Simple Coloring: A Missed Scenario ?

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Simple Coloring: A Missed Scenario ?

Postby daj95376 » Mon Jan 14, 2008 9:02 am

Earlier, Mike Barker posted this PM to discussion an NRCT Chains elimination in <9>. There are also several fish present to perform each of the five eliminations in <9>, but no fish performs more than one elimination. Even so, fish eliminations aren't what caught my attention.

Code: Select all
+--------------------------------------------------------------------+
|  4      16     136   |  2      136    9     |  5      7      8     |
|  138    5      2     |  18     13     7     |  4      6      9     |
|  7      9      68    |  48     46     5     |  1      23     23    |
|----------------------+----------------------+----------------------|
|  169    3      569   |  159    2      8     |  7      459    146   |
|  1289   16     568   |  159    7      4     |  39     2359   136   |
|  129    7      4     |  3      159    6     |  8      259    12    |
|----------------------+----------------------+----------------------|
|  5      2      39    |  7      49     1     |  6      8      34    |
|  16     8      16    |  459    459    3     |  2      49     7     |
|  39     4      7     |  6      8      2     |  39     1      5     |
+--------------------------------------------------------------------+

If you perform simple Blue/Green coloring on the strong links for <9> in this candidate grid, then you end up with [b5] being empty if Blue is true. Setting Green true (correctly) results in all five Blue cells being eliminated in one step.

Code: Select all
+-----------------------------------+
|  .  .  .  |  .  .  9  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  9  |
|  .  9  .  |  .  .  .  |  .  .  .  |
|-----------+-----------+-----------|
|  9  .  9B |  9  .  .  |  .  9  .  |
|  9  .  .  |  9  .  .  |  9B 9  .  |
|  9  .  .  |  .  9  .  |  .  9  .  |
|-----------+-----------+-----------|
|  .  .  9G |  .  9B .  |  .  .  .  |
|  .  .  .  |  9  9  .  |  .  9B .  |
|  9B .  .  |  .  .  .  |  9G .  .  |
+-----------------------------------+

As far as I know, this scenario -- checking to see if a color eliminates all of a candidate's values in a unit -- isn't part of simple coloring. Too bad!

Note: I have this nagging feeling that I mentioned this quite awhile back. If so, then please forgive the redundancy!
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Postby Sudtyro » Mon Jan 14, 2008 9:58 pm

daj,
That's an interesting observation...new to me, at least! I'd like to study that pattern a bit in comparison to those single-elimination fish that you mentioned. Are the fish non-finned and non-sashimi? Could you supply one or two as samples? (I'm still pretty useless at spotting most fish unless they're also fishy cycles.)
Thx!
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Re: Simple Coloring: A Missed Scenario ?

Postby ronk » Mon Jan 14, 2008 10:44 pm

daj95376 wrote:As far as I know, this scenario -- checking to see if a color eliminates all of a candidate's values in a unit -- isn't part of simple coloring. Too bad!

Angus Johnson never implemented this scenario AFAIK, but it was his third simple coloring "rule" here.
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Re: Simple Coloring: A Missed Scenario ?

Postby daj95376 » Tue Jan 15, 2008 1:23 am

ronk wrote:
daj95376 wrote:As far as I know, this scenario -- checking to see if a color eliminates all of a candidate's values in a unit -- isn't part of simple coloring. Too bad!

Angus Johnson never implemented this scenario AFAIK, but it was his third simple coloring "rule"

Thanks ronk:!: That's an excelent reference. Later in the thread, Angus Johnson gives credit to Ocean for the observation -- back in August 2005.

Now, I have to decide if I'm going to add the third scenario into my solver under Colors, or if it should have a separate designation.
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Postby daj95376 » Tue Jan 15, 2008 1:36 am

Sudtyro wrote:daj,
That's an interesting observation...new to me, at least! I'd like to study that pattern a bit in comparison to those single-elimination fish that you mentioned. Are the fish non-finned and non-sashimi? Could you supply one or two as samples? (I'm still pretty useless at spotting most fish unless they're also fishy cycles.)
Thx!

