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Eureka help

 
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ffred



Joined: 29 Oct 2012
Posts: 19
Location: Kent, Egland

PostPosted: Mon Oct 29, 2012 10:54 pm    Post subject: Eureka help Reply with quote

Hi. Several years ago I was persuaded to try this site & quickly got hooked. But I was very busy at both work and home & reluctantly gave up after a while. (I wish I'd joined then, and persevered.) Anyway, I've got more time now, so here goes.

I'd appreciate help with a question of terminology. The example's from a Menneske puzzle that I'm struggling with. It's a bit boring - I'll post one or two hopefully more interesting ones. (Menneskes seem to be out of fashion these days.)

You can sometimes spot a (strong) link by noting that all but one of a candidate's occurrences in a house are 'used up'. In this simple example, there are no other 6s in c2, c9 or box 9.
Code:

+-------+-------+-------+
| . . . | . . . | . . . |
| . 6 . | . . . | . . 6C|
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . 6D. | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . 6A|
| . . . | . . . | . . . |
| . 6 . | . . . | . 6B. |
+-------+-------+-------+


A <> 6 => B = C =6. Since these two see two of the three 6s in c2, D must be 6.
So we can say that 6r7c9 = r6c2.
This is just a link: maybe it be used in a chain that achieves something, maybe not.

Two questions.
1. What's this technique called?
2. Suggestions as to how to express in Eureka? You could say:
6A = B - r9c2 (a)
= C - r2c2 (b)
(a) and (b):- =6r2c6. But that's very clumsy looking.

Thanks in advance, Fred
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arkietech



Joined: 31 Jul 2008
Posts: 1723
Location: Northwest Arkansas USA

PostPosted: Tue Oct 30, 2012 8:33 am    Post subject: Re: Eureka help Reply with quote

ffred wrote:
Code:

+-------+-------+-------+
| . . . | . . . | . . . |
| . 6 . | . . . | . . 6C|
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . 6D. | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . 6A|
| . . . | . . . | . . . |
| . 6 . | . . . | . 6B. |
+-------+-------+-------+


A <6> B = C =6. Since these two see two of the three 6s in c2, D must be 6.
So we can say that 6r7c9 = r6c2.
This is just a link: maybe it be used in a chain that achieves something, maybe not.

Two questions.
1. What's this technique called?
2. Suggestions as to how to express in Eureka?


I would call it a skyscrapper.
6r2c9=r2c2-r9c2=6r9c8 => -6r7c9
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ffred



Joined: 29 Oct 2012
Posts: 19
Location: Kent, Egland

PostPosted: Tue Oct 30, 2012 9:01 am    Post subject: Reply with quote

Thanks Ted. Unfortunately, I didn't explain properly - my fault. The 6s in r2 & r9 aren't strongly linked. Perhaps I should just have put up the whole puzzle.

This is an atypical example. I've previously used this where the key action happens in a box. I'm away from home for a short while: when I get back I'll post one.

Fred
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ffred



Joined: 29 Oct 2012
Posts: 19
Location: Kent, Egland

PostPosted: Tue Oct 30, 2012 9:43 am    Post subject: Reply with quote

I guess I'm being silly. I didn't want to post the complete puzzle because my sheet is so scribbled over that I thought I'd wait until I got home & restart. But here it is, hopefully correct. (It may not look like it, but I've already done quite a few moves, with just 2 squares solved for my troubles.)
Code:

+------------------+----------------+-------------------+
| 8    129   1279  | 249  6    1479 | 123579 35   1239  |
| 3    1269  4     | 289  178  5    | 1279   1268 12689 |
| 2679 5     12679 | 289  3    1789 | 1279   1268 4     |
+------------------+----------------+-------------------+
| 46   3     68    | 4568 9    2    | 14     15   7     |
| 2479 249   5     | 348  1478 147  | 6      238  28    |
| 1    2468  2678  | 35   78   67   | 45     9    238   |
+------------------+----------------+-------------------+
| 269  7     2689  | 1    5    89   | 239    4    2369  |
| 5    1249  3     | 69   24   469  | 8      7    129   |
| 2469 12468 12689 | 7    248  3    | 129    126  5     |
+------------------+----------------+-------------------+

Play this puzzle online at the Daily Sudoku site

I think of it as a 'branched link' (still hoping that somebody can give the correct name) but, however you look at it, it's a fact that 6r7c9 = r6c2.

This does give a short chain:-
6r7c9 = r6c2- (6 = 728)r6c356 - (28 = 3)r6c9; r7c9 <> 3

PS: if anybody sees a good move, indeed any move, I'd be grateful!
Fred
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Tue Oct 30, 2012 2:24 pm    Post subject: Re: Eureka help Reply with quote

ffred wrote:
You can sometimes spot a (strong) link by noting that all but one of a candidate's occurrences in a house are 'used up'. In this simple example, there are no other 6s in c2, c9 or box 9.
Code:

+-------+-------+-------+
| . . . | . . . | . . . |
| . 6 . | . . . | . . 6C|
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . 6D. | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . 6A|
| . . . | . . . | . . . |
| . 6 . | . . . | . 6B. |
+-------+-------+-------+


A <> 6 => B = C =6. Since these two see two of the three 6s in c2, D must be 6.
So we can say that 6r7c9 = r6c2.
This is just a link: maybe it be used in a chain that achieves something, maybe not.

