The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|...|54.|
 |...|.2.|...|
 |...|.6.|...|
 |---+---+---|
 |...|...|.71|
 |.5.|...|.2.|
 |.4.|9..|...|
 |---+---+---|
 |...|5.4|6..|
 |2..|...|8..|
 |7..|3..|...|
 *-----------*

......54.....2........6...........71.5.....2..4.9........5.46..2.....8..7..3.....


Play/Print this puzzle online

[eleven]

This puzzle looks very familiar to me. I think, yogi posted one with the same pattern.

Code: Select all

 *------------------------------------------------------------*
 | #68+9  2     168-9   |  7     3  1-89   |  5  4    #68+9   |
 |  45    189   13689   |  148   2  1589   |  7  168   3689   |
 |  45    7     1389    |  148   6  1589   |  2  18    389    |
 |----------------------+------------------+------------------|
 |  3     89    689     |  2     5 #68     |  4  7     1      |
 |  1     5     7       | #68    4  3      |  9  2    #68     |
 | #68    4     2       |  9     1  7      |  3 #68    5      |
 |----------------------+------------------+------------------|
 |  89    189   189     |  5     7  4      |  6  3     2      |
 |  2     3     4       |  16    9  16     |  8  5     7      |
 |  7     6     5       |  3     8  2      |  1  9     4      |
 *------------------------------------------------------------*

One of r1c19 must be 9 because of the 2-digit oddagon in r16 and r5c9.
Then you have either remote pairs 68 in r1c1/r4c6 or r1c9/r4c6.
In other words r1c19,r4c6 must be 689.

Or: for ab = 68 or 86 you get

Code: Select all

 *------------------------------------------------------------*
 | #a9    2     168-9   |  7     3  1-89   |  5  4    #a9     |
 |  45    189   13689   |  148   2  1589   |  7  168   3689   |
 |  45    7     1389    |  148   6  1589   |  2  18    389    |
 |----------------------+------------------+------------------|
 |  3     89    689     |  2     5 #b      |  4  7     1      |
 |  1     5     7       | #a     4  3      |  9  2     #b     |
 | #b     4     2       |  9     1  7      |  3 #a     5      |
 |----------------------+------------------+------------------|
 |  89    189   189     |  5     7  4      |  6  3     2      |
 |  2     3     4       |  16    9  16     |  8  5     7      |
 |  7     6     5       |  3     8  2      |  1  9     4      |
 *------------------------------------------------------------*

[SpAce]

original: Show

Code: Select all

.-----------------------.-----------------.----------------.
| g(6)89  2    a[1]89-6 |  7    3   b189  | 5  4      89-6 |
|   45    189    13689  |  148  2    1589 | 7  168    3689 |
|   45    7      1389   |  148  6    1589 | 2  18     389  |
:-----------------------+-----------------+----------------:
|   3     89    e689    |  2    5  bd68   | 4  7      1    |
|   1     5      7      | c68   4    3    | 9  2   ab[6]8  |
|  f68    4      2      |  9    1    7    | 3  68     5    |
:-----------------------+-----------------+----------------:
|   89    189    189    |  5    7    4    | 6  3      2    |
|   2     3      4      |  16   9   b16   | 8  5      7    |
|   7     6      5      |  3    8    2    | 1  9      4    |
'-----------------------'-----------------'----------------'

(16)r1c3,r5c9 = (16,8)r184c6|(8)r5c9 - (8=6)r5c4 -xchain-> (6)r1c1 => -6 r1c39; stte

Code: Select all

.-----------------------.-----------------.----------------.
| f(6)89  2    a[1]89-6 |  7    3   b189  | 5  4      89-6 |
|   45    189    13689  |  148  2    1589 | 7  168    3689 |
|   45    7      1389   |  148  6    1589 | 2  18     389  |
:-----------------------+-----------------+----------------:
|   3     89    d689    |  2    5   c68   | 4  7      1    |
|   1     5      7      | b68   4    3    | 9  2    a[6]8  |
|  e68    4      2      |  9    1    7    | 3  68     5    |
:-----------------------+-----------------+----------------:
|   89    189    189    |  5    7    4    | 6  3      2    |
|   2     3      4      |  16   9   b16   | 8  5      7    |
|   7     6      5      |  3    8    2    | 1  9      4    |
'-----------------------'-----------------'----------------'