All of the fish are finned/sashimi. Those with A/B are more complex than those with f. Most are mutant. Those with F are Franken. Since my example is based on simple coloring, all you need to do is eliminate one Blue cell and the rest are subsequently eliminated. I suggest that you concentrate on the *** fish. They're also among the smallest fish.

Code: Select all
4-Fish r67b79\r9c358            A  202\130  <> 9  [r4c3]
4-Fish r67b79\r9c58b4           B  202\121  <> 9  [r4c3]
4-Fish r67c17\r49c5b6           B  220\211  <> 9  [r4c3]
4-Fish r67c17\r9c35b6           B  220\121  <> 9  [r4c3]
4-Fish r67c17\r9c5b46           A  220\112  <> 9  [r4c3]
4-Fish r67c1b9\r49c58           B  211\220  <> 9  [r4c3]
4-Fish r67c1b9\r9c358           B  211\130  <> 9  [r4c3]
4-Fish r67c1b9\r9c58b4          A  211\121  <> 9  [r4c3]
4-Fish r67c7b7\r9c35b6          A  211\121  <> 9  [r4c3]
4-Fish r67c7b7\r9c5b46          B  211\112  <> 9  [r4c3]
4-Fish r7c147\r459b8            f  130\301  <> 9  [r4c3]
4-Fish r7c147\r59b48            f  130\202  <> 9  [r4c3]
4-Fish r7c147\r59c3b8           f  130\211  <> 9  [r4c3]
4-Fish r7c17b5\r459c5           f  121\310  <> 9  [r4c3]
4-Fish r7c17b5\r59c35           f  121\220  <> 9  [r4c3]
4-Fish r7c17b5\r59c5b4          f  121\211  <> 9  [r4c3]
4-Fish r7c47b7\r459b8           B  121\301  <> 9  [r4c3]
4-Fish r7c47b7\r59c3b8          A  121\211  <> 9  [r4c3]
4-Fish r7c7b57\r459c5           B  112\310  <> 9  [r4c3]
4-Fish r7c7b57\r59c35           A  112\220  <> 9  [r4c3]

Code: Select all
4-Fish r69b89\r8c157            A  202\130  <> 9  [r5c7]
4-Fish r69b89\r8c15b6           B  202\121  <> 9  [r5c7]
4-Fish r69c48\r58c1b5           B  220\211  <> 9  [r5c7]
4-Fish r69c48\r8c17b5           B  220\121  <> 9  [r5c7]
4-Fish r69c48\r8c1b56           A  220\112  <> 9  [r5c7]
4-Fish r69c4b9\r8c17b5          A  211\121  <> 9  [r5c7]
4-Fish r69c4b9\r8c1b56          B  211\112  <> 9  [r5c7]
4-Fish r69c8b8\r58c15           B  211\220  <> 9  [r5c7]
4-Fish r69c8b8\r8c157           B  211\130  <> 9  [r5c7]
4-Fish r69c8b8\r8c15b6          A  211\121  <> 9  [r5c7]
4-Fish r9c348\r458b7            f  130\301  <> 9  [r5c7]
4-Fish r9c348\r48b67            f  130\202  <> 9  [r5c7]
4-Fish r9c348\r48c7b7           f  130\211  <> 9  [r5c7]
4-Fish r9c34b9\r458b7           B  121\301  <> 9  [r5c7]
4-Fish r9c34b9\r48c7b7          A  121\211  <> 9  [r5c7]
4-Fish r9c48b4\r458c1           f  121\310  <> 9  [r5c7]
4-Fish r9c48b4\r48c17           f  121\220  <> 9  [r5c7]
4-Fish r9c48b4\r48c1b6          f  121\211  <> 9  [r5c7]
4-Fish r9c4b49\r458c1           B  112\310  <> 9  [r5c7]
4-Fish r9c4b49\r48c17           A  112\220  <> 9  [r5c7]

Code: Select all
3-Fish r68b7\c158               fF 201\030  <> 9  [r7c5] ***
3-Fish r68b7\c18b8              fF 201\021  <> 9  [r7c5]
3-Fish r68b7\r7c18              f  201\120  <> 9  [r7c5]
3-Fish r68c3\c58b4              f  210\021  <> 9  [r7c5]
3-Fish r68c3\c8b48              f  210\012  <> 9  [r7c5]
3-Fish r68c3\r7c8b4             f  210\111  <> 9  [r7c5]

