The New Sudoku Players' Forum

[P.O.]

Code: Select all

2389    2348    1       268     234568  2358    7       46      23469           
23      5       24      9       12346   7       1234    8       12346           
6       23478   24789   128     12348   1238    12349   14      5               
23578   1       2578    4       2578    6       358     9       37               
235789  23478   245789  1278    12578   1258    13458   14567   13467           
578     6       4578    3       1578    9       1458    2       147             
4       27      2567    1267    123679  123     1259    157     8               
1278    9       2678    5       12678   4       12      3       127             
12578   278     3       1278    12789   128     6       1457    12479           

chain n°: 1
depth: 3  candidate: 4  from cell(s)
 ((1 9 3) (2 3 4 6 9)) ((2 7 3) (1 2 3 4)) ((2 9 3) (1 2 3 4 6))
 ((3 7 3) (1 2 3 4 9)) ((5 8 6) (1 4 5 6 7)) ((9 8 9) (1 4 5 7))

((4 0) (3 8 3) (1 4))
((1 0) (3 8 3) (1 4))
((1 1) (2 5 2) (1 2 3 4 6))
((6 2) (2 9 3) (1 2 3 4 6))
((4 3) (1 8 3) (4 6))


some singles:

(" r9c9b9 n4 " " r7c7b9 n9 " " r1c9b3 n9 " " r9c5b8 n9 " " r3c3b1 n9 "
 " r5c1b4 n9 " " r3c2b1 n7 " " r7c2b7 n2 " " r9c2b7 n8 " " r8c5b8 n8 "
 " r1c1b1 n8 " " r8c3b7 n6 ")


chain n°: 2
depth: 0  candidate: 2  from cell(s)
((2 5 2) (1 2 3 4 6)) ((2 7 3) (1 2 3)) ((2 9 3) (1 2 3 6))

((2 0) (2 1 1) (2 3))
((2 0) (2 3 1) (2 4))

ste.


[eleven]

pjb wrote : Are SDC and double ALS measuring the same thing?

With this example, possibly not. This is the puzzle : 3....9742...5..6.........1........611.986.........3.....1.2..3..4...5..75......28

Code: Select all

*---------------------------------------------------------*
| 3      1568  568    |P16     P18     9     | 7    4  2  |
| 2479   1279  247    | 5       347-1 B1247  | 6    8  39 |
| 246789 26789 24678  | 2347-6  347-8 B24678 | 39   1  5  |
|---------------------+----------------------+------------|
| 2478   23578 234578 | 2479    4579  P247   | 2389 6  1  |
| 1      2357  9      | 8       6     P247   | 23   57 34 |
| 24678  25678 245678 | 12479   14579  3     | 289  57 49 |
|---------------------+----------------------+------------|
| 789    789   1      | 479     2      8-47  | 5    3  6  |
| 268    4     2368   | 36      38     5     | 1    9  7  |
| 5      3679  367    | 13679   1379   16-7  | 4    2  8  |
*---------------------------------------------------------*
Sue de Coq: Base Cells r23c6  {24678} Pincer Cells r45c6 {247}  + r1c45 {168} => - 1 r2c5, - 6 r3c4, - 8 r3c5, -47 r7c6, - 7 r9c6; stte

Or 6 digits in 6 cells, 168 bound to b2, 247 to c6 => eliminate the others in b2 and c6.

[Cenoman]

Sorry, I'm coming late in this thread.

Are SDC and double ALS measuring the same thing?

For Phil's fifth and Leren's first (counter)-example, it has been proved yes.
Note for Leren's puzzle, that yzfwsf has found a SDC matching Leren's ALS-XZ Rule Loop, but the reverse was also possible (find an ALS-XZ Rule Loop matching Leren's SDC):

Hidden Text: Show

Code: Select all

*-----------------------------------------------------*
| 3   2  9  |P168   P1478     P1678  | 5    14  14678 |
| 458 48 17 |B1368   35-1478  P1678  | 168  2   9     |
| 458 6  17 |B189    259-1478 29-178 | 18   3   1478  |
|-----------+------------------------+----------------|
| 9   3  4  | 2      18        18    | 7    6   5     |
| 7   1  6  |P39     39        5     | 4    8   2     |
| 2   5  8  | 7      6         4     | 19   19  3     |
|-----------+------------------------+----------------|
| 468 7  3  | 168-9  1289      12689 | 1289 5   148   |
| 1   9  5  | 4      28        3     | 268  7   68    |
| 468 48 2  | 5      1789      16789 | 3    149 148   |
*-----------------------------------------------------*
Sue de Coq: Base Cells r23c4 {13689}  Pincer Cells r5c4 {39} + r1c456, r2c6 {14678}

