## "Schroedinger Cells"

Advanced methods and approaches for solving Sudoku puzzles

### "Schroedinger Cells"

https://tcollyer.blogspot.com/2020/10/t ... tions.html

Does this technique have another name? The Schroedinger Cells name comes from a CTC video; I mentioned in the comments that it seems like a Mutant Multifish, perhaps.

(This is more discussion stemming from Tatooine Sunset and a second puzzle featuring MSLS/MF/partitioning.)
mith

Posts: 369
Joined: 14 July 2020

### Re: "Schroedinger Cells"

(It also seems to be related to SK loops, perhaps - at least, taking the idea to an extreme resulting in an SK loop giving the same eliminations.)
mith

Posts: 369
Joined: 14 July 2020

### Re: "Schroedinger Cells"

Code: Select all
`+-----------------------+----------------------+--------------------+| 37       9      67    | 126    1267    4     | 1367   8     5     || 347      1      4567  | 56     8       567   | 9      2367  237   || 78       5678   2     | 3      9       1567  | 167    4     17    |+-----------------------+----------------------+--------------------+| -47(12)  2367   1467  | 12456  567-12  9     | 13457  237   8     || 5        278    1478  | 124    3       127   | 147    9     6     || 9        2367   1467  | 8      12567   12567 | 13457  237   12347 |+-----------------------+----------------------+--------------------+| 7(1)     4      579-1 | 1569   156     8     | 2      367   379   || 78(2)    578-2  3     | 2569   4       256   | 678    1     79    || 6        8(2)   89(1) | 7      (12)    3     | 48     5     49    |+-----------------------+----------------------+--------------------+`

this ?
Continuous Nice Loop: 1/2/4/7 2= r4c1 =1= r7c1 -1- r9c3 =1= r9c5 =2= r9c2 -2- r8c1 =2= r4c1 =1 => r7c3<>1, r8c2<>2, r4c1<>4, r4c1<>7

which makes the puzzle singles and basics left.

alternatively you could use it as a AHS 2RCC version {of an als 2rcc} since the 2 ahs share 2 digits they are both locked to either set and if they aren't then one of the sets is left empty.
http://forum.enjoysudoku.com/almost-locked-rules-for-now-t2510.html for the als 2rcc version
pretty sure no one has ever used the inverted functions besides me and the lone AHS-xz i published on here and theory work on ahs 2rcc is in my binder just for coded as its basically the inverse of als-2rcc { a tiddler function essentially to use off data instead of on}

edit: or as the others also pointed out 2x 2 string kites using same space { muti-fish}
Last edited by StrmCkr on Wed Oct 21, 2020 6:42 pm, edited 1 time in total.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 1205
Joined: 05 September 2006

### Re: "Schroedinger Cells"

Code: Select all
`*---------------------------------------------------------------*|  37     9      67    | 126    1267   4     | 1367  8    5     ||  347    1      4567  | 56     8      567   | 9     2367 237   ||  78     5678   2     | 3      9      1567  | 167   4    17    ||----------------------+---------------------+------------------||ga12-47  2367   1467  | 12456  567-12 9     | 13457 237  8     ||  5      278    1478  | 124    3      127   | 147   9    6     ||  9      2367   1467  | 8      12567  12567 | 13457 237  12347 ||----------------------+---------------------+------------------|| b17     4      579-1 | 1569   156    8     | 2     367  379   || f278    578-2  3     | 2569   4      256   | 678   1    79    ||  6     e28    c189   | 7     d12     3     | 48    5    49    |*---------------------------------------------------------------*`

Double Kite Loop : (1) r4c1 = r7c1 - r9c3 = (1-2) r9c5 = r9c2 - r8c1 = (2) r4c1 loop => - 47 r4c1, - 12 r4c5, - 1 r7c3, - 2 r8c2; btte.

That's just my name for this kind of pattern. Two Kites that have the same two end cells and thus form a loop. Leren

PS. I found a similar one a few weeks ago here. The PM for that one was :

Code: Select all
`*------------------------------------------------------------------------*|  2356789  23689 56789 | 4679 13689 134689  |  12489-57 1289-7 ec14579  ||ga57-689   689   1     | 2    689   4689    |fb45789  fb789      3      ||  23789    4     789   | 79   5     1389    |  1289-7   6       e179    ||-----------------------+--------------------+---------------------------||  1369     7     69    | 8    4     1269    |  12369    5        169    ||  14569    169   2     | 3    169   1569    |  14679    179      8      ||  1345689  13689 45689 | 569  1269  7       |  123469   1239     1469   ||-----------------------+--------------------+---------------------------||  124689-7 12689 46789 | 4569 23689 2345689 |  1356789  13789   d57-169 ||  46789    689   3     | 1    689   45689   |  56789    789      2      ||  12689    5     689   | 69   7     23689   |  13689    4        169    |*------------------------------------------------------------------------*`

Double Kite Loop : (5) r2c1 = r2c7 - r1c9 = (5-7) r7c9 = r13c9 - r2c78 = (7) r2c1 loop => - 57 r1c7, - 7 r1c8, - 689 r2c1, - 7 r3c7, - 7 r7c1, - 169 r7c9 but this was only a partial solution, so I didn't bother with it any further.

