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ronk
Joined: 07 May 2006
Posts: 398
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 Posted: Fri Jun 18, 2010 5:51 pm Post subject: |
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| daj95376 wrote: | If you start by assuming that something is true, then the only acceptable outcome is that the assumption is false. This is a common approach used by ronk, Asellus, and others. In Mogulmeister's chain:
| Code: | assumed to found to conclusion
be true be false
********** ********* **********
(2)r7c5 - r7c9 = r8c8 - r2c8 = r2c4 - r6c4 = r6c5 - (2)r7c5 => r7c5<>2
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This makes it sound like I'm a proponent of elimination-by-contradiction, but I'm not. Since day one, the convention for nice loop notation has been to put the discontinuity at both ends of the expression. (Where else would you put it?) The expression is shorthand for any of several possible pairs of implication streams, all having a common outcome ... r7c5<>2 in this case. Contradiction is not involved ... unless you want it to be.
I tried to include examples of pairs of implication streams but they were mangled ... apparently (almost) everywhere the "not equal" symbol '<>' appeared ... so I gave up. |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Sat Jun 19, 2010 3:06 pm Post subject: |
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I always tend to think in terms of the sudokuist who is adding to their repertoire and learning. The route Marty took is empirical rather than theorem based. I am a bit that way myself - I like to pop open the hood and tinker around which cements my understanding and allows me to ingest the theory and conventions and then hopefully apply them. I remember in the early days reading some of the Player's forum material by the "men in white coats" and not being able to digest it. I can now.
Formal training in the sciences/mathematics helps when looking at nomenclature and the representation of sudoku. We start looking at pattern based recognition aids and then hopefully progress to the wider more generalised theory that subsumes these (ie AICs & Nice Loops). It is immensely valuable to have Danny and Ronk's explanations and conventions. I learn a lot this way.
However, going back to the contradiction, it is imho, a great way to demonstrate a discontinuous loop because you start and end on the same cell. It is explicit and helps the learner.
Going forward, you then are able to accept this and no longer need to make this explict step and you can shorten your chain as suggested - avoiding what Ronk refers to as "awkwardness".  |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sat Jun 19, 2010 3:18 pm Post subject: |
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ronk calls it discontinuity and I call it contradiction.
to-mA-to ... to-mah-to !!! |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Sat Jun 19, 2010 3:20 pm Post subject: |
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Indeed............  |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Sun Jun 20, 2010 12:01 am Post subject: |
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| Mogulmeister wrote: | | Going forward, you then are able to accept this and no longer need to make this explict step and you can shorten your chain as suggested - avoiding what Ronk refers to as "awkwardness". |
The deduction under discussion has three strong links (inferences) and four weak links, so I think you confuse awkwardness with completeness. |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Sun Jun 20, 2010 9:19 am Post subject: |
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| I am not confused - merely pulling your leg old chap ! |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Fri Jun 25, 2010 12:47 pm Post subject: |
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I have been traveling recently and selected this puzzle as my first puzzle "warm up". Big mistake; it was more like a "burn up", but I did complete it!
1. AUR26 r13c26 outside implications:
(2)r8c6; r1c6<>2
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(6)r48c6 - r13c6 = r1c5 - (6=2)r1c2; r1c6<>2
2. kite 2 with hing box2; r8c8<>2
3. w-wing56 r8c8 & r9c4 SL5 r2c48; r9c9<>6
4. ER2 with hinge box6 SL r2c48; r5c4<>2
5. ANP(25=7)r25c4 - (7=5)r6c8 - r2c8 = (5)r2c4; r45c4<>5
6. Swordfish 5; r5c79,r6c5<>5
7. xy-wing -256 with vertex r4c6; r8c5<>2
8. BUG+1 forces r3c7=3
I looking at the posts, I think my first step was also noted by MM.
Ted |
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