With the same cells: ALS XZ Rule Loop : ALS 1 r5c4; ALS 2 r1c456, r2c46, r3c4; Z = 3 & 9 => same eliminations as SDC

As regards Leren's second counter-example:

The main difference is that, with the SDC you can get - 47 r7c6. With double ALS I can't see how you can get it, even though there were a number of double ALS moves available.

Leren, you are comparing an ALS-XZ Rule Loop in a set of cells that is not the Sue de Coq's.
Not surprising you find a different list of eliminations.
I assume that there is a typo when you write:

Sue de Coq: Base Cells r23c6 {24678} Pincer Cells r45c6 {247} + r1c45 {168} => - 1 r2c5, - 6 r3c4, - 8 r3c5, -47 r7c6, - 7 r9c6; stte

Should read Sue de Coq: Base Cells r23c6 {124678} Pincer Cells r45c6 {247} + r1c45 {168}
The SDC Base is an AAAALS: 6 digits, 2 cells -> freedom degree 4 !!!
So each Pincer ALS must be linked to the base by six restricted commons, in total (which is the case: r45c6 is linked by RCs 247, ric45 by RCs 168)
Consider the same cells, broken down into A, B (PM below): A is an ALS, but B is an AALS. They are triply linked, so you can consider the rank-0 logic: A -(168)- B => - 1 r2c5, - 6 r3c4, - 8 r3c5, -47 r7c6, - 7 r9c6; stte

Code: Select all

*---------------------------------------------------------*
| 3      1568  568    |A16     A18     9     | 7    4  2  |
| 2479   1279  247    | 5       347-1 B1247  | 6    8  39 |
| 246789 26789 24678  | 2347-6  347-8 B24678 | 39   1  5  |
|---------------------+----------------------+------------|
| 2478   23578 234578 | 2479    4579  B247   | 2389 6  1  |
| 1      2357  9      | 8       6     B247   | 23   57 34 |
| 24678  25678 245678 | 12479   14579  3     | 289  57 49 |
|---------------------+----------------------+------------|
| 789    789   1      | 479     2      8-47  | 5    3  6  |
| 268    4     2368   | 36      38     5     | 1    9  7  |
| 5      3679  367    | 13679   1379   16-7  | 4    2  8  |
*---------------------------------------------------------*

"ALS/AALS XZ Rule" Loop : ALS 1 r1c45; AALS 2 r2345c6; Z = 1 & 6 & 8 => - 8 r1c23, - 1 r2c5, - 6 r3c4, - 8 r3c5, - 8 r8c5, - 7 r9c6; stte

AIC for this loop: (1247=6|8)r2345c6 - (68=1)r1c45 loop =>same eliminations.

This example brings to light the needed adjustments when transposing an extended SDC to an equivalent ALS XZ rule (notably adjusting the number of links and the freedom degree of ALS's)

Are SDC and double ALS measuring the same thing? I had in mind the following:
(2=3)r2c1 - (3=2)r2c79, r13c8 - loop => same eliminations as Leren's SDC.
Are they ever non-equivalent? (I removed SDC from my solver because I thought they were)

I thought so either, but don't know, if it is proved. What i like is, that there are rather different ways to spot it, as shown here.

Note that in Phil's fifth puzzle, as well as in Leren first counter-example, the ALS-XZ doubly linked were equivalent because it was possible to merge the SDC base with the ALS initially triply linked, to form the new "big ALS"

Obviously, there are cases of doubly-linked ALSs that SDC doesn't cover, since it's limited to one line and one box and therefore cannot detect for example doubly-linked ALSs in two rows.

Clearly, the answer to Phil's question depends upon the definition given to the SDC pattern.
When the pattern was invented by Sue de Coq, it was limited to one line and one box, as stated by Marek. When I learned the pattern (in a document in French, around 2008) this limitation was not mentionned. Therefore, to me, the case considered by Marek, of "doubly-linked ALSs in two rows", was a Sue de Coq. It was clearly stated here. Now, see the puzzle in this thread: I have been tarred and feathered for that .
However the extension makes sense; the limitation to one box and one line brings nothing from the logical point of view, only the links between subsets do. See also a more recent puzzle here.