Two questions.
1. What's this technique called?
2. Suggestions as to how to express in Eureka?

Back in the dark ages of sudoku, turbot fish was a common pattern name. One of its five-sided forms has two non-adjacent weak links (sides). That leaves two adjacent strong links, sometimes called a strong corner, with the candidate at the strong corner being ultimately true.

However, your pattern has an extra candidate at r6c2, so this turbot fish may be said to be finned. In the normal sense of a finned fish, either the fin is true or the turbot fish is true. However, there is not a common exclusion for the two cases, so you end up with a derived strong inference (or link, if you prefer).

Notaton is a bit tricky. I'd write something like ...

(6)fin:r6c2 = turbotfish:{r7c9 = r9c8 - r9c2 = r2c2 - r2c9 = (6)r7c9} ==> (6)r6c2 = (6)r7c9 derived inference
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Tue Oct 30, 2012 3:33 pm    Post subject: Re: Eureka help Reply with quote

[Withdrawn: I was mistaken about the specifics of AJ's Type 3 Simple Coloring.]

Last edited by daj95376 on Thu Nov 01, 2012 3:31 pm; edited 1 time in total
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Tue Oct 30, 2012 7:42 pm    Post subject: Re: Eureka help Reply with quote

daj95376 wrote:

What you have is an example of Angus Johnson's third Coloring pattern. However, he didn't include it in his Simple Sudoku solver, so it's not considered part of the traditional Coloring options.

Have you ever seen the "3rd coloring type/pattern" before without an exclusion, without even a potential one?
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ffred



Joined: 29 Oct 2012
Posts: 19
Location: Kent, Egland

PostPosted: Tue Oct 30, 2012 8:39 pm    Post subject: Reply with quote

Many thanks. Well, I'm still a bit befogged, but it's given food for research. (You're talking concepts that are unknown to me. Well, I had heard of turbot fish but, perhaps wrongly, assumed that this was a redundant idea.)

Fred
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Tue Oct 30, 2012 10:13 pm    Post subject: Re: Eureka help Reply with quote

[Withdrawn: I was mistaken about the specifics of AJ's Type 3 Simple Coloring.]

Last edited by daj95376 on Thu Nov 01, 2012 3:31 pm; edited 1 time in total
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Tue Oct 30, 2012 11:19 pm    Post subject: Re: Eureka help Reply with quote

daj95376 wrote:
ronk wrote:
Have you ever seen the "3rd coloring type/pattern" before without an exclusion, without even a potential one?
To me, a "coloring pattern" is independent of whether or not it leads to an elimination. That's probably why Angus Johnson colors all relevant cells before identifying elimination cells. As for my solver, it's probably identified thousands of non-productive coloring patterns; but it didn't waste my time by listing them. Does that make them non-existent, not hardly!

Let me try a question then. Where on this digit 6 'grid' could a candidate have existed that would fallen prey to Type 3 coloring?
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keith



Joined: 19 Sep 2005
Posts: 3174
Location: near Detroit, Michigan, USA

PostPosted: Wed Oct 31, 2012 1:18 am    Post subject: Reply with quote

ffred:

From Sudopedia:

Single-digit Concept Diagrams

A number of solving techniques perform elimination based on the patterns for a particular digit, and hence called single-digit techniques. In order to highlight the concept without getting lost in the large number of candidates in a typical grid, the digit is usually generically referred to as X, and the community has also developed a kind of concept diagram. In such a diagram, each cell contains a symbol:

X
The digit X is a candidate in this cell. (It does not matter what other candidates this cell contains.)

- or /
The digit X is not a candidate in this cell.

. or no symbol
It does not matter whether this cell contains X as a candidate.

*
X can be eliminated from this cell.

Note that in such diagrams, - and * have different meanings from those seen in the pencilmark grid elimination diagrams. An example below:

Code:
.-------.-------.-------.
| X X X | * * * | * * * |
| - - - |       |       |
| - - - |       |       |
:------- ------- -------:
|       |       |       |
|       |       |       |
|       |       |       |
:------- ------- -------:
|       |       |       |
|       |       |       |
|       |       |       |
'-------'-------'-------'


This is the Pointing Triple technique, and it says that if the candidates for X in a box is confined to a row, then X can be eliminated from the cells in the row that are not in the box. (The logic is exactly the same with Pointing Pair.)

Some people choose to show such concept diagrams using an arbitrary digit instead of the symbol X. Usually, the digit 1 is used.

