The New Sudoku Players' Forum

[champagne]

How can you ignore the other digit 6 candidates in c5? Did you mean b5?

I did not change the main point.

Whatever digits are occupying r46c5, r2c4 and r6c8 are occupied by the same digits.

Probe: each digit occupying r46c5 => same digit in one of the 2 cells.

This is the situation where 6r46c5 is true. Then, other candidates in column c5 are false.

In my first "probe", 6r46c5 had been split in 6r4c5 true and 6r6c5 true.

Here, 6r46c5 true is seen globally.

My split in 2 cases was not necessary. We just skip from an "almost" swordfish to an "almost" Jellyfish.

I don't see anything as small as a swordfish here, [edit: but it may be because I don't know what you mean by "almost" fish. For me, they're just finned fish, both sashimi and non-sashimi.]

Sorry, but my vocabulary in the fish field is extremely poor.

In my first "probe", both xr2c4 and xr8c6 false created a 3x4 closed deadly pattern. What I call "almost swordfish"

In that case, both 6r2c4 and 6r8c6 create a close 4x5 deadly pattern. What I intend to call an "almost Jellyfish".

But I can rally any existing name for such structures.

champagne

[Pat]

Once two of the four digits occupy r5c46, r5 is no longer an effective cover set for the remaining two starfish, which then have five base sets and four cover sets. Because these last two starfish cannot then exist, the two shared fin cells r2c4 and r8c6 must hold the remaining two digits.


I agree that "splitting the problem" is in all likelihood required.

a belated comment

i do like those 4 creatures

my phrasing would differ (as usual) --

T = { r2c4 , r5c4 , r5c6 , r8c6 }

here's my phrasing of ronk's observation (all 4 using the same T) --

• if 4 not in T then (4)c3467b5\r1347 -- impossible; conclusion: 4 is in T
• if 6 not in T then (6)c3467b5\r3469 -- impossible; conclusion: 6 is in T
• if 7 not in T then (7)c3467b5\r1467 -- impossible; conclusion: 7 is in T
• if 9 not in T then (9)c3467b5\r1469 -- impossible; conclusion: 9 is in T
combining those 4 conclusions:
4,6,7,9 are all in T
since T is only 4 cells, we get:
{ 4,6,7,9 } = T

[Allan Barker]

T = { r2c4 , r5c4 , r5c6 , r8c6 }

here's my phrasing of ronk's observation (all 4 using the same T) --

• if 4 not in T then (4)c3467b5\r1347 -- impossible; conclusion: 4 is in T
• if 6 not in T then (6)c3467b5\r3469 -- impossible; conclusion: 6 is in T
• if 7 not in T then (7)c3467b5\r1467 -- impossible; conclusion: 7 is in T
• if 9 not in T then (9)c3467b5\r1469 -- impossible; conclusion: 9 is in T
combining those 4 conclusions:
4,6,7,9 are all in T
since T is only 4 cells, we get:
{ 4,6,7,9 } = T

Ah, this is very clear. In laymen's terms I would say:

Each of 4 layers forms a strong inference set in T={ r2c4 , r5c4 , r5c6 , r8c6 } thus all elements in T must contain a truth, producing eliminations.

I saw several such eliminations in Golden Nugget, like this one, even though the puzzle is not symmetrical. This seems to be a reasonably recurrent phenomenon.

[ronk]

T = { r2c4 , r5c4 , r5c6 , r8c6 }

here's my phrasing of ronk's observation (all 4 using the same T) --

• if 4 not in T then (4)c3467b5\r1347 -- impossible; conclusion: 4 is in T
• if 6 not in T then (6)c3467b5\r3469 -- impossible; conclusion: 6 is in T
• if 7 not in T then (7)c3467b5\r1467 -- impossible; conclusion: 7 is in T
• if 9 not in T then (9)c3467b5\r1469 -- impossible; conclusion: 9 is in T
combining those 4 conclusions:
4,6,7,9 are all in T
since T is only 4 cells, we get:
{ 4,6,7,9 } = T

Very nice! That POV works equally well for these finned franken jellyfish based on Allan Barker's post here ... even though no single set covers both shared endo-fins. I say this because I think using r5 as both a base set and a cover set is still invalid.

