Luxembourg's flag? a impression picture.

Possible proof of tough sudoku of 09 26 06:

1) Start at 22 filled - the given puzzle. Unique Possibilities to 26 filled. (UP 26).
2a) pair 25 at b26 forbids b5=2,b15=5
2b) Locked 5's at gi1 forbids i23=5
2c) fc on 8's: i3 == f3 -- f4 == c4 -- c8 == g8 forbids i7,g1=8
2d) h9=4 More...

08:32.

19:25

My last step as a 'chunk' fc:
h9=4 == i9=4 -- i4=4 =={triplet 268 at i234} -- i1=8 =={pair 45 at gi1} forbids h1=4.
This is length 3, classical depth 6.

I am curious as to which is easier to see, and which one should get the 'easier' rating?

Confusing the issue even more, one can of course write the elimination as an ALS within an fc:
To wit:
S1={i234=2468}
S2={g1=45,i1=458}
8's are weak across S1,S2, thus 4's are strong:
gi1=4 == i234=4 -- i9=4 == h9=4 forbids h1=4

I guess this is less clear, but it maintains More...

Final note:
(I hope)
If one performs the locked 4's elimination in box h8, one can also write:
{ALS on 4's at gi1, i234} X {coloring on 4's at (gi1, i4, g456, g1)} forbids h1=4

In either cross technique presentation, should one then label it length 2 (becuase of two chunks)?

ttt...I would bet dollars to dinars that those are American planes.

Good afternoon to all! Good on you Debbie! Glad your son is working to keep us safe! GATH: Another repeat picture!

Addendum: forget about forbidding h1=4 already.
much more elegant to eliminate a 'corner' candidate

2d) i3=8 == NT: i432=246 -- g654=4 == g1=4 -- g1=5 == i1=5
=> ~i1=8

clearly it's exponentially better to eliminate an 8 than a lowly 4.

ps. I propose that proof 'density' is a prime goal
on these pages (simpler but longer chains could be
provided in the subnotes for the beginner or those
with clogged arteries).

7:30 Good Maen

how come all you people are telling each other the answers some people like to work it out for themselves.

Steve, my proof was basically the same as yours with the 'chunk fc' except I didn't need your step 2c.

I could see that if . I was going to ask how to put 'if h1 = 4 i9 = 4, then pair 58 at g1 i1 forbids i3 = 8 & i234 = 26, therefore h1 ≠ 4' into an fc but you have already answered that.

Thanks

do u people spend all day working these things out why not just enjoy soduku???

What the?? I'm with you! I just enjoy doing the puzzle and relaxing. It makes to too much like work with all the theory stuff!

i dont understand half the stuff youguys are talking about, what is i3=8 & i234=26???

I agree LizBaby - Looking forward to seeing your photos. Must get my act in gear and upload some more myself!

Can anyone explain the code used in the solutions posted on this site. I have given an example of the code below. I can't understand any of it!! Help

1) Start 22, unique possibilities to (UP) 26.
2) c9=9 == hi9=49 -- hi9=2 == e9=2 -- e8=2 == e8=1 -- e1=1 == b1=1 -- b9=1 == b9=6 -- a9=6 == a9=3 forbids c9=3.
3) e1=8 == f3=8 -- f4=8 == c4=8 -- c8=8 ==

does anyone know where i can find a good desktop wallpaper???

I love the proofs. I want to thank everyone who posts one. From following the proofs I can now work out Xwings, XYwings and fc's. Such fun, even though I find it hard to see a fc myself, it does give me something to get my teeth into LOL. Otherwise you end up guessing which i used to do.
More...

Michael, look at the 'more' bit in my comment, I have tried to explain the terms in a laymans way.

4:13- but I made a few guesses- only because I was in a hurry, you don't ever have to guess (with two exceptions to this site), you can always use one trick or another. I have never used the proofs or formulas as mentioned above. I think you'd have to be an engineer to understand them!

for me, SUDOKU that's mean NO GUESS, if GUESS that's mean NOT SUDOKU ...!

a puzzle without a proof is ever a puzzle.

Where are the Archive pictures on the Tough? There's only a couple. Leia and I went looking for jigsaws tonight!

Hi Bruce!
You are of course correct that the latter manners to eliminate the lowly 4 at h1 do not need the fc on 8's.

BTW - it is also quite typical that there will be many, many ways to solve a puzzle. The presentation of alternate ideas is made as a point of interest, as efficiency More...

I needed to prove ,by trial, that in a pair containing 18 the choice of 1 was leading to impossibility!So the 8 is the right choice,that led ,straightforward,without any difficulty,to the solution!

Nov. 24, 2007.