AIC's net equivalent to forcing net

Advanced methods and approaches for solving Sudoku puzzles

AIC's net equivalent to forcing net

Postby champagne » Fri Nov 07, 2008 9:47 am

Several threads have already been opened starting on FATA MORGANA example.
That one should be dedicated to discussions on how some “forcing nets” or whatever is the appropriate name of what is explained later, can be (or not) transformed in AICs nets.

I will also use that post to comment some aspects linked on the same example to Allan Barker method described here
I have to apologize but I’ll use freely Allan findings, concentrating mostly on Permutations analysis,

This post is limited to the first topic

Fata Morgana is a puzzle proposed few months ago by Tarek.

Code: Select all
000000003001005600090040070000009050700000008050402000080020090003500100600000000


At the start, Fata Morgana has the following Map of Candidates:

Code: Select all
2458  2467  245678 |126789 16789 1678  |24589  1248  3     
2348  2347  1      |23789  3789  5     |6      248   249   
2358  9     2568   |12368  4     1368  |258    7     125   
----------------------------------------------------------
12348 12346 2468   |13678  13678 9     |2347   5     12467
7     12346 2469   |136    5     136   |2349   12346 8     
1389  5     689    |4      13678 2     |379    136   1679 
----------------------------------------------------------
145   8     457    |1367   2     13467 |3457   9     4567 
249   247   3      |5      6789  4678  |1      2468  2467 
6     1247  24579  |13789  13789 13478 |234578 2348  2457 

Allan Barker proposed an Initial loop working on Floors 1;3;6 and on the node/cell N42.

I will write the map focusing on these digits in the following way

Code: Select all
 +   ..6+ ..6+ | 1.6+ 1.6+ 1.6+ | ...+ 1..+  -
.3.+ .3.+   -  | .3.+ .3.+  -   |  -     +   +
.3.+   -  ..6+ | 136+  -   136+ |  +     -  1..+
------------------------------------------------
1.3+ 136+ ..6+ | 136+ 136+  -   | .3.+   -  1.6+
 -   136+ ..6+ | 136   -   136  | .3.+ 136+  -
13.+  -   ..6+ |  -   136+  -   | .3.+ 136  1.6+
------------------------------------------------
1..+  -    +   | 136+  -   136+ | .3.+  -   ..6+
 +    +    -   |  -   ..6+ ..6+ |  -   ..6+ ..6+
 -   1..+  +   | 13.+ 13.+ 13.+ | .3.+ .3.+   +


Each ’+’ represents any candidates “out floors”.
Each ’-’ is a given.

What is established in Allan Model (and checked by my solver) is that in that map, All valid permutation lead to one of the digits ‘136’ in N42.


My preferred explanation is the following (Allan source):

Code: Select all
1r5c46=>1r1c5^1r9c5=> 1r4c2|1r6c8  (^ exclusive or; | non exclusive or)
3r5c46=>3r2c5^3r9c5=>3r4c2|3r6c8
6r5c46=>6r1c5^6r8c5=>6r4c2|6r6c8


As r5c46 is filled by two of these groups, n42 is always assigned (1,3 or 6)
24r5c46 can be eliminated.

This is a mixture between forcing nets and use of “super candidates”. Nevertheless, I do not see a corresponding AIC net.

Super candidates are not a problem. Tests have been delayed by work on Allan model, but it is on the way.

The problem starts with 3r5c46 => 3r2c5^3r9c5.
This is very easy to state in a forcing chain POV.
This is a key point for the next =>.
I have no equivalence in AICs .

It seems to me that once you have that relation, you are not so far from an answer thru AIC’s nets, however, you still have the last difficulty: how do you express in AIC environment the fact that two distant cells (N42,N68) are linked. (in blind mode Any puzzle tailor made practice is forbidden)

I will show in other posts other ways to show that N42 is one of 1;3;6, but if anybody has ideas to express that situation in a kind of AIC’s net, he is welcome.

BTW, one difficulty I face for the time being is to find Allan first loop among other possibilities to show N42={1;3;6}, but this is another story.
champagne
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Postby ttt » Fri Nov 07, 2008 8:29 pm

Hi champagne,
For FM & TR ‘s first move, I studied and as manual solver I see that there is differences based on floors (136)r5c46 for FM & (157)r56c6 for TR:
- FM: floor (136)r5c46 with pairs [(13), (16), (36)] as start of net
- TR: floor (157)r56c6 with pairs [(15), (57)] as end of net.