Code: Select all

four overlapping finned franken jellyfish (at start of tarx0075)
                                      +--coversets
    |          |          |           |             |          |
    V          V          V           V             V          V
 .  .  . |  .  .  . |  .  .  .        .  .  . |  .  .  . |  .  .  .
 /  4  / | #4  4  / |  /  4  /        6  /  / | #6  6  / |  /  x  /
 .  .  . |  .  .  . |  .  .  .        .  .  . |  .  .  . |  .  .  .
---------+----------+----------      ---------+----------+----------
 .  .  . |  /  4  / |  .  .  .        .  .  . |  /  6  / |  .  .  .
 /  x  / | @4  / @4 |  /  4  /        6  /  / | @6  / @6 |  /  6  /
 .  .  . |  /  .  / |  .  .  .        .  .  . |  /  6  / |  .  .  .
---------+----------+----------      ---------+----------+----------
 .  .  . |  .  .  . |  .  .  .        .  .  . |  .  .  . |  .  .  .
 /  4  / |  /  4 #4 |  /  x  /        x  /  / |  /  6 #6 |  /  6  /
 .  .  . |  .  .  . |  .  .  .        .  .  . |  .  .  . |  .  .  .
(4)r258b5\c258 + fins (@ and #)      (6)r258b5\c158 + fins (@ and #)     
     

    |          |             |        |             |             |
    V          V             V        V             V             V
 .  .  . |  .  .  . |  .  .  .        .  .  . |  .  .  . |  .  .  .
 /  7  / | #7  7  / |  /  /  x        x  /  / | #9  9  / |  /  /  9
 .  .  . |  .  .  . |  .  .  .        .  .  . |  .  .  . |  .  .  .
---------+----------+----------      ---------+----------+----------
 .  .  . |  /  7  / |  .  .  .        .  .  . |  /  9  / |  .  .  .
 /  7  / | @7  / @7 |  /  /  7        9  /  / | @9  / @9 |  /  /  9
 .  .  . |  /  7  / |  .  .  .        .  .  . |  /  9  / |  .  .  .
---------+----------+----------      ---------+----------+----------
 .  .  . |  .  .  . |  .  .  .        .  .  . |  .  .  . |  .  .  .
 /  x  / |  /  7 #7 |  /  /  7        9  /  / |  /  9 #9 |  /  /  x
 .  .  . |  .  .  . |  .  .  .        .  .  . |  .  .  . |  .  .  .
(7)r258b5\c259 + fins (@ and #)      (9)r258b5\c159 + fins (@ and #)

[ttt]

Hi All,

Code: Select all

 *-----------*     Silver Plate
 |1..|...|..7|
 |.2.|4..|.6.|
 |..3|...|5..|
 |---+---+---|
 |.9.|.4.|...|
 |...|.62|.4.|
 |...|9..|8..|
 |---+---+---|
 |..5|...|..3|
 |.6.|2..|.8.|
 |7..|..1|...|
 *-----------*
 
 *-----------------------------------------------------------------------------*
 | 1       4(5)8   4689    |(35)68   23589   35689   | 2349    2(3)9   7       |
 | 589     2       789     | 4       135789  35789   | 139     6       189     |
 | 4689    4(7)8   3       |(17)68   12789   6789    | 5      (1)29    12489   |
 |-------------------------+-------------------------+-------------------------|
 | 23568   9       12678   |#(1357)8 4       3578    | 12367 @(1357)2  1256    |
 | 358   @(1357)8  178     |#(1357)8 6       2       | 1379    4       159     |
 | 23456  (1357)4  12467   | 9      (1357)   (357)   | 8      (1357)2  1256    |
 |-------------------------+-------------------------+-------------------------|
 | 2489   (1)48    5       | 6(7)8   789     46789   | 124679 (17)29   3       |
 | 349     6       149     | 2       3579    34579   | 1479    8       1459    |
 | 7      (3)48    2489    |(35)68   3589    1       | 2469    2(5)9   24569   |
 *-----------------------------------------------------------------------------*

The same for Silver Plate with (1357) & T(r5c2, r4c4, r5c4, r4c8) => r5c2<>8 & r4c8<>2
I found this before but can’t present as diagram then my question is: how to present it? As Allan’s …?
BTW, this form seems to apply for hard puzzles that contains “nearly SK loop”?

Thanks to all,

ttt

[ronk]

The same for Silver Plate with (1357) & T(r5c2, r4c4, r5c4, r4c8) => r5c2<>8 & r4c8<>2

Based on the overlapping finned jellyfish below, I believe the valid eliminations are r5c2<>8, r45c4<>8, r4c8<>2 and r4c6<>357. Does anyone see why?