So, extending SDC base up to an AAAALS seems accepted without any doubt, but extending SDC location to a pair of sectors other than (box, line) or to a triplet of sectors seems still too much transgressive.

Frankly speaking, I'm lost.
But no matter, this is just a naming question. It doesn't change anything in the logic of the patterns.

Are SDC and double ALS measuring the same thing?

To me the answer to Phil's question is YES, in all cases, provided consistent extended definitions of each term (SDC and double ALS) are accepted.
Nothing else than MHO.

[StrmCkr]

This is the puzzle : 3.9...5.........29.6.....3..3.2...6.7....5.8225.7.4....7.......19.4.3......5..3..

Here is a Sue de Coq Move for 12 eliminations, similar to Hodoku:

Code: Select all

*-----------------------------------------------------*
| 3   2  9  |P168   P1478     P1678  | 5    14  14678 |
| 458 48 17 |B1368   35-1478  P1678  | 168  2   9     |
| 458 6  17 |B189    259-1478 29-178 | 18   3   1478  |
|-----------+------------------------+----------------|
| 9   3  4  | 2      18        18    | 7    6   5     |
| 7   1  6  |P39     39        5     | 4    8   2     |
| 2   5  8  | 7      6         4     | 19   19  3     |
|-----------+------------------------+----------------|
| 468 7  3  | 168-9  1289      12689 | 1289 5   148   |
| 1   9  5  | 4      28        3     | 268  7   68    |
| 468 48 2  | 5      1789      16789 | 3    149 148   |
*-----------------------------------------------------*
Sue de Coq: Base Cells r23c4 {13689}  Pincer Cells r5c4 {39} + r1c456, r2c6 {14678}

and here is an ALS loop for 14 eliminations:

Code: Select all

*------------------------------------------------------*
| 3    2   9  |B168    4-178   B1678  | 5    14  14678 |
| 458  48  17 |B1368   345-178 B1678  | 168  2   9     |
| 458  6   17 |B189    2459-178 29-178| 18   3   1478  |
|-------------+-----------------------+----------------|
| 9    3   4  | 2      18      18     | 7    6   5     |
| 7    1   6  |A39     39      5      | 4    8   2     |
| 2    5   8  | 7      6       4      | 19   19  3     |
|-------------+-----------------------+----------------|
| 468  7   3  | 168-9  1289    12689  | 1289 5   148   |
| 1    9   5  | 4      28      3      | 268  7   68    |
| 468  48  2  | 5      1789    1689-7 | 3    149 148   |
*------------------------------------------------------*
ALS XZ Rule Loop : ALS 1 r5c4; ALS 2 r1c46, r2c46, r3c4; Z = 3 & 9

The difference seems to be that in Sue de Coq logic, r1c5 has to be in the pattern, for the 4 eliminations, whereas in ALS logic you don't get the 4 eliminations, but more overall.

Maybe there is a Sue de Coq without r1c5, but neither I nor Hodoku played it.

It's been so long since I've looked at Sue de Coq logic I've long since forgotten the details of just how it works. My money is on the ALS logic being simpler to understand and giving at least as many eliminations as Sue de Coq.

Leren

my code below uses this for cells. so its not in RC

Code: Select all

      1  2  3  4  5  6  7  8  9   Col
   ---------------------------
  1 | 0  1  2  3  4  5  6  7  8
  2 | 9 10 11 12 13 14 15 16 17
  3 |18 19 20 21 22 23 24 25 26
  4 |27 28 29 30 31 32 33 34 35
  5 |36 37 38 39 40 41 42 43 44
  6 |45 46 47 48 49 50 51 52 53
  7 |54 55 56 57 58 59 60 61 62
  8 |63 64 65 66 67 68 69 70 71
  9 |72 73 74 75 76 77 78 79 80
 Row

delayed response:

my als-xz doubly linked rule hits your missing eliminations for this: {do you account for each digit as "locked"}

