The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |..4|.52|..6|
 |.2.|3..|..7|
 |5..|...|...|
 |---+---+---|
 |...|9..|.8.|
 |.3.|.4.|.9.|
 |.6.|..3|...|
 |---+---+---|
 |...|...|..2|
 |8..|..9|.6.|
 |7..|13.|4..|
 *-----------*


Play/Print this puzzle online

[SteveG48]

Code: Select all

 *--------------------------------------------------*
 | 9    8    4    | 7    5    2    | 1    3    6    |
 | 6    2    1    | 3    9    8    | 5    4    7    |
 | 5    7    3    | 6    1    4    | 8    2    9    |
 *----------------+----------------+----------------|
 | 24   5    7    | 9    6    1    | 23   8    34   |
 | 12   3    8    |c25   4    7    | 6    9   c15   |
 |a124  6    9    |a258  8-2  3    | 27   17  b145  |
 *----------------+----------------+----------------|
 | 3    14   6    | 48   78   5    | 9    17   2    |
 | 8    14   5    | 24   27   9    | 37   6    13   |
 | 7    9    2    | 1    3    6    | 4    5    8    |
 *--------------------------------------------------*


2r6c14 =BUG+3= 1r6c9 - (1=25)r5c49 => -2 r6c5 ; stte

[Ngisa]

Code: Select all

+------------------+------------------+-------------------+
| 9       8      4 | 7       5      2 | 1      3      6   |
| 6       2      1 | 3       9      8 | 5      4      7   |
| 5       7      3 | 6       1      4 | 8      2      9   |
+------------------+------------------+-------------------+
| 24      5      7 | 9       6      1 | 2      8      34  |
|i12      3      8 |h25      4      7 | 6      9      5-1 |
| 124     6      9 |g258    g28     3 |f27     17     145 |
+------------------+------------------+-------------------+
| 3      c14     6 |c48     c78     5 | 9      17     2   |
| 8      b14     5 | 24     d27     9 |e37     6     a13  |
| 7       9      2 | 1       3      6 | 4      5      8   |
+------------------+------------------+-------------------+


(1)r8c9 = r8c2 - (1=487)r7c245 - (7)r8c5 = r8c7 - (7=2)r6c7 - r6c45 = r5c4 - (2=1)r5c1 => - 1r5c9; stte

Clement

[Sudtyro2]

Code: Select all

+-------------+------------+------------------+
|  9   8   4  | 7   5   2  |  1    3     6    |
|  6   2   1  | 3   9   8  |  5    4     7    |
|  5   7   3  | 6   1   4  |  8    2     9    |
+-------------+------------+------------------+
| c24  5   7  | 9   6   1  | b23   8     34   |
| d12  3   8  | 25  4   7  |  6    9   da5-1  |
| d124 6   9  | 258 28  3  | a27  a17   e145  |
+-------------+------------+------------------+
|  3   14  6  | 48  78  5  |  9    17    2    |
|  8   14  5  | 24  27  9  |  37   6     13   |
|  7   9   2  | 1   3   6  |  4    5     8    |
+-------------+------------+------------------+

Myth's CoALS rule applied to the two overlapping ALS tagged (d).

(5=172)b6p678 - r4c7 = r4c1 - (21=45)r5c19,r6c1 - (4|5=1)r6c9 => - 1r5c9; stte

SteveC

[Cenoman]

Code: Select all

 +------------------+------------------+------------------+
 |  9     8    4    |  7     5    2    |  1    3    6     |
 |  6     2    1    |  3     9    8    |  5    4    7     |
 |  5     7    3    |  6     1    4    |  8    2    9     |
 +------------------+------------------+------------------+
 | a24#   5    7    |  9     6    1    |  23   8    34    |
 | b12*   3    8    |  25*   4    7    |  6    9    5-1*  |
 |  124*  6    9    |  258*  28   3    |  27   17   145*  |
 +------------------+------------------+------------------+
 |  3     14   6    |  48    78   5    |  9    17   2     |
 |  8    A14   5    | A24#   27   9    |  37   6   B13#   |
 |  7     9    2    |  1     3    6    |  4    5    8     |
 +------------------+------------------+------------------+