Code: Select all
3-Fish r69b8\c158               fF 201\030  <> 9  [r8c8] ***
3-Fish r69b8\c15b9              fF 201\021  <> 9  [r8c8]
3-Fish r69b8\r8c15              f  201\120  <> 9  [r8c8]
3-Fish r69c4\c18b5              f  210\021  <> 9  [r8c8]
3-Fish r69c4\c1b59              f  210\012  <> 9  [r8c8]
3-Fish r69c4\r8c1b5             f  210\111  <> 9  [r8c8]

Code: Select all
3-Fish r67b9\c158               fF 201\030  <> 9  [r9c1] ***
3-Fish r67b9\c58b7              fF 201\021  <> 9  [r9c1]
3-Fish r67b9\r9c58              f  201\120  <> 9  [r9c1]
3-Fish r67c7\c15b6              f  210\021  <> 9  [r9c1]
3-Fish r67c7\c5b67              f  210\012  <> 9  [r9c1]
3-Fish r67c7\r9c5b6             f  210\111  <> 9  [r9c1]
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Postby Sudtyro » Tue Jan 15, 2008 2:05 am

daj95376 wrote:All of the fish are finned/sashimi.

Thanks, daj! "Color" me impressed!:)
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Postby ronk » Tue Jan 15, 2008 3:18 am

daj95376 wrote:All of the fish are finned/sashimi. Those with A/B are more complex than those with f. Most are mutant. Those with F are Franken.
Code: Select all
4-Fish r67b79\r9c358            A  202\130  <> 9  [r4c3]
4-Fish r67b79\r9c58b4           B  202\121  <> 9  [r4c3]
4-Fish r67c17\r49c5b6           B  220\211  <> 9  [r4c3]
4-Fish r67c17\r9c35b6           B  220\121  <> 9  [r4c3]
4-Fish r67c17\r9c5b46           A  220\112  <> 9  [r4c3]
4-Fish r67c1b9\r49c58           B  211\220  <> 9  [r4c3]
4-Fish r67c1b9\r9c358           B  211\130  <> 9  [r4c3]
4-Fish r67c1b9\r9c58b4          A  211\121  <> 9  [r4c3]
4-Fish r67c7b7\r9c35b6          A  211\121  <> 9  [r4c3]
4-Fish r67c7b7\r9c5b46          B  211\112  <> 9  [r4c3]
4-Fish r7c147\r459b8            f  130\301  <> 9  [r4c3]
4-Fish r7c147\r59b48            f  130\202  <> 9  [r4c3]
4-Fish r7c147\r59c3b8           f  130\211  <> 9  [r4c3]
4-Fish r7c17b5\r459c5           f  121\310  <> 9  [r4c3]
4-Fish r7c17b5\r59c35           f  121\220  <> 9  [r4c3]
4-Fish r7c17b5\r59c5b4          f  121\211  <> 9  [r4c3]
4-Fish r7c47b7\r459b8           B  121\301  <> 9  [r4c3]
4-Fish r7c47b7\r59c3b8          A  121\211  <> 9  [r4c3]
4-Fish r7c7b57\r459c5           B  112\310  <> 9  [r4c3]
4-Fish r7c7b57\r59c35           A  112\220  <> 9  [r4c3]

My list of 4-fish for r4c3<>9 is a bit shorter. I think it has to do with a difference in our treatment of endo-fins.
Code: Select all
sashimi mutant 4-fish implying r4c3<>9

r67b79\r9c58b4 + c3
r67c17\r49c5b6 + c3b4
r67c17\r9c35b6 + b4
r67c17\r9c5b46 + c3b4
r67c1b9\r49c58 + c3b4
r67c1b9\r9c358 + b4
r67c1b9\r9c58b4 + c3b4
r67c7b7\r9c5b46 + c3
r7c147\r459b8 + c3b4
r7c147\r59c3b8 + r4b4
r7c147\r59b48 + r4c3
r7c17b5\r459c5 + c3b4
r7c17b5\r59c35 + r4b4
r7c17b5\r59c5b4 + r4c3
r7c47b7\r459b8 + c3
r7c7b57\r459c5 + c3
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Postby daj95376 » Tue Jan 15, 2008 6:29 am

ronk wrote:My list of 4-fish for r4c3<>9 is a bit shorter. I think it has to do with a difference in our treatment of endo-fins.