Code: Select all

            +-- base sets (in addition to b5)                                             
    |       |             |              |       |             |                           
    V       V             V              V       V             V                           
 .  /  . |  /  .  . |  .  /  .        .  x  . |  3  .  . |  .  3  . <-- cover
 .  /  . |  /  .  . |  .  /  .        .  /  . |  /  .  . |  .  /  .     sets
 .  x  . |  1  .  . |  .  1  . <--    .  /  . |  /  .  . |  .  /  .
---------+----------+----------      ---------+----------+----------
 .  /  . | @1  /  x |  . #1  . <--    .  /  . | @3  /  3 |  . #3  . <--
 . #1  . | @1  /  / |  .  /  .        . #3  . | @3  /  / |  .  /  .   
 .  1  . |  /  1  x |  .  1  . <--    .  3  . |  /  3  3 |  .  3  . <--
---------+----------+----------      ---------+----------+----------
 .  1  . |  x  .  . |  .  1  . <--    .  /  . |  /  .  . |  .  /  .
 .  /  . |  /  .  . |  .  /  .        .  /  . |  /  .  . |  .  /  .
 .  /  . |  /  .  . |  .  /  .        .  3  . |  3  .  . |  .  x  . <--

 jellyfish:(1)c248b5\r3467 + fins     jellyfish:(3)c248b5\r1469 + fins
                               

 .  5  . |  5  .  . |  .  x  . <--    .  /  . |  /  .  . |  .  /  .
 .  /  . |  /  .  . |  .  /  .        .  /  . |  /  .  . |  .  /  .
 .  /  . |  /  .  . |  .  /  .        .  7  . |  7  .  . |  .  x  . <--
---------+----------+----------      ---------+----------+----------
 .  /  . | @5  /  5 |  . #5  . <--    .  /  . | @7  /  7 |  . #7  . <--   
 . #5  . | @5  /  / |  .  /  .        . #7  . | @7  /  / |  .  /  .   
 .  5  . |  /  5  5 |  .  5  . <--    .  7  . |  /  7  7 |  .  7  . <--
---------+----------+----------      ---------+----------+----------
 .  /  . |  .  .  . |  .  /  .        .  x  . |  7  .  . |  .  7  . <--
 .  /  . |  .  .  . |  .  /  .        .  /  . |  /  .  . |  .  /  .
 .  x  . |  5  .  . |  .  5  . <--    .  /  . |  /  .  . |  .  /  .

 jellyfish:(5)c248b5\r1469 + fins     jellyfish:(7)c248b5\r3467 + fins

For the symbol key, see a prior post in this thread


It might be wise to allow for the possibility that I'm wrong.

[ttt]

Based on the overlapping finned jellyfish below, I believe the valid eliminations are r5c2<>8, r45c4<>8, r4c8<>2 and r4c6<>357. Does anyone see why?

Code: Select all

            +-- base sets (in addition to b5)                                             
    |       |             |              |       |             |                           
    V       V             V              V       V             V                           
 .  /  . |  /  .  . |  .  /  .        .  x  . |  3  .  . |  .  3  . <-- cover
 .  /  . |  /  .  . |  .  /  .        .  /  . |  /  .  . |  .  /  .     sets
 .  x  . |  1  .  . |  .  1  . <--    .  /  . |  /  .  . |  .  /  .
---------+----------+----------      ---------+----------+----------
 .  /  . | @1  /  x |  . #1  . <--    .  /  . | @3  /  3 |  . #3  . <--
 . #1  . | @1  /  / |  .  /  .        . #3  . | @3  /  / |  .  /  .   
 .  1  . |  /  1  x |  .  1  . <--    .  3  . |  /  3  3 |  .  3  . <--
---------+----------+----------      ---------+----------+----------
 .  1  . |  x  .  . |  .  1  . <--    .  /  . |  /  .  . |  .  /  .
 .  /  . |  /  .  . |  .  /  .        .  /  . |  /  .  . |  .  /  .
 .  /  . |  /  .  . |  .  /  .        .  3  . |  3  .  . |  .  x  . <--