Fata Morgana - present as diagram:

Code: Select all
*-----------------------------------------------------------------------------*
 | 2458    2467    245678  | 126789  16789   1678    | 24589   1248    3       |
 | 2348    2347    1       | 23789   3789    5       | 6       248     249     |
 | 2358    9       2568    | 12368   4       1368    | 258     7       125     |
 |-------------------------+-------------------------+-------------------------|
 | 12348   12346   2468    | 13678   13678   9       | 2347    5       12467   |
 | 7       12346   2469    | 136     5       136     | 2349    12346   8       |
 | 1389    5       689     | 4       13678   2       | 379     136     1679    |
 |-------------------------+-------------------------+-------------------------|
 | 145     8       457     | 1367    2       13467   | 3457    9       4567    |
 | 249     247     3       | 5       6789    4678    | 1       2468    2467    |
 | 6       1247    24579   | 13789   13789   13478   | 234578  2348    2457    |
 *-----------------------------------------------------------------------------*


Loop for pairs [(13), (16), (36)]r5c46 => r4c2<>24

                                  ---------------------
                                 |                     |
(1)r9c2----(1)r9c5     (1)r6c8---      (6)r4c2*        |
 ||         ||          ||              ||             |
(1)r4c2*   (1)r1c5-----(1)r1c8         (6)r1c2----     |
 ||         ||          ||              ||        |    |
(1)r5c2    (1)r46c5    (1)r5c8      ---(6)r5c2    |    |
 |          |           |          |              |    |
  ----------.-----------           |   (6)r1c5----     |
            |                      |    ||             |
     (13)=(16)=(36)----------------.---(6)r46c5        |
          r5c46                    |    ||             |
            |                      |   (6)r8c5----     | 
  ----------.-----------           |              |    |
 |          |           |          |              |    |
(3)r5c2    (3)r46c5    (3)r5c8      ---(6)r5c8    |    |
 ||         ||          ||              ||        |    |
(3)r4c2*   (3)r9c5-----(3)r9c8         (6)r8c8----     |
 ||         ||          ||              ||             |
(3)r2c2----(3)r2c5     (3)r6c8---.-----(6)r6c8         |
                                 |                     |
                                  ---------------------

Tungsten Rod - present as diagram:

Code: Select all
*-----------------------------------------------------------------------------*
 | 34589   4568    34689   | 12356   123569  15689   | 24      1389    7       |
 | 3589    2       3789    | 4       13579   15789   | 1389    6       389     |
 | 1       4678    346789  | 2367    23679   6789    | 5       389     24      |
 |-------------------------+-------------------------+-------------------------|
 | 358     9       1378    | 13567   13567   2       | 1378    4       358     |
 | 2345    1457    12347   | 8       13457   157     | 6       13579   2359    |
 | 6       14578   123478  | 9       13457   157     | 12378   13578   2358    |
 |-------------------------+-------------------------+-------------------------|
 | 2489    1468    5       | 1267    12679   3       | 4789    789     4689    |
 | 49      3       1469    | 1567    8       15679   | 479     2       4569    |
 | 7       68      2689    | 256     2569    4       | 389     3589    1       |
 *-----------------------------------------------------------------------------*


(1)r4c45-(1=hp57)r56c6            => box 5: r4c45 & r56c5<>5 (edited)
 ||
(1)r4c3------(7)r4c3
 ||    |      ||
 ||    |     (7)r4c45-(7=hp15)r56c6
 ||    |      ||
 ||    |     (7)r4c7-(7)r8c7
 ||    |              ||
 ||    |             (7)r8c6-(7=hp15)r56c6
 ||    |              ||
 ||    |             (7)r8c4-(1)r8c4
 ||    |                      ||
 ||     ---------------------(1)r8c3
 ||                           ||
(1)r4c7------(7)r4c7         (1)r8c6-(1=hp57)r56c6
       |      ||
       |     (7)r4c45-(7=hp15)r56c6
       |      ||
       |     (7)r4c3-(7)r2c3
       |              ||
       |             (7)r2c6-(7=hp15)r56c6
       |              ||   
       |             (7)r2c5-(1)r2c5
       |                      ||
        ---------------------(1)r2c3
                              ||
                             (1)r2c6-(1=hp57)r56c6


Thanks,
ttt
Last edited by ttt on Sat Nov 08, 2008 12:40 am, edited 2 times in total.
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Postby champagne » Fri Nov 07, 2008 11:48 pm

Hi ttt,

Very efficent as usual.
I will analyze your TR diagram to see what kind of rule I can find to do as well as Allan.
For the time being, my solver as I'll show in a later post give alternative solutions not as nice as Allan loops.