DP(125)r56c149 (*) using externals (#)
(2)r4c1 - (2=1)r5c1
(24-1)r8c24 = (1)r8c9#
=> -1 r5c9; ste

[SpAce]

Code: Select all

.--------------.------------.----------------.
|   9    8   4 | 7    5   2 | 1   3     6    |
|   6    2   1 | 3    9   8 | 5   4     7    |
|   5    7   3 | 6    1   4 | 8   2     9    |
:--------------+------------+----------------:
|   24   5   7 | 9    6   1 | 23  8     34   |
| a(1)2  3   8 | 25   4   7 | 6   9   b(5)-1 |
|  a124  6   9 | 258  28  3 | 27  17   b145  |
:--------------+------------+----------------:
|   3    14  6 | 48   78  5 | 9   17    2    |
|   8    14  5 | 24   27  9 | 37  6     13   |
|   7    9   2 | 1    3   6 | 4   5     8    |
'--------------'------------'----------------'

(14)r56c1 = (45)r65c9 => -1 r5c9; stte

[SteveG48]

Code: Select all

 +------------------+------------------+------------------+
 |  9     8    4    |  7     5    2    |  1    3    6     |
 |  6     2    1    |  3     9    8    |  5    4    7     |
 |  5     7    3    |  6     1    4    |  8    2    9     |
 +------------------+------------------+------------------+
 | a24#   5    7    |  9     6    1    |  23   8    34    |
 | b12*   3    8    |  25*   4    7    |  6    9    5-1*  |
 |  124*  6    9    |  258*  28   3    |  27   17   145*  |
 +------------------+------------------+------------------+
 |  3     14   6    |  48    78   5    |  9    17   2     |
 |  8    A14   5    | A24#   27   9    |  37   6   B13#   |
 |  7     9    2    |  1     3    6    |  4    5    8     |
 +------------------+------------------+------------------+

DP(125)r56c149 (*) using externals (#)
(2)r4c1 - (2=1)r5c1
(24-1)r8c24 = (1)r8c9#
=> -1 r5c9; ste

Fascinating. Had I spotted that DP (I didn't), I would have immediately rejected it because either r6c1 or r6c9 has to be 4, breaking the pattern. Nevertheless, your logic solves the puzzle!

[SpAce]

Myth's CoALS rule applied to the two overlapping ALS tagged (d).

(5=172)b6p678 - r4c7 = r4c1 - (21=45)r5c19,r6c1 - (4|5=1)r6c9 => - 1r5c9; stte

Hi Steve! That's really cool! I've yet to spot any of those CoALS situations myself.

You once asked when to use the "==", and I think it would help here since the strong link (21==45) is not obvious without an explanation (which you did provide but the "==" would bind it with the right link). Btw, you could also cut the last term if you'd like to shorten the chain while still preserving the CoALS rule, but your longer version is perhaps more interesting.

(I realize that my own strong link might not be obvious either, but it's just a shorthand for native links between the digits so I don't think it warrants a special treatment. As seen before, other opinions about that exist.)

[SpAce]

Fascinating. Had I spotted that DP (I didn't), I would have immediately rejected it because either r6c1 or r6c9 has to be 4

I actually spotted and rejected it for that reason.

breaking the pattern.

The way I see it is that it doesn't really break anything, since the 4s could still be treated as normal internals. However, since they have a native strong link it makes the other internals (and thus the DP) superfluous. So, I just used the 4s.

Nevertheless, your logic solves the puzzle!

Somewhat counterintuitive, perhaps, but that's what makes interesting solutions! Because of the conjugate internals it never even occurred to me to look at the externals, but this example demonstrates that it might sometimes be worthwhile. Not sure, though, if it can produce a simpler solution than using a native link between the internals (here it doesn't). Such an example would be really interesting.

