## Mystery Puzzle No 8

Post puzzles for others to solve here.

### Mystery Puzzle No 8

Code: Select all
`*-----------*|548|...|...||.3.|...|8..||1..|...|..3||---+---+---||.72|..8|6..||...|...|3..||...|.47|..9||---+---+---||.1.|3..|.2.||256|9..|...||...|.6.|7..|*-----------*548.......3....8..1.......3.72..86........3......47..9.1.3...2.2569.........6.7..   `
Leren

Posts: 3916
Joined: 03 June 2012

### Re: Mystery Puzzle No 8

Hi Leren,
Here is my resolution with TDP.
- With two conjugated tracks:
P(6r3c6) : 6r3c6->6r1c8->9r1c5->5r3c5
P(6r1c4) : 6r1c4->6r5c6->9r5c5->5r3c5 => r3c5=5, stte
- With an anti-track:
P'(9r1c5) : -9r1c5->9r1c8->6r1c4->6r5c6->9r5c5 => -9r3c5, stte.
How would you write the equivalent with AICs?
Sincerely
Robert
Mauriès Robert

Posts: 329
Joined: 07 November 2019
Location: France

### Re: Mystery Puzzle No 8

Hi Leren.
Hi Robert.
Code: Select all
`+---------+-----------------+-----------------+| 5 4  8  | 1267  129  3    | 12  1679  127   || 6 3  79 | 12457 1259 1249 | 8   14579 12457 || 1 2  79 | 8     59   469  | 45  45679 3     |+---------+-----------------+-----------------+| 9 7  2  | 15    3    8    | 6   145   145   || 4 68 15 | 1256  1259 1269 | 3   1578  1257  || 3 68 15 | 1256  4    7    | 125 158   9     |+---------+-----------------+-----------------+| 7 1  4  | 3     8    5    | 9   2     6     || 2 5  6  | 9     7    14   | 14  3     8     || 8 9  3  | 124   6    124  | 7   145   145   |+---------+-----------------+-----------------+`

9r1c5=(9-6)r1c8=6r1c4-6r56c4=(6-9)r5c6=9r5c5=>-9r3c5=>stte
Ajò Dimonios

Posts: 199
Joined: 07 November 2019

### Re: Mystery Puzzle No 8

Code: Select all
`+---------------+------------------------+-------------------------+| 5    4     8  | 1267     b129     3    | a12     1679     a127   || 6    3     79 | 12457     1259    1249 | 8       14579     12457 || 1    2     79 | 8        c59      469  |d45      45679     3     |+---------------+------------------------+-------------------------+| 9    7     2  | 15        3       8    | 6       145       145   || 4    68    15 | 1256      1259    1269 | 3       1578     f125-7 || 3    68    15 | 1256      4       7    |e125     158       9     |+---------------+------------------------+-------------------------+| 7    1     4  | 3         8       5    | 9       2         6     || 2    5     6  | 9         7       14   | 14      3         8     || 8    9     3  | 124       6       124  | 7       145       145   |+---------------+------------------------+-------------------------+`

(7=1|2)r1c79 - (1|2=9)r1c5 - (9=5)r3c5 - r3c7 = (5-2)r6c7 = (2)r5c9 => - 7r5c9; lclste

Clement
Ngisa

Posts: 1191
Joined: 18 November 2012

### Re: Mystery Puzzle No 8

Ngisa wrote:(7=1|2)r1c79 - (1|2=9)r1c5

It should be (7=12)r1c79 (if not 7 in one of r1c79, then both 1 and 2 - and vice versa).
The shortcut for that is (7=129)r1c579 or (7=129)r1c795 or (7=9)r1c795 (if not 7 in one of r1c579, then each other digit 1,2, and 9 - and here the 9 can only be in r1c5)
[Added:]Note, that if you have an ALS, i.e. n+1 digits in n cells of the same unit, you can always split it, as it is useful, e.g. if you have abcde in 4 cells, you can split it (a=bcde) or (e=abdc) or (bd=ace), or (c=ae), or (be=cd) etc.