Here after a list of puzzles proposed by tarek? First of that list was FM and number 6 is "Trompe l'oeil", the second puzzle not solved by my solver.

All puzzles in that iist have a 3 floors exit where the situation is locked.
Just for you to improve your skills.

champagne

Code: Select all
........5..8..79...6..1..4....1.2.7.4...7...3.7.6......3..2..6...5...8..9.......7#tarx0002
........7..1..9.8..3.6..5.9.9..25.......6....3..9...4...7....91.2.5..3..8........#tarx0003
........7..9.5.2..1....6.8....5..6...9.....3...64.2....8.6.......4.2.9..7......61#tarx0004
........6..5..8.9..3.4..7....491........8..4.5....42....1..9.5..6....4.37........#tarx0005
........2..1...7...3..5..9......6.4...3.4.8...4.5.9....9..6..3...2...1..7....3...#tarx0006
........8..3.9.4..6....7.1....5.97...3.....2...74........7....6..4.5.3..81.......#tarx0007
.....6.....1.2...3.3.8...7...6.....5.5.3..7..2....1.......9..4...5...98..9.4....7#tarx0008
........7..2..96..8...6...3....92.....46..5...1..54.....5.4.9...3.....7.1.......8#tarx0009
........9..1...6...5..7..4....4.7.8...3.8...5.8...2....78.2..5..39...1..6........#tarx0011
........6..5.3.7..2....8.1....9..8...5..8..4...87.3....1.3.......7.9.5..6.......2#tarx0013
..1.......5...6..16.7...........1..3...4.5.8..9..2..5...5..3..7....8..4..3.5..2..#tarx0014
.....9..8..7....1..36.1.........25....14.....6...9..3.......2...1...5..47...3.19.#tarx0016
........8.5.....71..7..89....5..1.9.3..2.........6.4....1..5..9.6.3.....29....5..#tarx0019
........5..7.3.4..1.....62......39...7..9..6...98.4....2......1..8.4.3..5....9...#tarx0020
..2.....5.1.......8.3..9.4.....6..3.3..98......4..3..7......2....53....14....6.8.#tarx0022
........2..6....3..7...815....19.....5..8......4..5.7...2....6..15..97..3.......5#tarx0023
........5..4.7.9..3....8.6....7..8...1.....9...84.2....6.8....3..2.4.7..5........#tarx0024
.....7.....6.2...9.3.9...1...7.....5.9.3..1..2...6.........8.4...5...83..8.4....1#tarx0025
........6..7...1...9..4..8....4.8.3.5...3...9.3...2....4..2..9...1......65.3..7..#tarx0027
........2..7..8.5.96....1.....4........58..6..3...6..7..8..4.7..2..6.9..1.......6#tarx0029
........7..4.6.5..8....9.1....6..9...4.....3...92.5....1.9.....9.2.5.4..7.......8#tarx0030
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Postby ttt » Sat Nov 08, 2008 2:10 am

Hi champagne,
Thanks for your list. Quickly test for #tarx0003 based on floor (178)r6c56 I found r6c2379<>8 but presenting it requires more time…:D
I’ll try with #tarx0002 later…

Thanks again,
ttt
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Postby champagne » Sat Nov 08, 2008 2:27 am

ttt wrote:Hi champagne,
Thanks for your list. Quickly test for #tarx0003 based on floor (178)r6c56 I found r6c2379<>8 but presenting it requires more time…:D
I’ll try with #tarx0002 later…