 jellyfish:(1)c248b5\r3467 + fins     jellyfish:(3)c248b5\r1469 + fins
                               

 .  5  . |  5  .  . |  .  x  . <--    .  /  . |  /  .  . |  .  /  .
 .  /  . |  /  .  . |  .  /  .        .  /  . |  /  .  . |  .  /  .
 .  /  . |  /  .  . |  .  /  .        .  7  . |  7  .  . |  .  x  . <--
---------+----------+----------      ---------+----------+----------
 .  /  . | @5  /  5 |  . #5  . <--    .  /  . | @7  /  7 |  . #7  . <--   
 . #5  . | @5  /  / |  .  /  .        . #7  . | @7  /  / |  .  /  .   
 .  5  . |  /  5  5 |  .  5  . <--    .  7  . |  /  7  7 |  .  7  . <--
---------+----------+----------      ---------+----------+----------
 .  /  . |  .  .  . |  .  /  .        .  x  . |  7  .  . |  .  7  . <--
 .  /  . |  .  .  . |  .  /  .        .  /  . |  /  .  . |  .  /  .
 .  x  . |  5  .  . |  .  5  . <--    .  /  . |  /  .  . |  .  /  .

 jellyfish:(5)c248b5\r1469 + fins     jellyfish:(7)c248b5\r3467 + fins

For the symbol key, see a prior post in this thread


It might be wise to allow for the possibility that I'm wrong.

Yes, I consider r4c6 but hesitated… I think that for cases 1, 3, 5, 7 at T(r5c2, r4c4, r5c4, r4c8) we have to fill one of 3, 5, 7 at r4c6 then the rest invalid => (edited: delete r45c4<>8, r4c6<>357) r5c2<>8, r4c8<>2
Edit: I don't see how r45c4<>8 & r4c6<>357?

ttt

[Allan Barker]

Silver Plate ttt initial rank 0 loop

ttt, very beautiful. I have redrawn your elimination from your pencil marks. Edit: Note that 6N56 are considered as base sets in the following diagrams.

Images 2D Image, 3D Image, 3D Stereo,
Stereo: Divide left/right images with A4 size paper (long way) between screen and eyes, focus to see 1 image.

Code: Select all

     Silver Plate - initial grid
     EPAA 47 Nodes, Raw Rank = 4 (linksets - sets)
     14 Sets = {1357c2 1357c4 1357c8 6n56}
     18 Links = {35r1 17r3 1357r6 17r7 35r9 5n2 4n8 1357b5}
     --> (4n8) => r4c8<>2, (5n2) => r5c2<>8

     3b5  3r1  3r6  3r9  4n8  1r7  1r6  1r3  1b5  5n2  7r3  7r6  7r7  7b5  5r9  5r6  5r1  5b5

3C4: 344==314=======394                                                                       
     354   |         |                                                                         
      |    |         |                                                                         
3C2:  |    |   362==392===========================352                                         
      |    |    |                                  |                                           
3C8:  |   318==368=======348                       |                                           
      |         |         |                        |                                           
1C2:  |         |         |   172==162============152                                         
      |         |         |    |    |              |                                           
1C8:  |         |        148==178==168==138        |                                           
      |         |         |         |    |         |                                           
1C4:  |         |         |         |   134==144   |                                           
      |         |         |         |        154   |                                           
      |         |         |         |         |    |                                           
6N5: 365B======365B=======|========165A======165A==|========765D======765D======565C======565C
      |         |         |                        |         |         |         |         |   
6N6: 366E======366E=======|========================|========766G======766G======566F======566F
                          |                        |         |         |         |         |   
7C8:                     748=======================|========768==778   |         |         |   
                          |                        |         |    |    |         |         |   
7C2:                      |                       752==732==762   |    |         |         |   
                          |                        |    |         |    |         |         |   
7C4:                      |                        |   734=======774==744        |         |   
                          |                        |                  754        |         |   
                          |                        |                             |         |   
5C2:                      |                       552===========================562==512   |   
                          |                                                      |    |    |   
5C8:                     548===============================================598==568   |    |   
                                                                            |         |    |   
5C4:                                                                       594=======514==544 
                                                                                          554                                                                                                     
=== base set
--- cover set
A, B, C, ... designates same candidate in 2 or more sets

[ronk]

Code: Select all

     Silver Plate - initial grid
     EPAA 47 Nodes, Raw Rank = 4 (linksets - sets)
     14 Sets = {1357c2 1357c4 1357c8 6n56}
     18 Links = {35r1 17r3 1357r6 17r7 35r9 5n2 4n8 1357b5}
     --> (4n8) => r4c8<>2, (5n2) => r5c2<>8


As you know, the fishy approach doesn't work with cell units in the base set. What does your "analyzer" say for the following

Code: Select all

     16 Sets = {1357c2 1357c4 1357c8 1357b5}
     20 Links = {35r1 17r3 17r7 35r9 1357r456}

Or maybe the cover set should be:

Code: Select all

     18 Links = {35r1 17r3 17r7 35r9 1357r46 5n24}

TIA, Ron

[Allan Barker]

As you know, the fishy approach doesn't work with cell units in the base set.