(16)r1c3,r5c9 = (16)r18c6|(6)r5c4 - r4c6 =x= (6)r1c1 => -6 r1c39; stte

[Sudtyro2]

Code: Select all

+-------------------+-----------------+-----------------+
| 689*  2   d1689#  |  7    3  e189   | 5   4     689*  |
| 45    189  13689  |  148  2   1589  | 7   168  c3689# |
| 45    7    1389   |  148  6   1589  | 2   18    389   |
+-------------------+-----------------+-----------------+
| 3     89   689    |  2    5   8-6   | 4   7     1     |
| 1     5    7      | a68   4   3     | 9   2    b68*   |
| 68*   4    2      |  9    1   7     | 3   68*   5     |
+-------------------+-----------------+-----------------+
| 89    189  189    |  5    7   4     | 6   3     2     |
| 2     3    4      |  1-6  9  f16    | 8   5     7     |
| 7     6    5      |  3    8   2     | 1   9     4     |
+-------------------+-----------------+-----------------+

In 6s, a 5-link oddagon(*) with two guardians(#).
6r5c4 = r5c9 - r2c9 == (6-1)r1c3 = r1c6 - (1=6)r8c6 => -6 r8c4,r4c6; stte

SteveC

[Ngisa]

Code: Select all

+-----------------------+-------------------+------------------+
|c6*89    2      g16*89 | 7      3    f189  | 5    4      689  |
| 45      189    h13689 | 148    2     1589 | 7    18-6   3689 |
| 45      7       1389  | 148    6     1589 | 2    18     389  |
+-----------------------+-------------------+------------------+
| 3       89     c689   | 2      5    d68   | 4    7      1    |
| 1       5       7     | 68     4     3    | 9    2      68   |
|b68      4       2     | 9      1     7    | 3   a68     5    |
+-----------------------+-------------------+------------------+
| 89      189     189   | 5      7     4    | 6    3      2    |
| 2       3       4     | 16     9    e16   | 8    5      7    |
| 7       6       5     | 3      8     2    | 1    9      4    |
+-----------------------+-------------------+------------------+


(6)r6c8 = r6c1 - r1c1&r4c3 = r4c6 - (6=1)r8c6 - r1c6 = (1-6)r1c3 = (6)r2c3 => - 6r2c8; btte

Clement

[eleven]

I found yogi's puzzle here.
It's the same.

[SteveG48]

Code: Select all

 *--------------------------------------------------------------------*
 |c689    2      1689   | 7      3     c189    | 5      4     c689    |
 | 45     189    13689  | 148    2      1589   | 7      168    3689   |
 | 45     7      1389   | 148    6      1589   | 2      18     389    |
 *----------------------+----------------------+----------------------|
 | 3      89    a689    | 2      5      8-6    | 4      7      1      |
 | 1      5      7      |a68     4      3      | 9      2     b68     |
 |b68     4      2      | 9      1      7      | 3      68     5      |
 *----------------------+----------------------+----------------------|
 | 89     189    189    | 5      7      4      | 6      3      2      |
 | 2      3      4      | 16     9     d16     | 8      5      7      |
 | 7      6      5      | 3      8      2      | 1      9      4      |
 *--------------------------------------------------------------------*


6r4c3,r5c4 = 6r6c1&r5c9 - (6=891)r1c169 - (1=6)r8c6 => -6 r4c6 ; stte

[Cenoman]