Maybe not. For 12 of the fish, I think our results are comparable -- even when an endo-fin cell exists.
(Below, I modified our output a bit.)

Here, I create two fish to your one because I'm not bound to include c3 and b4 in the cover set at the same time.

Code: Select all
r67b79\r9c58   + c3     A  202\130  <> 9  [r4c3]
r67b79\r9c58   + b4     B  202\121  <> 9  [r4c3]
r67b79\r9c58   + c3b4

r67c7b7\r9c5b6 + c3     A  211\121  <> 9  [r4c3]
r67c7b7\r9c5b6 + b4     B  211\112  <> 9  [r4c3]
r67c7b7\r9c5b6 + c3b4

Here, I create two fish to your one because I'm not bound to include c3 and r4 in the cover set at the same time.

Code: Select all
r7c47b7\r59b8  + c3     A  121\211  <> 9  [r4c3]
r7c47b7\r59b8  + r4     B  121\301  <> 9  [r4c3]
r7c47b7\r59b8  + c3r4

r7c7b57\r59c5  + c3     A  112\220  <> 9  [r4c3]
r7c7b57\r59c5  + r4     B  112\310  <> 9  [r4c3]
r7c7b57\r59c5  + c3r4

I did notice that having r7 and b7 in the base set resulted in your abbreviating '+ c3c3' to '+ c3' in the cover set.
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Postby tarek » Tue Jan 15, 2008 10:33 am

daj95376 wrote:Here, I create two fish to your one because I'm not bound to include c3 and r4 in the cover set at the same time.

Could you direct me to the post where you first explained this +1 method

I -for the moment- would be against it even if it's valid because the beauty of fish is in its n*n formation.

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Postby ronk » Tue Jan 15, 2008 3:01 pm

daj95376 wrote:I create two fish to your one because I'm not bound to include c3 and b4 in the cover set at the same time.

Code: Select all
r67b79\r9c58   + c3     A  202\130  <> 9  [r4c3]
r67b79\r9c58   + b4     B  202\121  <> 9  [r4c3]
r67b79\r9c58   + c3b4

I think the difference is more fundamental than that. For this fish ...
Code: Select all
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
---------+----------+----------
 9  . -9 |  9  .  . |  .  9  .
 9  .  . |  9  .  . |  9  9  .
*9  .  . |  . *9  . |  . *9  .
---------+----------+----------
 .  . @9 |  . *9  . |  .  .  .
 .  .  . |  9  9  . |  . *9  .
*9  .  . |  .  .  . | *9  .  .

sashimi mutant jellyfish r67b79\r9c58b4 + c3 (due to endo-fin r7c3)


... the only candidate of the base set in c3 is the endo-fin. Therefore c3 must be a fin sector (unit), and there is no benefit in looking at it as a cover sector. [edit2: Even if there were another candidate of the base set in c3, e.g. r6c3, c3 would still need to be a fin sector.]

daj95376 wrote:I did notice that having r7 and b7 in the base set resulted in your abbreviating '+ c3c3' to '+ c3' in the cover set.

As explained above, IMO c3 is never a cover sector ... so there was no "abbreviation."
Last edited by ronk on Wed Jan 16, 2008 8:27 am, edited 2 times in total.
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Postby Sudtyro » Tue Jan 15, 2008 3:04 pm

daj95376 wrote:
Code: Select all
3-Fish r68b7\c158               fF 201\030  <> 9  [r7c5] ***

Could you clarify the notation in just this one sample? Besides being lazy, I'm also intimidated by those 27 pages in the UFG!:(

I understand fish fundamentals of the base and cover sets. It would seem that (9)r7c3 and (9)r8c4 are in the base but not the cover. So, since they can both see the CEC, does that therefore require them to be the fins?

