The New Sudoku Players' Forum

[daj95376]

9r7c4 = [AIC: 3r6c5 = r6c4 - (3=4)r7c4 - (4=9)r8c5] - 9r6c5 = [Kite: 9r6c4 = r6c8 - r5c7 = 9r2c7] => r2c4<>9; stte

Hmmm!!! For some time now, people have abandoned network structures in favor of folding logic into a chain structure. They often use the initial false assumption to bypass writing Kraken Cell logic. I was always leery of these structures, and here's an example why.

What if a basic step existed for -9r7c4 prior to this grid? Then blue's chain would reduce to:

3r6c5 = r6c4 - (3=4)r7c4 - (4=9)r8c5 - 9r6c5 = [Kite: 9r6c4 = r6c8 - r5c7 = 9r2c7] => ???

I don't see this chain reaching a conclusion! Not without including: (3-9)r6c5 = [Kite: 9r6c4 = r6c8 - r5c7 = 9r2c7] to form a forcing chain.

I suspect that blue was trying to circumvent writing the following:

Code: Select all

 Kraken Cell r7c4:

 3r7c4 - r6c4 = (3-9)r6c5 \
                           = [Kite: 9r6c4 = r6c8 - r5c7 = 9r2c7] - 9r2c4
 4r7c4 - (4=9)r8c5 - r6c5 /

 9r7c4                                                           - 9r2c4


You'll notice that I succumbed to using the Kite instead of its network equivalent. _ _


Crazy Time:

If you were to use the initial false assume "9r7c4 =", then you can turn the above Kraken Cell logic into a wicked (embedded) lasso by:

(a) start with "9r2c4 -" and work your way r-to-l along the lower path to "- 4r7c4"

(b) transition to the upper path using "= 3r7c4"

(c) and then return along the upper path until you reach "- 9r2c4"

Now, that would be an interesting way to fold everything together into a chain structure!!!

[Luke]

Danny, I admire your efforts to make a silk purse of this. Steve's initial solution (and many others like this) has generated a little discussion. That's cool and I don't mean to discourage discussion, but I can't understand what is interesting about solving in this way.

I *personally* have never accepted the practice of looking at a bivalue, assuming the false value was true, and then networking in multiple directions through the grid until the soon to be revealed and inevitable contradiction leads to an elimination/solution.

Applying such networks to these fun dailies is inelegant at best, unless maybe there's some clever/odd/ironic twist involved.

For me, it goes against my ingrained sudoku principles to network off a bald assumption, esp one that (in these cases) is always false.

[blue]

Hi Danny,

I suspect that blue was trying to circumvent writing the following:

Code: Select all

 Kraken Cell r7c4:

 3r7c4 - r6c4 = (3-9)r6c5 \
                           = [Kite: 9r6c4 = r6c8 - r5c7 = 9r2c7] - 9r2c4
 4r7c4 - (4=9)r8c5 - r6c5 /

 9r7c4                                                           - 9r2c4


You'll notice that I succumbed to using the Kite instead of its network equivalent. _ _

No, I did it quite innocently, looking for a story to put to the XSUDO picture for this "logic" (using the term loosely):

Code: Select all

5 Truths = {39R6 9C7 7N4 8N5}
7 Links = {9r2 3c4 9c45 6n5 4b8 9b6}
1 Elimination --> r2c4<>9

The full diagram has two Kraken-like towers in it, and so I would have hesitated to call it a "Kraken cell" elimination.
(On the other hand, with the smaller patterns boxed up like below, it looks very much like a chain).

Code: Select all

                           +-----------------------+
                           | Kite:        (rank 1) |
                           |                       |
                           | 9r6c8 - r5c7 = 9r2c7 ----- 9r2c4
                           |  ||                   |  /
                           | 9r6c4 ------------------
                           |  ||                   |
                           +-----------------------+
                              ||
+-----------------------+     ||
| AIC:         (rank 1) |     ||
|                       |     ||
| 3r7c4 - r6c4 = 3r6c5 ----- 9r6c5
|  ||                   |  /
| 4r7c4 - (4=9)r8c5 ------
|  ||                   |
+-----------------------+
   ||
  9r7c4 ----------------------------------------------- 9r2c4


9r7c4 = [AIC: 3r6c5 = r6c4 - (3=4)r7c4 - (4=9)r8c5] - 9r6c5 = [Kite: 9r6c4 = r6c8 - r5c7 = 9r2c7] => r2c4<>9; stte

Hmmm!!! For some time now, people have abandoned network structures in favor of folding logic into a chain structure. They often use the initial false assumption to bypass writing Kraken Cell logic. I was always leery of these structures, and here's an example why.

What if a basic step existed for -9r7c4 prior to this grid? Then blue's chain would reduce to:

3r6c5 = r6c4 - (3=4)r7c4 - (4=9)r8c5 - 9r6c5 = [Kite: 9r6c4 = r6c8 - r5c7 = 9r2c7] => ???

I don't see this chain reaching a conclusion! Not without including: (3-9)r6c5 = [Kite: 9r6c4 = r6c8 - r5c7 = 9r2c7] to form a forcing chain.

I don't like that you removed the "[AIC: ... ]" marker around the first section.
You definitely do need the "(3-9)r6c5" link, as you noted.

If "a basic step existed for -9r7c4 prior to this grid", then things would be like they always are for discountinuous loop eliminations: the next node in the chain would represent a valid pattern [ in this case the "AIC" node ]; it would eliminate the next thing in the chain; and so on, until the original target was eliminated.

The situation is a little unusual here, since the AIC and Kite nodes give "ranked" eliminations. If they had been on the more normal side of things ... locked set and locked candidate patterns ... then you could finish the puzzle using only those techniques. An X-Wing node in the chain, would mean you might need to use an X-Wing to finish the puzzle ... heaven forbid.

The worst case here, is that instead of being in the "complex pattern => elimination; stte" situation, you could find yourself stuck with a 2-step solution using simpler patterns. It's an interesting (tongue in cheek) twist on the "adding a clue can make a puzzle more difficult" idea.