Thanks again,
ttt


My solver says you can eliminate in that puzzle

7: r24c1 r5c46 r6c7 r9c68
8: r1c356 r5c9 r6c239
and "extra floors candidates" in nodes 47 and 52

may be you have a small typing mistake in your post. 8r6c7 is not in my list. May be also my program has other bugs:D
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Postby ronk » Sat Nov 08, 2008 2:48 am

ttt wrote:Tungsten Rod - present as diagram:
Code: Select all
(1)r4c45-(1=hp57)r56c6*           => r4c56 & r56c5<>5
 ||
(1)r4c3------(7)r4c3
 ||    |      ||
 ||    |     (7)r4c45-(7=hp15)r56c6*
 ||    |      ||
 ||    |     (7)r4c7-(7)r8c7
 ||    |              ||
 ||    |             (7)r8c6-(7=hp15)r56c6*
 ||    |              ||
 ||    |             (7)r8c4-(1)r8c4
 ||    |                      ||
 ||     ---------------------(1)r8c3
 ||                           ||
(1)r4c7------(7)r4c7         (1)r8c6-(1=hp57)r56c6*
       |      ||
       |     (7)r4c45-(7=hp15)r56c6*
       |      ||
       |     (7)r4c3-(7)r2c3
       |              ||
       |             (7)r2c6-(7=hp15)r56c6*
       |              ||   
       |             (7)r2c5-(1)r2c5
       |                      ||
        ---------------------(1)r2c3
                              ||
                             (1)r2c6-(1=hp57)r56c6*

ttt, nice diagram, but I don't understand how the diagram justifies your listed eliminations ... => r4c56 & r56c5<>5.

Each "end node" of the net is either (7=hp15)r56c6 or (1=hp57)r56c6 (which I flagged with an asterisk above). This eliminates digit 5 candidates elsewhere in b5 and c6 ... specifically r4c4, r456c5, r128c6<>5.

And r56c6<>5 certainly can't be correct, did you perhaps mean r56c6=5:?:

[edit: Oops, I incorrectly read your elimination r56c5<>5 as r56c6<>5.]
Last edited by ronk on Sun Nov 09, 2008 3:02 am, edited 2 times in total.
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Postby champagne » Sat Nov 08, 2008 3:30 am

ronk wrote:This eliminates digit 5 candidates elsewhere in b5 and c6 ... specifically r4c4, r456c5, r128c6<>5.

And r56c6<>5 certainly can't be correct, did you perhaps mean r56c6=5:?:


Here is the list of eliminations found by my solver

5: r1c146 r2c6 r4c45 r5c159 r6c59 r8c6 r9c5
7: r3c36 r7c7
and node N25 for candidates "out floors".

Ths fits with ronk's list. One is in excess in ttt's list
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Postby ttt » Sat Nov 08, 2008 4:05 am

ronk wrote:how the diagram justifies your listed eliminations ... => r4c56 & r56c5<>5.

Each "end node" of the net is either (7=hp15)r56c6 or (1=hp57)r56c6 (which I flagged with an asterisk above). This eliminates digit 5 candidates elsewhere in b5 and c6 ... specifically r4c4, r456c5, r128c6<>5.

And r56c6<>5 certainly can't be correct, did you perhaps mean r56c6=5:?:

Correct : r4c45 & r56c5<>5
Yes, I only considered 5’s on box 5 and the rest SS does:D . Based on Allan’s first move I saw that any 1’s at row 4 then always pair (15)r56c6 or (57)r56c6.

champagne wrote:may be you have a small typing mistake in your post. 8r6c7 is not in my list. May be also my program has other bugs:D
For #tarx0003, I think that can eliminate r6c7=8 if we considerate UR(17)r68c56 that mean can’t pair (17)r6c56. I’ll present it later…

Thanks and have nice weekend…:D !
ttt
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Location: vietnam

per analysis

Postby champagne » Sat Nov 08, 2008 11:05 pm

As announced, I prepared a kind of academic study to show why Allan Model works and somehow where I face problems in the preliminary phase

I have to apologize but I’ll use freely Allan Findings, concentrating mostly on Permutations analysis ,

Allan Barker method starts by the search of sets groups bearing a capability to eliminate/assign candidates.

Set: any of rows, columns, boxes, cell/nodes not yet assigned.

The only rule applied by Allan is that a set has one and only one candidate valid. Only sets belonging to the group analyzed are considered. In that academic study, nothing prevents for example to validate two candidates in a Cell/Node if that node does nt belong to the sets group.