Code: Select all

Als A ) 3 9 @ 39
Als b) 1 3 4 6 7 8 9 @ 3 4 5 12 14 21
RC: 3 9
Z:1 3 4 6 7 8 9 

eliminates :
13 22 23 <> 1
30 48 57 66 75 <> 3
0 1 2 6 7 8 13 22 23 31 40 49 58 67 76 <> 4
13 22 23 <> 6 7 8
30 48 57 66 75 <> 9

the other als i find for these cells is: which doesn't have the R1C5

Code: Select all

Als A ) 3 9 @ 39
Als b) 1 3 6 7 8 9 @ 3,5,12,14,21
RC: 3 9
Z:1 3 4 6 7 8 9

eliminates:
 4 13 22 23 <> 1
30 48 57 66 75 <> 3
13 22 23 <> 6
4 13 22 23 32 41 50 59 68 77 <> 7
30 48 57 66 75 <> 9

my
sue de coq engine: has 22 variations {depending how it breaks the sets into "aals"}
and they are split into 2 classes one with "R1C5" and one without.

Code: Select all

A) 1 8 9  @ 21
b) 1 3 4 6 7 8 @ 3 4 5 12 14
c) 3 9 @ 39
RC: 1 8 9 
Z: 1 3 4 6 7 8 9

eliminates:
13 22 23 <> 1
30 48 57 66 75 <> 3
0 1 2 6 7 8 13 22 23 31 40 49 58 67 76 <> 4
13 22 23 <> 6 7 8
30 48 57 66 75 <> 9 

Code: Select all

A) 1 8 9  @ 21
b) 1 3 6 7 8 @ 3 5 12 14
c) 3 9 @ 39
RC: 1 8 9 
Z: 1 3 6 7 8 9

eliminates:
4 13 22 23 <> 1
30 48 57 66 75 <> 3
13 22 23 <> 6
4 13 22 23 32 41 50 59 68 77 <> 7
30 48 57 66 75 <>9

so i cant find a "real" difference between the two types for eliminations i'll need a better example to examine.

pjb wrote:
Are SDC and double ALS measuring the same thing? I had in mind the following:

(2=3)r2c1 - (3=2)r2c79, r13c8 - loop => same eliminations as Leren's SDC.

Are they ever non-equivalent? (I removed SDC from my solver because I thought they were)

Phil

to best of my programing skill and knowledge they are equivalent in elimination when they overlap exactly.

i was also under the same false sense of scrutiny that als-xz and sue de coqs where the exact same as every example I've seen played out had an als counter part.

however:
they have slightly different abilities to detect in constructs where by there is a types of sue de coqs that simply are not als-xz
when the initial set cannot be combined to form an als which is the bases of an ALS-xz as sue de coqs use AALS

sue de coq use an initial set of n cells with n+2 digits and 2 sets of n cells with n+1 digits : so that N digits in N cells with N digits locked to N sectors

ALS xz: uses n cells with n+1 digits and 1 set of n cells with N+1 digit so that: 2 digits locked to 2 sectors to lock all N digits to each sector

in these definitions
xz has slightly more flexibility as it isn't limited to the N digits in N sectors when examining the 2 sectors it resides in

sue de coq definition has flexibility in that i can see more sectors at once and uses a bigger initial set size

xz rule loses flexibility when a set cannot be combined into a N cells with N+1 digit set
then it needs to upgrade into the aals 2RC rule {see the link above} and gains the muti sector view point power.

why?
Als N cells with N+1 digits
AALS are formed by breaking N cells with N+1 digits into parts groups with less cells but more digits.

not all als can be an aAls {like 1 cell with 2 digits} and vice versa not all aals have an als in them.

N^als - N^RC is the parent class for everything als stuff

Code: Select all

which can be broken into: {named techniques}
 [ als sets with N cells with N+x digits  where x > 1 and   x  N+1 sets are added ]
ADDS  { DDS with +1 set added for eliminations }
  DDs  { death blossom {N+3}, sue de coq {n+2}, AAls - 2RC{n+2}, }
 
[als sets with N cells with N+1 digits   and  1  N+1 sets are added]
  als - xy  { xz with +1 set added for eliminations }   
  als - xz  {N+1  - 2 sets}

a good example of a sue de coq with no als-xz -> but has an aals 2RC

Code: Select all

---------------------------------------------------------*
| 3      1568  568    |A16     A18     9     | 7    4  2  |
| 2479   1279  247    | 5       347-1 B1247  | 6    8  39 |
| 246789 26789 24678  | 2347-6  347-8 B24678 | 39   1  5  |
|---------------------+----------------------+------------|
| 2478   23578 234578 | 2479    4579  B247   | 2389 6  1  |
| 1      2357  9      | 8       6     B247   | 23   57 34 |
| 24678  25678 245678 | 12479   14579  3     | 289  57 49 |
|---------------------+----------------------+------------|
| 789    789   1      | 479     2      8-47  | 5    3  6  |
| 268    4     2368   | 36      38     5     | 1    9  7  |
| 5      3679  367    | 13679   1379   16-7  | 4    2  8  |
*---------------------------------------------------------*