And, what does the "201\030" notation mean? Sorry to be slow on all this!
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Postby daj95376 » Tue Jan 15, 2008 6:31 pm

tarek wrote:
daj95376 wrote:Here, I create two fish to your one because I'm not bound to include c3 and r4 in the cover set at the same time.

Could you direct me to the post where you first explained this +1 method

I -for the moment- would be against it even if it's valid because the beauty of fish is in its n*n formation.

I'm not sure what you're requesting, but I'll do my best to answer what I think is your question.

In Obi-Wahn's Arithmetic thread ...

http://forum.enjoysudoku.com/viewtopic.php?p=41058#p41058

... he proposed eliminating fin cells by adding cover sectors; i.e., Nx(N+k) Fish. At some point, it was decided that the k additional cover sectors should be designated through a "+" notation.

Although I still use fin cells and NxN Fish notation, ronk (and maybe Pat) have been working with Nx(N+k) Fish.

In order to show commonality in the examples above, I placed the common sectors of our fish on the left and the distinctive sectors after a "+".

Since ronk and I have batted comparative notation around a lot in private messages, I was pretty sure that he would understand why I could create two fish when he could only create one. However, I forgot that others might find my examples difficult to follow. I'm sorry if that's true for you.
Last edited by daj95376 on Tue Jan 15, 2008 2:49 pm, edited 1 time in total.
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Postby tarek » Tue Jan 15, 2008 6:46 pm

Ah, thanx daj95376.

If it is that simple to show with your notation that the n*(n-1)+1 is actually 2 n*n fish (and demonstrate them), then I would favour that.

If 2 eliminations need both fish to act simultaneously the I would show that as one step containing a grouped fish (or a batch elimination). if the 2 eliminations can be broken into 1 elimination then 1 elimination then I would prefer 2 seperate steps.

This is a personal preference ....

if an elimination however cannot be explained without resorting to this notation [ N*(N-1)+1 or N*(N+K)] then that is a different issue all together.

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Postby daj95376 » Tue Jan 15, 2008 7:03 pm

tarek wrote:Ah, thanx daj95376.

If it is that simple to show with your notation that the n*(n-1)+1 is actually 2 n*n fish (and demonstrate them), then I would favour that.

If 2 eliminations need both fish to act simultaneously the I would show that as one step containing a grouped fish (or a batch elimination). if the 2 eliminations can be broken into 1 elimination then 1 elimination then I would prefer 2 seperate steps.

This is a personal preference ....

if an elimination however cannot be explained without resorting to this notation [ N*(N-1)+1 or N*(N+K)] then that is a different issue all together.

While I'm digesting your reply, let me say specifically what I was trying to show.

In each of the four examples above, an Nx(N-1) sub-Fish covers every one of the base set cells -- except two that directly see the elimination cell. The two base cells do not see each other, and the elimination cell is not yet covered.

If you use NxN Fish like I do, then you only need one more cover sector to include the elimination cell. This means that I have two choices for finned NxN Fish.

If you are using Nx(N+k) Fish, then you must use two cover sectors -- one for each remaining base cell. This means that there is only one Nx(N+1) Fish possible.
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Postby daj95376 » Tue Jan 15, 2008 8:53 pm

Sudtyro wrote:
daj95376 wrote:
Code: Select all
3-Fish r68b7\c158               fF 201\030  <> 9  [r7c5] ***

Could you clarify the notation in just this one sample? Besides being lazy, I'm also intimidated by those 27 pages in the UFG!:(

I understand fish fundamentals of the base and cover sets. It would seem that (9)r7c3 and (9)r8c4 are in the base but not the cover. So, since they can both see the CEC, does that therefore require them to be the fins?

And, what does the "201\030" notation mean? Sorry to be slow on all this!

Yes, you have correctly identified the two fin cells for the correct reason. I'm sorry about the extraneous "201\030" notation. I use it to help quickly select desirable fish from a list of alternate fish choices. It reads like this ...

Code: Select all
2 row    sectors in the base  set
0 column sectors in the base  set
1 box    sector  in the base  set
\
0 row    sectors in the cover set
3 column sectors in the cover set
0 box    sectors in the cover set

I often select the entry with the most zeroes.
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