The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|.6.|1..|
 |...|..3|6.2|
 |5..|..9|.8.|
 |---+---+---|
 |...|..7|.15|
 |63.|...|.78|
 |27.|5..|...|
 |---+---+---|
 |.2.|3..|..4|
 |9.3|1..|...|
 |..6|.5.|...|
 *-----------*


Play/Print this puzzle online

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 | 3     48    2478  | 2478  6     5     | 1     49    79    |
 | 478   1     9     | 478   478   3     | 6     5     2     |
 | 5     6     247   | 247   1     9     | 347   8     37    |
 *-------------------+-------------------+-------------------|
 | 48    9     48    | 6     23    7     | 23    1     5     |
 | 6     3     5     |a49   b249   1     | 249   7     8     |
 | 2     7     1     | 5    b389-4 8-4   |e349  e3469  369   |
 *-------------------+-------------------+-------------------|
 | 1     2     78    | 3    c789   68    | 5    d69    4     |
 | 9     5     3     | 1     478   2468  |d78   d26   d67    |
 | 478   48    6     | 789   5     28    |e3789 e239   1     |
 *-----------------------------------------------------------*


(4=9)r5c4 - r56c5 = r7c5 - (9=2678)b9p2456 - (2|6|7|8=UR=4)r69c78 => -4 r6c56 ; stte

[Cenoman]

Code: Select all

 +--------------------+-------------------------+----------------------+
 |  3     48   2478   |  2478y    6      5      |  1      49     79    |
 | B478   1    9      |  478y   Aa478x   3      |  6      5      2     |
 |  5     6    247    |  247      1      9      |  347    8      37    |
 +--------------------+-------------------------+----------------------+
 |  48    9    48     |  6        23     7      |  23     1      5     |
 |  6     3    5      |  49       249    1      |  249    7      8     |
 |  2     7    1      |  5        3489   48     |  349    3469   369   |
 +--------------------+-------------------------+----------------------+
 |  1     2   D78     |  3       b789    6-8    |  5      69     4     |
 |  9     5    3      |  1       b478    2468   |  78     26     67    |
 | C478   48   6      | b789z     5      28     |  3789   239    1     |
 +--------------------+-------------------------+----------------------+

Kraken cell (478)r2c5 =>-9r5c4
(4)r2c5 - (479=8)b8p257
(7)r2c5 - r2c1 = r9c1 - (7=8)r7c3
(8)r2c5 - r12c4 = (8)r9c4
=> -8 r7c6; ste

[SpAce]

Just an example related to yesterday's subchain discussion.

Code: Select all

.-----------------.------------------------.------------------.
|  3    48   2478 |  2478    6        5    | 1      49    79  |
| f478  1    9    |  478    e48-7     3    | 6      5     2   |
|  5    6    247  |  247     1        9    | 347    8     37  |
:-----------------+------------------------+------------------:
|  48   9    48   |  6       23       7    | 23     1     5   |
|  6    3    5    |  49      249      1    | 249    7     8   |
|  2    7    1    |  5       3489     48   | 349    3469  369 |
:-----------------+------------------------+------------------:
|  1    2   h78   |  3    bdi(7)8-9  b68   | 5    ab6[9]  4   |
|  9    5    3    |  1      d478      2468 | 78     26    67  |
| g478  48   6    | c89-7    5        28   | 3789   239   1   |
'-----------------'------------------------'------------------'

(9)r7c8 = (6,89)r7c865 - (8|9=7)r9c4 - @(7)r78c5 =x-chain= (7)r7c5 => -9 r7c5, @:-7r2c5,r9c4; stte

Or slightly simpler (still contains the same subchain, but not used):

Code: Select all

.-----------------.----------------------.-------------------.
|  3    48   2478 | 2478    6       5    | 1      49     79  |
| e478  1    9    | 478    d478     3    | 6      5      2   |
|  5    6    247  | 247     1       9    | 347    8      37  |
:-----------------+----------------------+-------------------:
|  48   9    48   | 6       23      7    | 23     1      5   |
|  6    3    5    | 49      249     1    | 249    7      8   |
|  2    7    1    | 5       3489    48   | 349    3469   369 |
:-----------------+----------------------+-------------------:
|  1    2   g78   | 3    bch(7)8-9  68   | 5    ab6[9]   4   |
|  9    5    3    | 1      c478     2468 | 78     26    b67  |
| f478  48   6    | 789     5       28   | 3789   239    1   |
'-----------------'----------------------'-------------------'


(9)r7c8 = (9,67)r7c5,b9p26 - (7)r78c5 =x-chain= (7)r7c5 => -9 r7c5; stte

[SpAce]

(4=9)r5c4 - r56c5 = r7c5 - (9=2678)b9p2456 - (2|6|7|8=UR=4)r69c78 => -4 r6c56 ; stte

Very nice!

[Cenoman]

(4=9)r5c4 - r56c5 = r7c5 - (9=2678)b9p2456 - (2|6|7|8=UR=4)r69c78 => -4 r6c56 ; stte

I find this very nice too !

I would never had written that, though. To me, the weak link (9=2678)b9p2456 - 6r6c8, between ALS b9p2456 and candidate 6r6c8 would mean that 6r6c8 is in sight of all 6s in the ALS.
But your logic is correct, since NQ(2678)b9p2456 has only one arrangement of the four digits, encompassing 6r7c8. I have to overcome my inhibition for this kind of implicit writing !

