Tough Sudoku

Quite easy, almost boring today:

1) Start at 22 filled - the given puzzle. Unique Possibilities to 24. (UP 24).
2) Hidden pair 34 at d6f4 forbids d6=57, f4=78 UP 25.
3a) Locked 8's at ef5 forbids ab5=8.
3b) Locked 8's at a79 forbids b78=8 and c89=8. UP 32
4) Locked 7's at def5 forbids abh5=7. UP 33.
5) d6=3 == g6=3 -- g79=3 == hi8=3 forbids d8=3. UP 81.
Max depth 2. Total sets: 7. Rating .09.

5.51 - Red Arrows?

A great picture of the Red Arrows display team from Great Britain.

Steve, you've been too modest. Your step 5 is not easy to find at all!

Good Maen to all! A repeat photo but still a nice shot. The Canadian Air Force Snowbirds will be here in Ottawa on Canada Day, July 1st.

15 solid minutes to see this colorful air show..
cool..
cheers

Seen that picture of the air show used before.

Steve, the puzzle based on your proof is fairly predictable till step 5. I always see the logic behind the step when I see it written out, but cannot spot it easily when I'm doing the puzzle by myself. Guess it needs more practice.

Still don't understand the ratings, though

Watching England-Ecuador in the World Cup, so was quite distracted today.

Not this pic again..........

The ratings are just an arbitrary measure of proof efficiency. If the proof given is the most efficient proof, then they also serve as a rough measure of puzzle difficulty. In the end, there is no real way to rate a puzzle objectively without first making some subjective judgements. Given that, I have adopted a rather simple formula that looks at only the 'depth' of each step. Depth being the number of 'strong' sets needed in the step. Strong sets being a set of which at least one of the members is true.
For the purpose of ratings, I also require that the strong set have at least two memebers in it.

The formula, which is not very good, is:
Difficulty of proof = 1/100 th of sum of difficulty of the steps.

Difficulty of step = 2**(depth of step)-1.
Note that UP contributes zero to puzzle rating.
A locked set (the only depth 1 step possible) has a difficulty of 1.
A pair has difficulty of 3, whether it be a hidden pair, naked pair, (Also X wing, and two deep coloring)
Triples, swordfish, xy wings, and many other contraptions have difficulty of 7.
Very long fc's or very large matrices quickly add a lot to the difficulty ratings.

Suggestions for a better rating system, as long as it is not too complicated, are welcome.

In a general way, the ratings serve to label a puzzle or proof as more or less difficult, but they do not put a very fine point on the difficulty.

To my way of thinking, ratings versus difficulty are sort of like this:
Rating = 0 - A puzzle of all 'UP's, super easy.
Rating .01 to .1 - Easy
Rating .11 to .3 - Medium
Rating .31 to .5 - Hard and probably interesting
Rating .51 to 1 - Tough and certainly interesting.
Rating 1.01 to 2 - Very tough, and probably painful.
Rating above 2 - Monstrously tough, and certainly painful.

Thanks Andrei!
I did check and was surprised that Simple Sudoku gets stuck with this puzzle. Guess I just was lucky and stumbled quickly upon the coloring-like step.

39:17

Start at 22. Up to 24.
d6f4=34 -> ef5=8 -> a79=38 -> g8=8. Up to 33.
g6=2 ->(g79=39 -> d8=3) and (ab6=47 -> d6=3) so g6<> 2 -> b6=2. Up to 81.

Thanks to Steve for your notation explanation.

10:05 and i didn't think it was all that easy... had to guess a couple of times. good mAen all!

Thats not about stupid british red arrows.... GO USA!!!

Good, sensible post Garrett??????

9:52 after setup - easy for a tough today.

ok

I am getting better and quicker at solving the toughs. i can't follow the proofs most of the time. I have my own system which seems to work but probably isn't very scientific...I have a look once I have got all the easy solves and then follow an alternative through until it either shows me it can't be possible or it is the correct answer cos i've solved it. cheers

12:01 A repeat, but still a great photo! maEn all!

AGAIN with the jets? Time to submit some more photos for the TOUGH!

Where are the Picture Archives? There were only 5 days worth when I went to count how many times the jets had appeared!

I think that repeats means Gath needs more photos Kate.

8:23 Maen

neally day over and i only just get here to do my puzzles......better late than never

That is some pretty cool stonework!

I didn't see jets!

HAS ANYONE GOT A PHOTO OF THE ENGLAND TEAM IF THEY HAVE PLEASE PUT IT ON

Aug. 6, 2007.

SE=7.1

16:37.