Sudoku Puzzles

Another nice photo Keyan - haven't seen one of yours for awhile now.

Good to see a reappearance Keyan!

Great arial shot. Look sort of desolate.

Good morning to all1 Another nice photo Keyan, and that will make a great hard puzzle Gath!

Easy one today!!

This is beautiful, Keyan. Is it taken from a mountain or an airplane? Thanks

Beautiful picture ! Good MeAn to all !

That looks like California, Keyan. Which lake is it?

18:51

8:08. My best time ever for a tough puzzle. Guess it wasn't so tough after all. Beautiful picture Keyan.

Are you serious, Mark? I thought this one was unusually difficult!

Nice picture!

5:39

11:17 It was a tough puzzle, but I check the 'check moves' button and that helps. Don't know if that's cheating.

Canuk Greg, I was thinking the same thing. I'm heading to puzzle now.

maEn all! Thanks for the comments.

The picture was taken from a plane -- I think in California, but I don't know the name of the lake.

I also found the puzzle rather tougher than usual.

Thanks forth photos Keyan. It's great to share your travels. I'm still working on the puzzle. I haven't got far- and have run out of time- so if anyone wants to carry on...

22 filled
e3 =Unique possibility
hidden pair g4h5
At 23 filled If a5=6, b7=6, g6= 6 leaving no 6s in Bh7.

If f5=9, e3=9, c6=9, b7 = 9 leaving no 9s in Ci. Therefore f3=9

Locked 4s f45

This one is truly tough. I'm nowhere near a solution, but I'm posting what I have so far in case it might help somebody find one:

1) Start 22, Unique Possibilities to (UP) 23.
2) Hidden pair 69 at b57 forbids b5=247, b7=2458. UP 24.
3) f3=9 == f5=9 -- e6=9 == c6=9 -- c9=9 == g9=9 More...

Wow ..., great picture! Where is Keyan Bowes? 41:28 Hhmmm, how can I do faster? I need a lot of time for fc on 6&9's ...

Maen all
time for a little breaky before our turkey this pm

Clark -- thanks for your explanation. I'm trying to follow it but I don't understand what it is that makes numbers locked.

The following proof has not really been checked for typo's. Also, it is not pared down. When I have time, I might revisit it. Max depth, though is 7 I think.

Possible proof of tough sudoku of 10 08 06:

1) Start at 22 filled - the given puzzle. Unique Possibilities to 23 filled. More...

Too long so it is truncated - rest of proof is here:

8a) Locked 8's at f79 forbids f5=8
8b) a6=6 == g6=6 -- i5=6 == i5=7 -- f5=7 == f5=4 -- f4=4 == f4=1 -- d6=1 == d6=5 forbids a6=5
8c) h8=1 == e8=1 -- e12=1 == d3=1 -- a3=1 == a2=1 -- a2=2 == a5=2 -- h5=2 == h7=2 forbids h7=1
8d) More...

21:33

I'm a few days late here but I finally have a proof, with the help of a couple of steps lifted from Steve's:

1) Start 22, Unique Possibilities to (UP) 23.
2) Hidden pair 69 at b57 forbids b5=247, b7=2458. UP 24.
3) f3=9 == f5=9 -- e6=9 == c6=9 -- c9=9 == g9=9 forbids g3=9. UP More...

The proof is just a little too long for one post, so here is the rest of it:

25) Almost Locked Set (ALS) logic: S1={d3=18, d5=38, d6=15}, S2={d6=15, e4=135}. 3s are weak across the sets, so 5s are strong. This means that d6=5 == e4=5, which forbids e6=5. UP 40.
26) Hidden pair 38 at More...