Code: Select all

sue de coq
a) 1 2 4 6 7 8 @ 14 23 32 41
B) 1 6 @ 3
c) 1 8 @ 4
RC: 1 6 8
Z: 1 2 4 6 7 8 

eliminations :
 5 12 13 21 22 <> 1 6 8
5 50 59 68 77 <> 2 4 8

Code: Select all


AALS- 2RC 
a) 1 2 4 6 7 8 @ 14 23 32 41
B) 1 6 @ 3
c) 1 8 @ 4
RC: 1 6 8
Z: 1 2 4 6 7 8 

eliminations :
 5 12 13 21 22 <> 1 6 8
5 50 59 68 77 <> 2 4 8

TLDR

Are SDC and double ALS measuring the same thing?

To me the answer to Phil's question is YES, in all cases, provided consistent extended definitions of each term (SDC and double ALS) are accepted.
Nothing else than MHO

100% Agree

[yzfwsf]

.
a good example of a sue de coq with no als-xz -> but has an aals 2RC

Code: Select all

---------------------------------------------------------*
| 3      1568  568    |A16     A18     9     | 7    4  2  |
| 2479   1279  247    | 5       347-1 B1247  | 6    8  39 |
| 246789 26789 24678  | 2347-6  347-8 B24678 | 39   1  5  |
|---------------------+----------------------+------------|
| 2478   23578 234578 | 2479    4579  B247   | 2389 6  1  |
| 1      2357  9      | 8       6     B247   | 23   57 34 |
| 24678  25678 245678 | 12479   14579  3     | 289  57 49 |
|---------------------+----------------------+------------|
| 789    789   1      | 479     2      8-47  | 5    3  6  |
| 268    4     2368   | 36      38     5     | 1    9  7  |
| 5      3679  367    | 13679   1379   16-7  | 4    2  8  |
*---------------------------------------------------------*

[code]

Almost Locked Set XZ-Rule: A=r23457c6 {124678},B=r1c45 {168}, X=16, Z=/ => r1c5<>1 r2c5<>1 r3c4<>6 r9c6<>7 r3c6<>8 r1c2<>8 r1c3<>8 r3c5<>8 r7c1<>8 r7c2<>8 r8c5<>8

[StrmCkr]

Almost Locked Set XZ-Rule: A=r23457c6 {124678},B=r1c45 {168}, X=16, Z=/ => r1c5<>1 r2c5<>1 r3c4<>6 r9c6<>7 r3c6<>8 r1c2<>8 r1c3<>8 r3c5<>8 r7c1<>8 r7c2<>8 r8c5<>8

has R7C6 adding this cell changes the aals to an als allowing an als-xz to work.

this cell isn't used in the example

[AnotherLife]

Hello, Phil,

Are SDC and double ALS measuring the same thing? I had in mind the following:

(2=3)r2c1 - (3=2)r2c79, r13c8 - loop => same eliminations as Leren's SDC.

Are they ever non-equivalent? (I removed SDC from my solver because I thought they were)

Phil

In general, Sue de Coq is not equivalent to doubly linked ALS's.

1.

Obviously, there are cases of doubly-linked ALSs that SDC doesn't cover, since it's limited to one line and one box and therefore cannot detect for example doubly-linked ALSs in two rows.

I will give a reference to my post where the doubly linked ALS's cannot be treated as Sue de Coq (my step 2). This is the corresponding resolution state (in YZF_Sudoku or HoDoKu format):
:0000:x:7.8...3.....2.1...5.........4....8263...8....+8..1...93.9.6....4.+8..7.5...........:323 133 333 334 434 934 336 436 636 936 737 738 838 739 839 345 152 552 752 153 553 753 554 556 756 262 662 273 375 283 192 292 392 692 293 395::

2. Here is another reference to Cenoman's reply to my post where Sue de Coq cannot be subsumed under doubly linked ALS-XZ, but it can be treated as an ALS triply linked to an AALS. This is the resolution state:
:0000:x:.2.....8...71......96..7.......6..+143+19..+285+6.6...13.......5+43..4.2.8...9....41..:614 744 464 764 465 765::

Both Sue de Coq and doubly linked ALS-XZ are examples of multi-sector locked sets, that is, a more generalized concept.