Same as Ajó:
Code: Select all
` *-----------------------------------------------------------------* |  5  4    8    | a1267   a129    3      | a12    1679   a127     | |  6  3    79   |  12457   1259   1249   |  8     14579   12457   | |  1  2    79   |  8       5-9   b469    |  45    45679   3       | |---------------+------------------------+------------------------| |  9  7    2    |  15      3      8      |  6     145     145     | |  4  68   15   |  1256   d1259  c1269   |  3     1578    1257    | |  3  68   15   |  1256    4      7      |  125   158     9       | |---------------+------------------------+------------------------| |  7  1    4    |  3       8      5      |  9     2       6       | |  2  5    6    |  9       7      14     |  14    3       8       | |  8  9    3    |  124     6      124    |  7     145     145     | *-----------------------------------------------------------------*`

(9=1276)r1c5794 - 6r3c6 = (6-9)r5c6 = 9r5c5 => -9r3c5, stte
eleven

Posts: 2461
Joined: 10 February 2008

### Re: Mystery Puzzle No 8

Similar to Clement:
Code: Select all
` +-----------------+------------------------+------------------------+ |  5    4    8    | b1267   a129    3      | b12    69-17  b127     |  |  6    3    79   |  12457   125-9  124-9  |  8     14579   12457   |  |  1    2    79   |  8      c59    c469    | c45    679-45  3       |  +-----------------+------------------------+------------------------+ |  9    7    2    |  15      3      8      |  6     145     145     |  |  4    68   15   |  1256    1259   1269   |  3     1578    1257    |  |  3    68   15   |  1256    4      7      |  125   158     9       |  +-----------------+------------------------+------------------------+ |  7    1    4    |  3       8      5      |  9     2       6       |  |  2    5    6    |  9       7      14     |  14    3       8       |  |  8    9    3    |  124     6      124    |  7     145     145     |  +-----------------+------------------------+------------------------+`

(9=1|2)r1c5 - (127=6)r1c479 - (6=459)r3c567 loop => -9 r2c56, -17 r1c8, -45 r3c8; lclste

In other terms, in r1c4579, r3567: 7 digits (1245679) in 7 cells, none can be twice, so all must be there.
The rank-0 logic can be described also as Doubly linked ALS-XZ, or as Sue de Coq [e.g. AAALS (12679)r1c45, ALS ((127)r1c79, ALS (4569)r3c567]
lclste finish only, so bad !
Cenoman
Cenoman

Posts: 1496
Joined: 21 November 2016
Location: Paris, France

### Re: Mystery Puzzle No 8

Code: Select all
` 5       4       8      |a1267  c129    3      | 12    b69-17  127     6       3       79     | 12457  125-9  1249   | 8      14579  12457   1       2       79     | 8      5-9    f469   | 45     45679  3      ------------------------+----------------------+--------------------- 9       7       2      | 15     3      8      | 6      145    145     4       68      15     | 1256  d1259  e69-12  | 3      1578   1257    3       68      15     | 1256   4      7      | 125    158    9      ------------------------+----------------------+--------------------- 7       1       4      | 3      8      5      | 9      2      6       2       5       6      | 9      7      14     | 14     3      8       8       9       3      | 124    6      124    | 7      145    145    `

(6)r1c4 = (6-9)r1c8 = r1c5 - r5c5 = (9-6)r5c6 = r3c6 - loop => -9 r23c5, -17 r1c8, -12 r5c6; stte
Also type 4 UR at r23c38 => lclste

Phil
pjb
2014 Supporter

Posts: 2221
Joined: 11 September 2011
Location: Sydney, Australia

### Re: Mystery Puzzle No 8

Mauriès Robert wrote: P'(9r1c5) : -9r1c5->9r1c8->6r1c4->6r5c6->9r5c5 => -9r3c5, stte.How would you write the equivalent with AICs?

Hi Robert, the nearest I can come to your chain with eureka notation is (9) r1c5 = (9-6) r1c8 = r1c4 - r3c6 = (6-9) r5c6 = (9) r5c5 => - 9 r3c5

However, this is also a continuous loop and has other direct eliminations. Phil has posted this loop, albeit with a different starting point.