Considering the title of the thread, I should have expressly noted the cell base-sets, will fix.

What does your "analyzer" say for the following

Code: Select all

     16 Sets = {1357c2 1357c4 1357c8 1357b5}
     20 Links = {35r1 17r3 17r7 35r9 1357r456}

Or maybe the cover set should be:

Code: Select all

     18 Links = {35r1 17r3 17r7 35r9 1357r46 5n24}

TIA, Ron

I was working on this question just as I saw your post, so I will post what I had found so far, it is similar.
Before analyzing the above, I would like to ask why are there no cell cover sets in the top example? Is there an assumption about the fins seeing each vertically (in the n direction)?

1. T{r5c2, r4c4, r5c4, r4c8} does not form strong inference sets within each layer. Proof, (e.g., layer 5) the 4 base sets can be occupied at 5(r1c2, r9c4, r4c6, r6c8) leaving T = 0. Thus, the following 4 layer jellyfish produces no eliminations.

Code: Select all

EPAC 50 Nodes, Raw Rank = 4 (linksets - sets)
     16 Sets = {1357c2 1357c4 1357c8 1357b5}
     20 Links = {1r3467 3r1469 5r1469 7r3467} + T{5n2 45n4 4n8}
     -->  <no elimination>

2. T(r5c2, r4c4, r5c4, r4c8, r4c6) does form a 5 member strong inference set inside each layer, but this needs 5 layers to ensure that T = 1. If box set 8b5 is used as a 5th layer,then the following produces 2 eliminations:

Code: Select all

EPAD 53 Nodes, Raw Rank = 4 (linksets - sets)
     17 Sets = {1357c2 1357c4 1357c8 13578b5}
     21 Links = {1r3467 3r1469 5r1469 7r3467} + T{ 4n468 5n24}
     --> (4n8) => r4c8<>2, (5n2) => r5c2<>8

.
Edit: It is of course possible I have done something wrong or misunderstood a key point.

[champagne]

Hi all,

The rule I applied for tarx0075 works as well here.

Let's see ont the third floor using a partial view of Allan diagram

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3C4: 344==314=======394                                                                       
     354   |         |                                                                         
      |    |         |                                                                         
3C2:  |    |   362==392========352                                         
      |    |    |                                                                         
3C8:  |   318==368=======348                                                                 
      |         |                                                                   
6N5: 365B======365B =
      |         |           
6N6: 366E======366E 

Question "what if 3r6c56 true?"

then

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3C4: 314=======394                                                                       
      |         |                                                                         
      |         |                                                                         
3C2:  |       392========352                                         
      |                                                                               
3C8: 318============348             

A kind of degenerated 2x3 matrix.
again can not have both 348 and 352 false.

I did not check for others, but with the symmetry, it should give the same results;

Another point is "what after?" but I have to check several point before bringing comments on that.

champagne

[champagne]

Hi all,

Nice findings with theses starts, but I would like to share some experiences and perplexity.

In tarx0075, first assigned following Allan model is 2r6c2.
I introduced it as given and processed the puzzle in my standard way.
Results were worth than without that given. Likely this new given opened new doors, but did not simplify the main path.

I already made a comparison in another thread between clearings made int both ways and found small overlapping.

Same here; these 2 eliminations don't come in the first ten of my process.

Other experience, I tried (but I am far from ttt's skills) to merge in tarx0075 eliminations from Allan model, easy steps of my process and ttt's views on the "almost SK loop, nothing easy came.

It seems that both ways (Allan Model and AIC's nets) are fighting against completely different weaknesses of the puzzle.

If true, you have to make a significant part of the way within one logic before trying to merge results.

champagne

[champagne]

Based on the overlapping finned jellyfish below, I believe the valid eliminations are r5c2<>8, r45c4<>8, r4c8<>2 and r4c6<>357. Does anyone see why?

What says my solver based on Allan model :

using floors 1357 you can only eliminate 8r5c2 and 2r4c8


using floors 13457 your can eliminate 1r3c9 4r7c2 plus 8r5c2 and 2r4c8

using floors 13678 you can eliminate 1r6c9 7r3c6 8r5c2
and you have likely a new dual effect on r2c5 and r4c8


I don't see what you have , but this does not mean you are wrong.

champagne

[ronk]

What does your "analyzer" say for the following

Code: Select all

     16 Sets = {1357c2 1357c4 1357c8 1357b5}
     20 Links = {35r1 17r3 17r7 35r9 1357r456}

Before analyzing the above, I would like to ask why are there no cell cover sets in the top example? Is there an assumption about the fins seeing each vertically (in the n direction)?