I revisited Allan search on a multi floors basis:
Floor: all sets and candidates of the same digit

The smallest combination active in FATA Morgana I include floors 1;3;6. Opening the thread, I reduced the map of candidates to that one


Code: Select all
 +   ..6+ ..6+ | 1.6+ 1.6+ 1.6+ | ...+ 1..+  -
.3.+ .3.+   -  | .3.+ .3.+  -   |  -     +   +
.3.+   -  ..6+ | 136+  -   136+ |  +     -  1..+
------------------------------------------------
1.3+ 136+ ..6+ | 136+ 136+  -   | .3.+   -  1.6+
 -   136+ ..6+ | 136   -   136  | .3.+ 136+  -
13.+  -   ..6+ |  -   136+  -   | .3.+ 136  1.6+
------------------------------------------------
1..+  -    +   | 136+  -   136+ | .3.+  -   ..6+
 +    +    -   |  -   ..6+ ..6+ |  -   ..6+ ..6+
 -   1..+  +   | 13.+ 13.+ 13.+ | .3.+ .3.+   +


Each ’+’ represents any candidates “out floors”.
Each ’-’ is a given.

In that map, we see very well the sets in columns.

Allan Barker first loop includes
16R1;3R2;136R5;6R8;13R9
136C2; 136C5; 136C8
136B5

In the previous map, all candidates not included in that lot will be replaced by ‘o’,

Code: Select all
 +   ..6+ ..6+ | 1.6+ 1.6+ 1.6+ | ...+ 1..+  -
.3.+ .3.+   -  | .3.+ .3.+  -   |  -     +   +
.o.+   -  ..o+ | ooo+  -   oo6+ |  +     -  o..+
------------------------------------------------
o.o+ 136+ ..o+ | 136+ 136+  -   | .o.+   -  o.o+
 -   136+ ..o+ | 136   -   136  | .o.+ 136+  -
oo.+  -   ..o+ |  -   136+  -   | .o.+ 136  o.o+
------------------------------------------------
o..+  -    +   | ooo+  -   ooo+ | .o.+  -   ..o+
 +    +    -   |  -   ..6+ ..6+ |  -   ..6+ ..6+
 -   1..+  +   | 13.+ 13.+ 13.+ | .3.+ .3.+   +


What is established in Allan Model (and checked by my solver) is that in that map, All valid permutations lead to one of the digits ‘136’ in N42.

Allan build has a “sets/link sets “ model to prove it in a nicer way, but we are sure we must find a kind of “forcing net” to check it. What we did already.

Let’s try it here following strictly the sets rule.:

I think the start will always be in the cell having no extra candidate (here N54; N56; N68).
As N54;N56 are linked in selected sets 136r5 and 136B5, it is our assumed start point;
We have then as in the former explanation:

^ means exclusive or
| means non exclusive or

1(n54 n56) => 1r1c5 ^1r9c5 => 1r4c2 | 1r6c8 and in similar ways
3(n54 n56)=> 3r4c2 | 3r6c8
6(n54 n56)=> 6r4c2 | 6r6c8

This is not enough to conclude with our limited group of sets, but taking any of the three possible combinations for n54;n56 (1&3 1&6 3&6), we quickly come to the conclusion that N42 is assigned.

Code: Select all
1&6 => 1r1c5;6r8c5 not valid in column 8
    => 6r1c5;1r9c5 not valid in column 2

(in fact 1&6 is not valid. This is not seen directly in that set group, but is well shown here. )

Code: Select all
3&6 => 3r2c5;6r2c5 not valid in column 2
    => 3r9c5;6r8c5 not valid in column 8
    => 3r2c5;6r8c5 then r4c2=3 in column 2
    => 3r9c5;6r1c5 then r4c2=6 in column 2


and similar way for 1&3

If you look in details in that solution, you’ll see that nearly all sets of the group have been used.

It’s not the case for N68, so we can skip it out of the group of sets.

My solver found that you can eliminate four sets of that group and still have the capacity to conclude.


My solver did not find up to now that group of sets. I had to force it. In place it found another group I’ ll show in a next post. This is for me a drawback to apply Allan second and most important step, the construction of a Sets Link Sets group.