The way I would have written this UR solution:
UR(39) using mixed internals-external
(4)r6c78
(6)r6c8 - (6=9)r7c8 -r7c5 = r9c4 - (9=4)r5c4
(9)r9c4 - (9=4)r5c4
=> -4 r6c56; ste

or boldly: (4)r6c78 == (6)r6c8 - (6=9)r7c8 - r7c5 = (9)r9c4# - (9=4)r5c4 => -4 r6c56; ste

[Sudtyro2]

Code: Select all

+------------------+---------------------+------------------+
|  3     48  2478  |  2478  6      5     | 1     49    79   |
| d478*  1   9     | c478#  478*   3     | 6     5     2    |
|  5     6   247   |  247   1      9     | 347   8     37   |
+------------------+---------------------+------------------+
|  48    9   48    |  6     23     7     | 23    1     5    |
|  6     3   5     |  49    249    1     | 249   7     8    |
|  2     7   1     |  5     3489   48    | 349   3469  369  |
+------------------+---------------------+------------------+
|  1     2  f78*   |  3     789*  f68    | 5     9-6   4    |
|  9     5   3     |  1    b478#   248-6 | 78    26   a67   |
| e478*  48  6     |  789   5      28    | 3789  239   1    |
+------------------+---------------------+------------------+

In 7s, a 5-link oddagon(*) with two guardians(#).
(6=7)r8c9 - 7r8c5 == 7r2c4 - r2c1 = r9c1 - (78=6)r7c36 => -6 r7c8,r8c6; stte

SteveC

[SpAce]

The way I would have written this UR solution:
UR(39) using mixed internals-external
(4)r6c78
(6)r6c8 - (6=9)r7c8 -r7c5 = r9c4 - (9=4)r5c4
(9)r9c4 - (9=4)r5c4
=> -4 r6c56; ste

That's the clearest way to write it, for sure, and also the most efficient in terms of resources (cells, digits) used. Yet it's so explicit that it's also slightly boring. Personally I like the additional challenge of complex AICs over krakens, even if it loses some clarity, and I think Steve does too. It doesn't mean it's better -- just more fun for the writer (and also for some readers who like such side-puzzles -- but probably less fun for others). Yet I fully agree that a kraken almost always wins in clarity.

or boldly: (4)r6c78 == (6)r6c8 - (6=9)r7c8 - r7c5 = (9)r9c4# - (9=4)r5c4 => -4 r6c56; ste

I find this the hardest to understand, and to me it's not even a correct AIC. I think you'd have to use either a more explicit memory chain or a nested AIC if the guardians are spread out like that. Both options make it quite complex. I'd use the 9r7c8 external and write:

(4)r6c78 == (6,9)r67c8|(9)r7c8 - r7c5 = (94)r95c4 => -4 r6c56

I have to overcome my inhibition for this kind of implicit writing !

I think you're already on your way, at least in some other aspects Look at the shortcut in your second chain here. It's similar (though simpler) to eleven's logic here. Personally I think using such bent sets or larger spread structures as nodes requires more complex implicit tracking than looking at the internal digit arrangements of a basic ALS in one house. I have no problem with either, of course (except I don't think it's strictly speaking a "Death Blossom" if it depends on such a trick, but that's nitpicking).

My only point is that it's often impossible write complex chains without using some implicit logic within the nodes. I appreciate that you (usually) like to avoid it when it's not absolutely necessary, which results in very clear solutions. Personally I embrace it even when it's not necessary, because it makes it easier to use when there's no other option. So it's a learning tool for me.

[SteveG48]

Thank you both for your kind comments.

That's the clearest way to write it, for sure, and also the most efficient in terms of resources (cells, digits) used. Yet it's so explicit that it's also slightly boring. Personally I like the additional challenge of complex AICs over krakens, even if it loses some clarity, and I think Steve does too. It doesn't mean it's better -- just more fun for the writer (and also for some readers who like such side-puzzles -- but probably less fun for others). Yet I fully agree that a kraken almost always wins in clarity.

Just so! The whole purpose of a Kraken, to my way of thinking, is to replace a complex (or worse) AIC with a clear set of individual chains.


As SpAce says, I do prefer an AIC if I can come up with one, just because it's more fun for me that way. In this particular case, I think the AIC is so simple that it's just not an issue. The only real complexity is recognizing the exact positioning of the 6 in box 9.

[SpAce]

The whole purpose of a Kraken, to my way of thinking, is to replace a complex (or worse) AIC with a clear set of individual chains.

I do prefer an AIC if I can come up with one, just because it's more fun for me that way. In this particular case, I think the AIC is so simple that it's just not an issue. The only real complexity is recognizing the exact positioning of the 6 in box 9.

Exactly. I didn't see any problem with yours, and thought it was very elegant. Compare it with my fixed solution here. That AIC was also fun to write, but I realize that it's not necessarily fun to follow. That's why I provided a kraken as well as a matrix to help decipher it. Different POVs serve different purposes.

PS. One problem with krakens is that they're much harder to mark on the grid than (even complex) AICs.