Leren

<Edit> Fixed typo spotted by SpAce. Thanks for spotting that.
Last edited by Leren on Fri Jan 17, 2020 8:50 am, edited 3 times in total.
Leren

Posts: 3916
Joined: 03 June 2012

### Re: Mystery Puzzle No 8

Leren wrote:Hi Robert, the nearest I can come to your chain with eureka notation is (9) r1c5 = (9-6) r1c8 = r1c4 - r5c6 = (6-9) r5c6 = (9) r5c5 => - 9 r3c5
However, this is also a continuous loop and has other direct eliminations. Phil has posted this loop, albeit with a different starting point.

Thanks Leren, but this is rather the first case (conjugated tracks) that I would have liked to know how to write like an AIC.
Robert
Mauriès Robert

Posts: 329
Joined: 07 November 2019
Location: France

### Re: Mystery Puzzle No 8

Hi Robert, OK let's see how we go :

P(6r3c6) : 6r3c6->6r1c8->9r1c5->5r3c5 ... 6 r3c6 - r1c4 = (6-9) r1c8 = r1c5 - (9=5) r3c5

P(6r1c4) : 6r1c4->6r5c6->9r5c5->5r3c5 ... 6 r1c4 - r3c6 = (6-9) r5c6 = r5c5 - (9=5) r3c5

How's that. Leren
Leren

Posts: 3916
Joined: 03 June 2012

### Re: Mystery Puzzle No 8

Hi Robert,

Mauriès Robert wrote:- With two conjugated tracks:
P(6r3c6) : 6r3c6->6r1c8->9r1c5->5r3c5
P(6r1c4) : 6r1c4->6r5c6->9r5c5->5r3c5 => r3c5=5, stte
- With an anti-track:
P'(9r1c5) : -9r1c5->9r1c8->6r1c4->6r5c6->9r5c5 => -9r3c5, stte.
How would you write the equivalent with AICs?

The direct translation of your conjugated tracks is a two-way Kraken (which is an AIC if stretched onto a single line):

Code: Select all
`(6)r3c6 - r3c8 = (6-9)r1c8 = r1c5 - (9=5)r3c5||                            (6)r1c4 - r3c6 = (6-9)r5c6 = r5c5 - (9=5)r3c5=> +5 r3c5; stte`

However, that can be shortened and looped (because 9r1c5 and 9r5c5 see each other, i.e. they're weakly linked):

Code: Select all
`(6)r3c6 - r3c8 = (6-9)r1c8 = (9)r1c5||                            |(6)r1c4 - r3c6 = (6-9)r5c6 = (9)r5c5=> -17 r1c8, -12 r5c6, -9 r23c5; stte`

That would be a Kraken-loop, I guess.

On the other hand, your anti-track maps directly onto an AIC:

(9)r1c5 = (9-6)r1c8 = r1c4 - r3c6 = (6-9)r5c6 = (9)r5c5 => -9 r23c5; stte

Again, since the end points are weakly linked, it's actually a loop with the same additional eliminations. Personally I'd also compact it a bit:

(96)r1c58 = r3c8 - r3c6 = (69)r5c65 - loop => -17 r1c8, -12 r5c6, -9 r23c5; stte

Lesson learned: your two-way conjugated tracks and anti-tracks are equivalent, at least when non-branching chains are sufficient. I'd recommend sticking to the anti-track in those cases because it can be written on one line. You only need conjugated tracks when you have 3+ cases to track, or possibly when a branching net is needed and it's easier to write that way. It's the same exact difference as what we have between AICs and Krakens. It makes no sense to use two-way Krakens unless the AIC would be really long.

Of course the simplest option would be to ditch the anti-track and only use conjugated tracks for everything. That would be the most in line with your goal of extreme simplicity because then there would be only one thing to learn instead of two. (Similarly we could write everything as Krakens and ditch AICs. Obviously we don't want to do that, though.)

PS. Ajò's and Leren's AICs and Phil's loop are practically equivalent to the above.
-SpAce-: Show
Code: Select all
`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2519
Joined: 22 May 2017