The second remark is about the fact that 1&6 can not be a solution for N54 N56. This is something that come each time I work on that puzzle As a consequence, 3r5c46 is valid. This does not appear in the list of eliminations done out of that floors combination. As usual, there is room for improvement.

BTW, this floors analysis could be a basis for another ranking method.
champagne
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Postby champagne » Sat Nov 08, 2008 11:29 pm

ttt wrote:For #tarx0003, I think that can eliminate r6c7=8 if we considerate UR(17)r68c56 that mean can’t pair (17)r6c56. I’ll present it later…
Thanks and have nice weekend…:D !
ttt

Secret weapons out of the field of permutations are authorized:D
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Postby ttt » Sun Nov 09, 2008 6:58 am

tarx0003

Code: Select all
*-----------*
 |...|...|..7|
 |..1|..9|.8.|
 |.3.|6..|5.9|
 |---+---+---|
 |.9.|.25|...|
 |...|.6.|...|
 |3..|9..|.4.|
 |---+---+---|
 |..7|...|.91|
 |.2.|5..|3..|
 |8..|...|...|
 *-----------*
After SSTS
 *-----------------------------------------------------------------------------*
 | 24569   4568    245689  | 12348   13458   12348   | 1246    1236    7       |
 | 24567   4567    1       | 2347    3457    9       | 246     8       2346    |
 | 247     3       248     | 6       1478    12478   | 5       12      9       |
 |-------------------------+-------------------------+-------------------------|
 | 1467    9       468     | 13478   2       5       | 1678    1367    368     |
 | 12457   14578   2458    | 13478   6       13478   | 9       12357   2358    |
 | 3       15678   2568    | 9       178     178     | 12678   4       2568    |
 |-------------------------+-------------------------+-------------------------|
 | 456     456     7       | 2348    348     23468   | 2468    9       1       |
 | 1469    2       469     | 5       1478    14678   | 3       67      468     |
 | 8       146     3       | 1247    9       12467   | 2467    2567    2456    |
 *-----------------------------------------------------------------------------*


Present as diagram: => r6c2379<>8

Code: Select all
(1)r45c4-(1=hp78)r6c56
 ||
(1)r9c4----(1)r9c2
 ||    |    ||
 ||    |   (1)r6c2-(1=hp78)r6c56
 ||    |    ||
 ||    |   (1)r5c2-(7)r5c2
 ||    |            ||
 ||    |           (7)r6c2-(7=hp18)r6c56
 ||    |            ||
 ||    |           (7)r2c2-(7)r2c4
 ||    |                    ||
 ||     -------------------(7)r9c4                     
 ||                         ||
 ||                        (7)r45c4-(7=hp18)r6c56
 ||
(1)r1c4-(1)r1c7
         ||
        (1)r6c7-(1=hp78)r6c56
         ||
        (1)r4c7-(7)r4c7
                 ||
                (7)r6c7-(7=hp18)r6c56 
                 ||
                (7)r9c7--(7)r8c8=AUR(17)r68c56
                       |          ||
                       |         (8)r6c56
                       |          || 
                       |         (1)r8c1-(1)r9c2 
                       |                  ||
                       |                 (1)r6c2-(1=hp78)rr6c56
                       |                  ||
                       |                 (1)r5c2-(7)r5c2
                       |                          ||
                       |                         (7)r6c2-(7=hp18)r6c56
                       |                          || 
                       |                         (7)r2c2-(7)r2c4
                       |                                  ||
                        ---------------------------------(7)r9c4
                                                          ||
                                                         (7)r45c4-(7=hp18)r6c56 

Wow… not nice, but the effect is quite good for this puzzle:D

ttt
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Postby ttt » Mon Nov 10, 2008 8:40 am

Hi champagne,
I studied more for tarx0002 & tarx0006 with the same way as my first move for tarx0003 then see that:
- tarx0002: floor (589)r5c46 and UR(58)r57c46 => r5c238<>9
- tarx0006: floor (127)r5c46 and UR(12)r57c46 => r5c389<>7

I’m thinking how to present it better than above diagram:D

ttt
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Postby ttt » Mon Nov 10, 2008 10:17 pm

Attempt for Fata Morgana again:

Code: Select all
*-----------------------------------------------------------------------------*
 | 2458    2467    245678  | 126789  16789   1678    | 24589   1248    3       |
 | 2348    2347    1       | 23789   3789    5       | 6       248     249     |
 | 2358    9       2568    | 12368   4       1368    | 258     7       125     |
 |-------------------------+-------------------------+-------------------------|
 | 12348   12346   2468    | 13678   13678   9       | 2347    5       12467   |
 | 7       12346   2469    | 136     5       136     | 2349    12346   8       |
 | 1389    5       689     | 4       13678   2       | 379     136     1679    |
 |-------------------------+-------------------------+-------------------------|
 | 145     8       457     | 1367    2       13467   | 3457    9       4567    |
 | 249     247     3       | 5       6789    4678    | 1       2468    2467    |
 | 6       1247    24579   | 13789   13789   13478   | 234578  2348    2457    |
 *-----------------------------------------------------------------------------*

Move 1: Present as diagram => r5c278<>3

Code: Select all
(1)r46c5-(1=hp36)r5c46*
 ||
(1)r9c5-(1)r9c2
 ||      ||
 ||     (1)r5c2-(1=hp36)r5c46*
 ||      ||
 ||     (1)r4c2-(6)r4c2
 ||              ||
 ||             (6)r5c2-(6=hp13)r5c46* 
 ||              ||
 ||              ||     -----------------------------
 ||              ||    |                             |
 ||             (6)r1c2---(6)r3c3=AUR(16)r35c46      |
 ||                                ||                |
 ||                               (3)r5c46*          |
 ||                                ||                |
 ||                               (1)r3c9            |
 ||                                |                 |
 ||     ---------------------------                  |
 ||    |                                             |
(1)r1c5-----(1)r1c8                                  |
       |     ||                                      |
       |    (1)r5c8-(1=hp36)r5c46*                   |
       |     ||                                      |
       |    (1)r6c8-(6)r6c8                          |
       |             ||                              | 
       |            (6)r5c8-(6=hp13)r5c46*           |
       |             ||                              |
       |            (6)r8c8-(6)r8c5                  |
       |                     ||                      |
        --------------------(6)r1c5                  |
       |                     ||                      |
       |                    (6)r46c5-(6=hp13)r5c46*  |
       |                                             |
       |                                             |
        ---------------------------------------------


Move 2: Present as diagram => r5c238<>6

Code: Select all
(1)r46c5-(1=hp36)r5c46*
 ||
(1)r1c5-(1)r1c8
 ||      ||
 ||     (1)r5c8-(1=hp36)r5c46*
 ||      ||
 ||     (1)r6c8-(3)r6c8=(3)r9c8----(3)r7c7=AUR(13)r57c46     
 ||                            |            ||               
 ||                            |           (6)r5c46*         
 ||                            |            ||               
 ||                            |           (1)r7c1-----------------     
 ||                            |                                   |
 ||     -----------------------                                    |
 ||    |                                                           |
(1)r9c5---(3)r9c5=(3)r2c5-(3)r2c2=(3)r4c2-(1)r4c2                  |
       |                                   ||                      | 
        ----------------------------------(1)r9c2                  |
       |                                   ||                      |
       |                                  (1)r5c2-(1=hp16)r5c46*   |
       |                                                           |
        -----------------------------------------------------------

From here the SE rating down to ER9.0 (I don’t know SE rating for original puzzle) then it’s not too difficult to solve. The same way for tarx0002 - tarx0003 - tarx0006, I’m not check more and not sure for the rest:D

Edited: too many typos - especially for Move 1, hope not much more...

ttt
Last edited by ttt on Tue Nov 11, 2008 4:41 am, edited 1 time in total.
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Postby champagne » Mon Nov 10, 2008 11:49 pm

Hi ttt,

I had a look to the first of your last diagrams.
Nothing to object except a small typing mistake.

I am impressed by your use of AUR patterns.

congratulations

champagne
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Postby eleven » Tue Nov 11, 2008 6:36 am

Hm, i didnt quite get it. If (second diagram) the typo is, that (6)r6c56 should be (6)r5c46, i still cant see, how the case
(1)r1c5, (1)r6c8, (3)r9c8, (1)r7c1, (1)r4c2 is handled.
Sorry, i have no practice with these diagrams, i'm just guessing what it means.
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