Sudoku Puzzles

Another warm, sunny day in Toronto!

44:41

Good Morning, Nick.

Anne, what a relaxing picture this is. The color of the water looks inviting. Thank you!

Have a nice sailing Anne!!!

A path of many ways to solve this one.
Start at 22, basic techniques UP27 (note : pair 67 at f45)
1) (67)UR bf45 => b45<>7, locked 7’s at b89
2) (3=8)i7-(8)ef7=(8-3)f8=(3)f7 => loop
=> bcg7<>8, cg7<>3, f8<>9
3) (9=1)g7-(1)h8=(1)h6-(1)d6=(1-9)d2=(9)f2 More...

20:07

Let's sail away...
On this fine day!

"What a day for a daydream.........."

WOW.

I. Want. To. Be. There. NOW!!!

A much more twisted route:
1) Start at 22, Uniq1ue Possibilities to (UP)26.
2) locked 4's at e13, => d23<>4.
3) locked 9's at gh1, => ef1<>9.
4) proving chain: (3=5)d3 - (5)f2 = (triple 389)f278 - (38=5)f1 - (5=3)d3. => d3=3. UP 27.
5) (hp67)f45, => More...

Please excuse the extra lines.

Anne! You are toying with us!!! Pull in here and let us aboard!

I don't care if I'm aboard or on the beach. I just want to relax, shut my brain down and vegetate all day.

over an hour :(

Sailing

Jeff from Maryland,

Thanks for pointing out the mistake in my 7/6 proof. I posted a correction there.

Regards,
Dave

dave,
I had a great time tracing thru your proof, thanks for posting. I do have a few questions/comments.
1. Should the chain in step 11 read:
(3)e5 = (3-1)e4 = (1)g4 - (1)h6 = (pair 78)h36 - (78=3)h5 ?
2. It took me a few minutes to convince myself that this chain can be used to make More...

dave, you're welcome for 7/6 and thank you for posting the correction. I remember how grateful I was when I first started reading the proofs for the corrections that were posted. When they weren't posted I often would spend way too much time trying to find where I had gone wrong. A few people have sent me messages about typos/errors in my proofs and I hope they all continue to do so.

Lovely Anne!!

16.23 Wait for meeee!

An alternate path:
Start at 22, basic techniques UP27 (note : pair 67 at f45)
1) (67)UR bf45 => b45<>7, locked 7’s at b89
2) (hp25)d56=(2)d9-(2)e7=(2-hp15)bc7=(1)g7-(1)h8=(1)h6 => d6<>1, UP34
Note : pair (38) at fi7 & f78
3) (5)a6=(5)a4-(5=3)i4-(3)i2=(3)c2-)3=7)a1 => a6<>7, UP81

Dave,after UP 27 , if you can prove that g7 is not 1 , then bc7 = 1 or 5,and the rest are UPs to 81 . I tried g3=1 and found a forced sequence of 35 moves before a contradiction occurred .Maybe there is a neater way of proving g3 not = to 1 .Alfred.

Should read "g7" (not g3) in previous comment.

Anne, I think I prefer your Middleton to ours. It looks great. The village of Middleton was the original "Milton Keynes" but was re-named Middleton when the twelve villages became what is now Milton Keynes
Happy sailing.

Gave up on puzzle but checked the pic. Your Middleton is nearly as pretty as ours, Anne. You can see it in my aerial photos on my page.

Another path:

1)Start at 22, basic techniques to UP=27
2)Wrap around chain (Dave's step 11)
(3)e5=(3-1)e4=(1)g4-(1)h6=(78)h36-(78=3)h5
=>h18<>78,g6<>1,e4<>29,g5<& More...

Jeff,

Yes, thanks for making cake out of my manure.

The pair 78 is at h36 not h37 and it forbids 78 and allows 3 (78=3) at h5 not e6, and the "extra" lines 15 and 16 belong should precede line 16.

Concerning line 11, since it wraps, the weak link (pair 78)h36 - More...

Alfred,

Yes indeed, the puzzle unravels nicely with just a few basic techniques if you can eliminate the 1 at g7. However, I have not been able to find a good way to do so. Anyone?

Thanks,

Dave