[StrmCkr]

In general, Sue de Coq is not equivalent to doubly linked ALS's.

depends on the definition used of what maxes up the als-xz or the coq.

in general the als-xz is 2 als's composed of 2: n cells with N+1 digits

there is 1 definition that lists Sue de coq as an AALS that has 2 n cells with n+1 digits that are connected to it.

in which any als -xz can also identify as doubly linked: with a hand full it cannot when the aals used doesn't come from any larger n cells with N+1 digits.

however if you define the als-xz as an aals-xz {aals 2rc rule} then it finds it just fine.

or
you scale up into als-xy {with triple/double link rules} and it also appears but not always as again there is N als with >1 freedoms that do not form n+1 sizes.

{gave an example of this above}
if its 2 sectors with up to n digits locked in N sectors then its under
N^als N^RC rules

this technique isn't discussed at all past say 2007: but in essence it is the parent for everything including: Muti sector locked sets

depending on your definition and scope there is degrees of overlap between the two unless you choose to scale each definition up then you arrive at the
N^als- n^Rc formation for both and they are equivalent.


for me personally i use the following as definitions there is some overlap with in the techniques

als-xz is 2 sets of n cells with N+1 digits

Sue de Coq :
1 set of N+1 cell with N+2 digits
2 sets of: n cells with n+1 digit als' attached to it.
where all N digits are locked into exactly N sectors.

aals-2RC:
is 1 set of N cells with N+2 digits
2 sets of: n cells with n+1 digit als' attached to it.

with the purple highlighted object being the most important restriction that makes a coq a coq.

[AnotherLife]

In general, Sue de Coq is not equivalent to doubly linked ALS's.

depends on the definition used of what maxes up the als-xz or the coq.

If we stick to the conventional definitions used in HoDoKu and YZF_Solver, then Sue de Coq is not subsumed under doubly linked ALS-XZ and vice versa (see the examples in my previous post). If we extend their definitions, I believe we will finally come to MSLS's.

[StrmCkr]

If we stick to the conventional definitions used in HoDoKu and YZF_Solver, then Sue de Coq is not subsumed under doubly linked ALS-XZ and vice versa (see the examples in my previous post). If we extend their definitions, I believe we will finally come to MSLS's.

Code: Select all

.-------------------.-------------------.-------------------.
| 145    2     1345 | 3459  3459    369 | 5679  8     13579 |
| 458    358   7    | 1     234589  369 | 2569  2469  2359  |
| 1458   9     6    | 3458  23458   7   | 25    24    1235  |
:-------------------+-------------------+-------------------:
| 2578   578   258  | 3589  6       39  | 279   1     4     |
| 3      1     9    | 47    47      2   | 8     5     6     |
| 24578  6     2458 | 589   589     1   | 3     279   279   |
:-------------------+-------------------+-------------------:
| 12678  78    128  | 679   179     5   | 4     3     2789  |
| 1567   4     135  | 2     1379    8   | 5679  679   579   |
| 9      3578  2358 | 367   37      4   | 1     267   2578  |
'-------------------'-------------------'-------------------'

Sue de Coq: r2c789 - {234569} (r2c6 - {369}, r3c78 - {245}) => r1c79,r3c9<>5, r3c9<>2, r2c25<>3, r2c5<>

shows up as:
AALs - 2RC
sue de coq :

pretty much the same points made:
the only
sue de coqs not sub summed by als-xz rule is the few that cannot be combined into n cells with n+1 cells. which are instead the A*ALS forms.

[AnotherLife]

here's a kicker to try:
turn on allow overlaps in als and all sue de coqs found in hodoku show up as als-xz double linked
its search function and naming is based on als-xz finding function.

Ok, I have turned on 'Allow overlap' (my version of HoDoKu is v2.2.0). Will you try my example given above: :0000:x:.2.....8...71......96..7.......6..+143+19..+285+6.6...13.......5+43..4.2.8...9....41..:614 744 464 764 465 765::
How can you replace Sue de Coq by ALS-XZ?