The fish-related techniques is a large class of single-digit techniques. Such single-digit concept diagrams have been further specialized to fish diagrams, by introducing a special symbol F for fins.

=============

So, your diagram might be
Code:
+-------+-------+-------+
| . / . | . . . | . . / |
| . 6 . | . . . | . . 6 |
| . / . | . . . | . . / |
+-------+-------+-------+
| . / . | . . . | . . / |
| . / . | . . . | . . / |
| . 6 . | . . . | . . / |
+-------+-------+-------+
| . / . | . . . | / / 6 |
| . / . | . . . | / / / |
| . 6 . | . . . | / 6 / |
+-------+-------+-------+


Like ronk, I am not seeing stars.
Keith Laughing
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Wed Oct 31, 2012 1:53 am    Post subject: Reply with quote

keith wrote:
Like ronk, I am not seeing stars.
Keith Laughing

Laughing Good one, took me a few seconds to get it though. Good write up too!
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Wed Oct 31, 2012 11:34 am    Post subject: Reply with quote

[Withdrawn: I was mistaken about the specifics of AJ's Type 3 Simple Coloring.]

Last edited by daj95376 on Thu Nov 01, 2012 3:30 pm; edited 1 time in total
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Wed Oct 31, 2012 2:13 pm    Post subject: Reply with quote

daj95376, I agree your latest illustration is an example of Type 3 coloring, but I don't see where you previously mentioned adding a strong link (6 in r4).
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Wed Oct 31, 2012 6:52 pm    Post subject: Reply with quote

[Withdrawn: I was mistaken about the specifics of AJ's Type 3 Simple Coloring.]

Last edited by daj95376 on Thu Nov 01, 2012 3:30 pm; edited 2 times in total
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ffred



Joined: 29 Oct 2012
Posts: 19
Location: Kent, Egland

PostPosted: Wed Oct 31, 2012 7:06 pm    Post subject: Reply with quote

Keith, thanks for the lesson. I should have known this (maybe did at the back of my mind).

Ronk, thanks for the turbot fish idea - very pretty - I'd never have thought of that. But I don't think it fits in with my general idea.

The only colouring I've ever tried was called multi-colouring (I think) & I wasn't very keen & didn't pursue it. I will look up Type 3 colouring, but meanwhile I'd be grateful if someone could tell me if the following (from memory) is another example of this kind of colouring. r3c2 is a naked pair. (I don't myself think of this as essentially a single-digit technique.)

Code:

+-------+-------+-------+
| . . . | . . . | / . . |
| . . . | . . . | / . . |
| . 28. | . . . | 2 . . |
+-------+-------+-------+
| . . . | . . . | / . . |
| . . . | . . . | / . . |
| . . . | . . . | / . . |
+-------+-------+-------+
| 2 2 2 | . . . | 2 . . |
| 2 2 / | . . . | / . . |
| / 2 / | . . . | / . . |
+-------+-------+-------+

r3c2 = 2 => r8c1 = 2 (the other 2s in b7 being seen by either r3c2 or r7c7)
So 8r3c2 = 2r8c1, perhaps useful as a link of a chain (as was the case), or not.
(Saying r3c2 = 2 => r8c1 = 2 would have been of no interest on its own.)
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Wed Oct 31, 2012 7:15 pm    Post subject: Reply with quote

ffred wrote:
Code:
+-------+-------+-------+
| . . . | . . . | / . . |
| . . . | . . . | / . . |
| . 28. | . . . | 2 . . |
+-------+-------+-------+
| . . . | . . . | / . . |
| . . . | . . . | / . . |
| . . . | . . . | / . . |
+-------+-------+-------+
| 2 2 2 | . . . | 2 . . |
| 2 2 / | . . . | / . . |
| / 2 / | . . . | / . . |
+-------+-------+-------+


You have an almost Empty Rectangle pattern constrained by [c7] and [b7]. It results in the strong inference: (2)r8c1 = (8)r3c2 .
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Thu Nov 01, 2012 12:24 am    Post subject: Reply with quote

ronk wrote:
daj95376, I agree your latest illustration is an example of Type 3 coloring, but I don't see where you previously mentioned adding a strong link (6 in r4).

daj95376, I found Angus Johnson's post from 2005 here. I had forgotten his "Type 3" was for simple coloring, which we don't have in this example. Perhaps it is X-coloring, but I can't check that out right now. Maybe later.
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Thu Nov 01, 2012 4:41 am    Post subject: Reply with quote

ronk wrote:
I found Angus Johnson's post from 2005 here. I had forgotten his "Type 3" was for simple coloring, which we don't have in this example. Perhaps it is X-coloring, but I can't check that out right now. Maybe later.

I agree that AJ's Type 3 Simple Coloring doesn't match ffred's grid. I was mistaken about the specifics of AJ's Type 3 Simple Coloring.
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