maria45 wrote:Hi Carcul,
this didn't seem a "monster" to me. My solution uses 15 forcing chains:
First, are you being ironic? If 15 mostly long, convoluted and complex 'chains' do not a monster make, what is? Are you saying this is just another trivial puzzle for you, aren't we the slow ones? (Even calling them '15' chains is misleading -- many are actually multiple deductions combined.)
Second, some of these are not forcing chains. In a forcing chain, each step must follow from the previous and lead to the next. If one step requires two or more of the previous steps, you've got something else -- a forcing NET at best. It's confusing to try to follow your logic if you secretly redefine long accepted terms. The point of forcing chains is that they can be followed along by eye without having to make any marks or erasures -- and if it turns out the chain doesn't work -- no backtracking is needed and the puzzle is not spoiled. Forcing nets do NOT have this capability. I forcing chain can also be marked with a single, simply connected closed loop that visits each cell used. Many of your thingy's cannot be marked this way -- attempting to do so leaves a creats a multiply connected spider web, not a closed loop.
For example, your first statement:
maria45 wrote:e4=1 or e4=9, d8=9, d45=4, f4=7, h4=1 > cg4!=1 > c5=1, g3=1
(I don't understand how you decide when to use ',' and when to use '>' in your notation. It seems arbitrary.)
But f4=7 does NOT imply that h4=1, only that h4<>7. If (e4=9 AND f4=7), then h4=1. But this step is not part of your given solution -- I only see it because I'm actually marking my puzzle -- solving it as I go. Ok, from that point ...
Either e4=1 or h4=1, therefore cg4<>1, therefore c5=1, then g3=1
But again, c5=1 does NOT imply that g3=1, only that g34=1. If (c5=1 AND (e4=1 OR h4=1)), then g3=1. But you didn't state this.
What is the arbitrary limitation you are using that would prevent me from starting with a cell chosed at random in the puzzle, solving at will from each candidate in turn, with a dozen or more links, half of which are only implied by two or more previous links taken together, and calling it a forcing chain?
This was one of your shortest and simplest "forcing chains" -- and I cannot follow by eye without crossing out and circling candidates as I go.
- Code: Select all
*--------------------------------------------------------------------*
| 259 2689 2679 | 3 489 89 | 2457 1 249 |
| 359 1 4 | 6 2 7 | 358 359 389 |
| 239 2389 279 | 1489 1489 5 | 2347 3479 6 |
|----------------------+----------------------+----------------------|
| 6 5 3 | 2489 489 289 | 1 49 7 |
| 4 7 8 | 19 13569 1369 | 2356 3569 239 |
| 1 29 29 | 47 34567 36 | 3456 8 34 |
|----------------------+----------------------+----------------------|
| 7 236 126 | 128 1368 4 | 9 36 5 |
| 8 3469 5 | 179 13679 1369 | 3467 2 134 |
| 239 23469 1269 | 5 13679 12369 | 34678 3467 1348 |
*--------------------------------------------------------------------*
Ok -- I'll fill in the conclusions from your first three "forcing chains" and make any other trivial deductions:
e4=1 or e4=9, d8=9, d45=4, f4=7, h4=1 > cg4!=1 > c5=1, g3=1
d4=2 or g4=2, g5=8, d58=49 > d4!=49
c4=4 or f4=4, d8=4 > c8!=4
- Code: Select all
*--------------------------------------------------------------------*
| 2579 2689 2679 | 3 489 89 | 2457 1 249 |
| 359 1 4 | 6 2 7 | 358 359 389 |
| 2379 2389 279 | 489 1 5 | 2347 379 6 |
|----------------------+----------------------+----------------------|
| 6 5 3 | 28 489 289 | 1 49 7 |
| 4 7 8 | 19 3569 1369 | 2356 3569 239 |
| 1 29 29 | 47 34567 36 | 3456 8 34 |
|----------------------+----------------------+----------------------|
| 237 236 1 | 278 3678 4 | 9 367 5 |
| 8 3469 5 | 179 3679 1369 | 3467 2 134 |
| 2379 23469 2679 | 5 3679 12369 | 34678 3467 1348 |
*--------------------------------------------------------------------*
Apparantly, you looked at this candidate grid and this monstrosity was clearly obvious to you:
c4=4 or c7=4, a5=4, f4=4, d8=4, d56=9, e4=1, f5=7, f9=3, f6=6, e5=5, e6=3, f7=5, hk9=14, k7=8, b7=3 > c7!=3
Ok, the first few links seem fine:
c4=4 or c7=4, a5=4, f4=4, d8=4, d56=9, e4=1, f5=7 -- say what? Exactly how does e4=1 imply that f5=7? Stumped? It *doesn't*. But f4=4 (from three links earlier in the 'chain') DOES imply f5=7.
Continuing from f5=7, f9=3 --- What's that you say? f5=7 does NOT imply f9=3. Again, f4=4 does, but you didn't say that. This 'chain' is increasingly looking like a 'web' in which the links could have been written in many other arbtirary sequences, as the sequence doesn't matter.
Continuing from f9=3, f6=6, e5=5 -- Not again. f6=6 doesn't imply e5=5, f5=7 does.
Continuing from e5=5, e6=3. I give up. Not only does e5=5 not impley e6=3 -- NONE of the previous steps imply it either! Instead, you must have figured that if (e5<>3 AND f5<>3 AND f6<>3), then e6=3. How exactly is that a chain? How exactly does one *see* that without actually solving the puzzle, crossing out candidates and filling in numbers as you go? And if it turns out to be a dead end, how exactly do you backtrack without having made a copy in advance?
I cannot finish to the end of this 'chain'. It is too convoluted, too much of a web, too much for me to follow even using pencil and paper. It appears to me that you just bifurcated the puzzle by placing c4=4 in one copy and c7=7 in another, then solved at will, making whatever exclusions as you went. Then, seeing where the two paths overlapped, you created this 'chain'.
Theses 'chains' are not 'chains' -- nor are they a solution. They are an partial record of an arbitrary brute force search.
It would have been no less valid and no more difficult to follow if you had simply stated that your fourth forcing chain was:
c4=4 or c7=4, therefore c7!=3.
1) KP to KP4. Mate in 22.
by Carcul » Mon Feb 13, 2006 5:28 pm 
