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Marty R. · Posted: Wed Jul 15, 2015 5:46 pm Post subject: Dan's July14 puzzle.

Dan (arkietech) originally posted this on the Enjoy Sudoku forum.

It's different and I thought some of you might find it interesting. It'll test one part of your game. There is a small variety of solutions. I did not check thoroughly, but I think there are no available standard VH moves.

Clement · Posted: Fri Jul 17, 2015 4:44 pm Post subject:

Marty R. · Posted: Fri Jul 17, 2015 7:32 pm Post subject:

My first solution was the BUG+3. Then I looked at the 36-39-69 DP, which gave the identical elimination.

I had some difficulty getting through the basics.

dongrave · Joined: 06 Mar 2014 Posts: 568

I sure had a tough time with this one! How could I be left with so few unsolved cells (each with only 2 or 3 candidates) and not be able to find a standard VH move (i.e. x-wing, xy-wing, or xyz-wing)? I finally gave up. If there is one there, I sure don't see it.

Oh well, what about those forcing chains that I always see represented in Eureka notation? I'll go find one of those. Then it occurred to me - those chains are really nothing more than a simple proof by contradiction. Who cares what they call them or how they're represented? They're all the same thing! They assume that a cell is the wrong value and then arrive at a contradiction.

So I just took the first unsolved bi-value cell (r1c1 which is either 6 or 9) and assumed that it was a 6. Since it didn't lead to a contradiction, I assumed that it was the other value (i.e. 9) and I quickly saw that if r1c1=9, then then r1c3<>9 so r7c3=3 (because of the naked 68 pair in c3) so r5c3=1 so r6c1=9 but it can't be 9 because r1c1 is 9!

Wait a minute! Is it really that simple? I'm starting to think that it is! Am I wrong or are these 'forcing chains' nothing more than 'trial and error' proofs by contradiction? If they are, then I began wondering - since I could have begun with any of the unsolved cells, which solution would be the 'best'? The purist in me tells me that it would be the one with the fewest number of steps before arriving at a contradiction (but maybe that's just me). Anyway, I'd appreciate any thoughts about this. Thanks, Don.

bat999 · Joined: 09 Jul 2015 Posts: 55 Location: UK

Marty R. · Posted: Sat Jul 18, 2015 4:05 pm Post subject:

I took a look at that thread on Enjoy Sudoku and don't understand a thing I'm reading. Maybe that's why I have such difficulty finding chains.

dongrave · Joined: 06 Mar 2014 Posts: 568

Hey! Thanks for the link batman! I appreciate it! I just clicked on it and took a quick glance and it looks like real interesting reading! If it didn't make sense to Marty, it'll probably have my head spinning - but I'm going to check it out anyway! Thanks again, Don.

bat999 · Joined: 09 Jul 2015 Posts: 55 Location: UK

Marty R. · Posted: Sun Jul 19, 2015 6:09 pm Post subject:

Maybe we all do indeed use trial and error. There are some very good-players doing these puzzles and some of them can see the grid in ways that I can't. I'm extremely impressed with some of the ingenious solutions. However, you can't dismiss the fact that some are using computer help to find moves. But even those who do use computers know a lot based on conversations with them.