There are plenty more if I take the time to look, for example here Leren
Last edited by Leren on Wed Oct 21, 2020 9:08 am, edited 3 times in total.
Leren

Posts: 4013
Joined: 03 June 2012

### Re: "Schroedinger Cells"

Hi mith,

mith wrote:https://tcollyer.blogspot.com/2020/10/t ... tions.html

Does this technique have another name? The Schroedinger Cells name comes from a CTC video; I mentioned in the comments that it seems like a Mutant Multifish, perhaps. (It also seems to be related to SK loops, perhaps - at least, taking the idea to an extreme resulting in an SK loop giving the same eliminations.)

Both are correct categorizations, as far as I'm concerned. It is indeed an RC-type (i.e. Mutant) Multifish with two digits. That's exactly what SK-Loops are, except with four digits:

This:

MF (12 RC): 4x4 {12R9 12C1 \ 12b7 4n1 9n5}
SK-Loop (Easter Monster):

MF (1267 RC): 16x16 {1267R28 1267C28 \ 27b19 16b37 2n56 8n45 56n2 45n8}
The identical structure should be easy to see. Only the scale is different.

--
Added. For practical purposes, I think Leren's Double Kite Loop is a descriptive name. (DK-Loop might be a bit confusing abbreviation but not an entirely wrong association.) Another descriptive name could be Hidden Remote Pair (I just came up with that).

Btw, SteveK originally called his loop Hidden Pair Loop (others started to call it SK-Loop). It might work for this smaller cousin too.
-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: 2674
Joined: 22 May 2017

### Re: "Schroedinger Cells"

The loop can be made with Empty Rectangles and in two different ways.
ghfick

Posts: 121
Joined: 06 April 2016

### Re: "Schroedinger Cells"

ghfick wrote:The loop can be made with Empty Rectangles and in two different ways.

What two ways? I can see just one way to do it with ERs only. I can also see at least four more ways to do it with some ERs. All of them (especially the pure one) are of course inefficient compared to the straight-forward route. Yet they're kind of interesting because they represent many different kinds of Multifishes:

Pure ER-loop:

a. MF (12 B): 6x6 {12B478 \ 1r7 2r8 1c3 2c2 4n1 9n5}
Mixed ER-loops:

b. MF (12 RB): 4x4 {12R9 12B4 \ 1c3 2c2 4n1 9n5}
c. MF (12 CB): 4x4 {12C1 12B8 \ 1r7 2r8 4n1 9n5}
d. MF (12 RCB): 4x4 {1R9 2C1 1B4 2B8 \ 1c3 2r8 4n1 9n5}
e. MF (12 RCB): 4x4 {2R9 1C1 1B8 2B4 \ 1r7 2c2 4n1 9n5}
The simple loop (for reference):

f. MF (12 RC): 4x4 {12R9 12C1 \ 12b7 4n1 9n5}
corresponding chains: Show
a. (1)r4c1 = r456c3 - r79c3 = r7c1 - r7c45 = (1-2)r9c5 = r8c46 - r8c12 = r9c2 - r456c2 = (2)r4c1 - loop
b. (1)r4c1 = r456c3 - r9c3 = (1-2)r9c5 = r9c2 - r456c2 = (2)r4c1 - loop
c. (1)r4c1 = r7c1 - r7c45 = (1-2)r9c5 = r8c46 - r8c1 = (2)r4c1 - loop
d. (1)r4c1 = r456c3 - r9c3 = (1-2)r9c5 = r8c46 - r8c1 = (2)r4c1 - loop
e. (1)r4c1 = r7c1 - r7c45 = (1-2)r9c5 = r9c2 - r456c2 = (2)r4c1 - loop
f. (1)r4c1 = r7c1 - r9c3 = (1-2)r9c5 = r9c2 - r8c1 = (2)r4c1 - loop

SpAce

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### Re: "Schroedinger Cells"

There's a nice double ALS (r378c1 and r9c2379, X-Z values 1 and 2 => -1 r7c3, -2 r8c2, -7 r14c1) that gives a btte solution.
Phil
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