[Cenoman]

...produce a simpler solution than using a native link between the internals

When you are the fourth or fifth poster, producing a simpler solution is often too high a challenge. Producing a different solution is enough...
But, using a 3-candidate SIS inferred from a DP while a native strong link exists between two, is unreasonable, even if different.
Had I checked the existing strong links, I'd have refrained myself from the DP solution.

[SteveG48]

Had I checked the existing strong links, I'd have refrained myself from the DP solution.

Then we would have lost one of the most interesting solutions posted.

[SpAce]

...produce a simpler solution than using a native link between the internals

When you are the fourth or fifth poster, producing a simpler solution is often too high a challenge. Producing a different solution is enough...

Sure, but that was not my point. (Besides, you produce simpler solutions with a high frequency even in those situations.) Just to be sure, I wasn't criticizing anything at all. I found your solution interesting, just like Steve. I'm just curious about what kind of conclusions can be made about such situations in general. Is it always "unreasonable" to do what you did here, or could it actually pay off too?

But, using a 3-candidate SIS inferred from a DP while a native strong link exists between two, is unreasonable, even if different.
Had I checked the existing strong links, I'd have refrained myself from the DP solution.

I agree with what Steve said about that. Even if it wasn't "reasonable" from some point of view, it was educational to show that it could be done despite the native link. It leaves the door open for more investigation. As I said, it's not yet clear to me if such an approach could in some cases produce a simpler solution than using the native link. Here it didn't, but that alone doesn't prove anything.

You have far more experience and skills with DPs using all combinations of guardians, so perhaps you could answer that question directly? I'm not at all certain what the relationship between internals and externals is in every case. Mostly it seems to me that one could use either kind to get to the same result, but one (or mixed) is just simpler than the other. Is it just that, though, or can there be more fundamental differences? If so, then it's conceivable that externals could produce a simpler solution than a native link between internals. I just don't know if that can really happen or not.

[Cenoman]

...such an approach could in some cases produce a simpler solution than using the native link.
...perhaps you could answer that question directly?

Answer this question exactly, no I can't. The reason is simple, when I see the native link, I drop the DP. I hardly imagine how a DP solution could be simpler, with justifying a strong link identified as native. So I have not the least example in mind.

The question could be raised if a DP provides a derived strong link otherwise justified with a long chain.

I'm not at all certain what the relationship between internals and externals is in every case. Mostly it seems to me that one could use either kind to get to the same result, but one (or mixed) is just simpler than the other. Is it just that, though, or can there be more fundamental differences?

This other question is relevant. I have no theory about it, just some observations made on puzzles. Very often, similar solutions may be found with internals or externals. The number of guardians or the length of chains are then the choice criteria. But I have seen puzzles where a solution was available with externals while there was none with internals, or reversely. I have no example to show right now, but I can commit to signal the next puzzle where I observe that.

Note: when I write "no solution", I mean "no reasonable solution, with simple chains". Solutions with complex derived weak links using krakens or nets may exist in such cases. I sometimes search them, for fun.

[SpAce]

Answer this question exactly, no I can't. The reason is simple, when I see the native link, I drop the DP. I hardly imagine how a DP solution could be simpler, with justifying a strong link identified as native. So I have not the least example in mind.

That's my feeling too, and I'm more confident about it if you suspect so as well. However, since it seems that we all tend to drop such DPs on sight (except by accident), I guess there's not much real data. Perhaps we could keep our eyes open for such situations and see if anyone can find a counterexample.

This other question is relevant. I have no theory about it, just some observations made on puzzles. Very often, similar solutions may be found with internals or externals. The number of guardians or the length of chains are then the choice criteria. But I have seen puzzles where a solution was available with externals while there was none with internals, or reversely.

Again, I've made similar observations but with a lot less data (so I'm not very confident about my own conclusions). Sometimes I've noticed it myself, but more often when I've considered a certain DP but haven't found an acceptable solution -- and then you've produced something nice with the same DP using some non-obvious combo of guardians. From that I've concluded that different guardian combos can indeed work quite differently.

I have no example to show right now, but I can commit to signal the next puzzle where I observe that.

That'd be great!