[edit: Yes, that's the assumption, and I should have included them.]

2. T(r5c2, r4c4, r5c4, r4c8, r4c6) does form a 5 member strong inference set inside each layer, but this needs 5 layers to ensure that T = 1. If box set 8b5 is used as a 5th layer,then the following produces 2 eliminations:

Code: Select all

EPAD 53 Nodes, Raw Rank = 4 (linksets - sets)
     17 Sets = {1357c2 1357c4 1357c8 13578b5}
     21 Links = {1r3467 3r1469 5r1469 7r3467} + T{ 4n468 5n24}
     --> (4n8) => r4c8<>2, (5n2) => r5c2<>8

Thanks, that looks correct to me. However, given the inclusion of T{4n468 5n24} in the cover set, also including 1357r4 seems redundant. From the perspective of your analyzer, is it not redundant

[edit: Unfortunately, now with T{13578}{4n468 5n24}, elimination r5c2<>8 doesn't seem valid.]

don't see what you have , but this does not mean you are wrong.

My post is so wrong, it's not even laughable. Thanks to all for being tactful.

[Allan Barker]

2. T(r5c2, r4c4, r5c4, r4c8, r4c6) does form a 5 member strong inference set inside each layer, but this needs 5 layers to ensure that T = 1. If box set 8b5 is used as a 5th layer,then the following produces 2 eliminations:

Code: Select all

EPAD 53 Nodes, Raw Rank = 4 (linksets - sets)
     17 Sets = {1357c2 1357c4 1357c8 13578b5}
     21 Links = {1r3467 3r1469 5r1469 7r3467} + T{ 4n468 5n24}
     --> (4n8) => r4c8<>2, (5n2) => r5c2<>8

Thanks, that looks correct to me. However, given the inclusion of T{4n468 5n24} in the cover set, also including 1357r4 seems redundant. From the perspective of your analyzer, is it not redundant

Oops, yes, they are redundent. I have removed them below, both eliminations are there.
This now looks very much like your previous tarx0075 fish, same number of base/cover sets, only difference is this is an N=5 example. tarx0075 was N=4. The logic looks very clean.

Code: Select all

EPAD 53 Nodes, Raw Rank = 0 (linksets - sets)
     17 Sets = {1357c2 1357c4 1357c8 13578b5}
     17 Links = {35r1 17r3 1357r6 17r7 35r9 [color=red]4n468 5n24[/color]} Rank 0 in red.
     --> (4n8) => r4c8<>2, (5n2) => r5c2<>8

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3C4: 344B=354F======314=======394                                                         
      |    |         |         |                                                         
3C2:  |    |         |   362==392====================================================352 
      |    |         |    |                                                           |   
3C8:  |    |        318==368====================================================348   |   
      |    |              |                                                      |    |   
3B5: 344B=354F=346=======365                                                     |    |   
      |    |    |        366                                                     |    |
      |    |    |                                                                |    |   
5C4: 544C=554G==|==================514=======594                                 |    |   
      |    |    |                   |         |                                  |    |   
5C8:  |    |    |                   |   568==598================================548   |   
      |    |    |                   |    |                                       |    |   
5C2:  |    |    |                  512==562======================================|===552 
      |    |    |                        |                                       |    |   
5B5: 544C=554G=546======================565                                      |    |   
      |    |    |                       566                                      |    |   
8B5: 844==854==846                                                               |    |   
      |    |    |                                                                |    |   
7C4: 744D=754H==|=================================734=======774                  |    |   
      |    |    |                                  |         |                   |    |   
7C8:  |    |    |                                  |   768==778=================748   |   
      |    |    |                                  |    |                        |    |   
7C2:  |    |    |                                 732==762=======================|===752 
      |    |    |                                       |                        |    |   
7B5: 744D=754H=746=====================================765                       |    |   
      |    |                                           766                       |    |   
1C8:  |    |                                                     138==168==178==148   |   
      |    |                                                      |    |    |         |   
1C2:  |    |                                                      |   162==172=======152 
      |    |                                                      |    |                 
1C4: 144A=154E===================================================134   |                 
      |    |                                                           |                 
1B5: 144A=154E========================================================165