Code: Select all

 +----------------------+--------------------+--------------------+
 | a689*  2    b1689    |  7     3   c189    |  5    4    a689*   |
 |  45    189   13689   |  148   2    1589   |  7    168   3689   |
 |  45    7     1389    |  148   6    1589   |  2    18    389    |
 +----------------------+--------------------+--------------------+
 |  3     89    689     |  2     5   e68     |  4    7     1      |
 |  1     5     7       | f68    4    3      |  9    2     8-6    |
 | a68*   4     2       |  9     1    7      |  3   a68*   5      |
 +----------------------+--------------------+--------------------+
 |  89    189   189     |  5     7    4      |  6    3     2      |
 |  2     3     4       |  16    9   d16     |  8    5     7      |
 |  7     6     5       |  3     8    2      |  1    9     4      |
 +----------------------+--------------------+--------------------+

Almost skyscraper
[(6)r1c9*=r1c1-r6c1=r6c8] = (6-1)r1c3 = r1c6 - (1=6)r8c6 - r4c6 = (6)r5c4 => -6 r5c9; ste

[SpAce]

I found yogi's puzzle here.
It's the same.

Interesting. I didn't recognize it, and ended up with a completely different solution. Looks like my old (non-p&p) solution was pretty similar to Steve's:

(6=841)r523c4 - (1=896)r1c619 - r6c1&r5c9 = (6)r6c8 => -6 r5c9; stte

[SteveG48]

(16)r1c3,r5c9 = (16)r18c6|(6)r5c4 - r4c6 =x= (6)r1c1 => -6 r1c39; stte

Nice one. Very nice.

I assume that the notation =x= means that it's a derived strong link with the details left to the reader. I'd just as soon you wrote it out.

[SpAce]

(16)r1c3,r5c9 = (16)r18c6|(6)r5c4 - r4c6 =x= (6)r1c1 => -6 r1c39; stte

Nice one. Very nice.

I assume that the notation =x= means that it's a derived strong link with the details left to the reader. I'd just as soon you wrote it out.

Thanks, Steve! Yes, it's a derived strong link and the 'x' denotes an X-Chain fragment. You're right; I should have written it out but I just wanted to do some experimenting with teleportation, inspired by a recent discussion with eleven. The (now hidden) original had what I really wanted to try (implication), but it wasn't a good match with the new version.

Personally I have no problem if someone wants to jump over trivial chain elements, as long as those cells are clearly marked in the grid and the chain type is marked in the link (in this case '=x=' for X-Chain). Similarly one could skip a lengthy XY-Chain with a derived weak link (1=2) -xy- (3=4). Usually those parts of a chain aren't very interesting, and X-Chains can't even be packed (except with the hated 3D-notation) so they can add a lot of length and clutter. That said, most of the time such skipping probably shouldn't be used anyway, but if and when it is, I guess we should have some conventions that everyone can understand.

The more interesting case is when neither a derived strong or a weak link works, or rather, when both would be needed. That's when the implication is needed (what I call "teleporting" in this context). However, since '->' looks kind of out place in an AIC (even though it works logically and doesn't break reversibility or anything), I'm wondering if it could be replaced with '-='. In other words, could this:

(16)r1c3,r5c9 = (16,8)r184c6|(8)r5c9 - (8=6)r5c4 -xchain-> (6)r1c1 => -6 r1c39

...be this:

(16)r1c3,r5c9 = (16,8)r184c6|(8)r5c9 - (8=6)r5c4 -xchain= (6)r1c1 => -6 r1c39

Or is it even more confusing?

Of course the implication is never really necessary because one can always add (or possibly remove) an extra node and a link to make a normal derived link work, but sometimes it just doesn't work as nicely. That's why I think I'd like to have that option, even though I fully realize that it should be used very sparingly (like any skipping of chain parts). Any thoughts on this?

(If I remember correctly, Cenoman has sometimes used implication within a complex AIC or kraken. If I also remember correctly, I probably complained about it a bit because it's not an official Eureka symbol and can cause confusion. I still have the same reservations, but I'm perhaps more open to accepting it.)