The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |6..|..9|5..|
 |..5|6..|..7|
 |..9|51.|...|
 |---+---+---|
 |97.|...|.2.|
 |..3|...|9..|
 |.4.|...|.56|
 |---+---+---|
 |...|.72|4..|
 |4..|..6|3..|
 |..6|9..|..5|
 *-----------*


Play/Print this puzzle online

[Ngisa]

Code: Select all

+----------------------+----------------------+------------------------+
| 6        38       4  | 7        2       9   | 5        h3-1       18 |
| 138      138      5  | 6        34      348 | 2         9         7  |
| 7        2        9  | 5        1      f38  | 6        g34        48 |
+----------------------+----------------------+------------------------+
| 9        7        18 | 4        6       5   | 18        2         3  |
| 5        6        3  | 2        8       17  | 9         147       14 |
| 18       4        2  |d13       9      e137 | 178       5         6  |
+----------------------+----------------------+------------------------+
| 138      5        18 |c138      7        2  | 4         6         9  |
| 4        9        7  |b18       5        6  | 3        a18        2  |
| 2        138      6  | 9        34       134| 17        178       5  |
+----------------------+----------------------+------------------------+


(1=8)r8c8 - r8c4 = (8-3)r7c4 = r6c4 - r6c6 = r3c6 - r3c8 = (3)r1c8 => - 1 r1c8; stte

Clement

[Sudtyro2]

Code: Select all

+---------------+---------------+---------------+
| 6   d38  4    | 7   2    9    | 5    13  18   |
|c138 c138 5    | 6   34* b348* | 2    9   7    |
| 7    2   9    | 5   1    38   | 6    34  48   |
+---------------+---------------+---------------+
| 9    7   18   | 4   6    5    | 18   2   3    |
| 5    6   3    | 2   8    17   | 9    147 14   |
| 18   4   2    | 13  9    137  | 178  5   6    |
+---------------+---------------+---------------+
| 138  5   18   | 138 7    2    | 4    6   9    |
| 4    9   7    | 18  5    6    | 3   g18  2    |
| 2   e138 6    | 9   34* a134* | 7-1 f178 5    |
+---------------+---------------+---------------+

Almost UR(34)r29c56, using internals:
1r9c6==8r2c6 - r2c12 = r1c2 - r9c2 = r9c8 - (8=1)r8c8 => - 1r9c7; stte

SteveC

[Marty R.]

Code: Select all

┌─────────────────┬─────────────────┬─────────────────┐
│   6    38     4 │   7     2     9 │   5    13    18 │
│                 │                 │                 │
│ 138   138     5 │   6    34   348 │   2     9     7 │
│                 │                 │                 │
│   7     2     9 │   5     1    38 │   6    34    48 │
├─────────────────┼─────────────────┼─────────────────┤
│   9     7    18 │   4     6     5 │  18     2     3 │
│                 │                 │                 │
│   5     6     3 │   2     8    17 │   9   147    14 │
│                 │                 │                 │
│  18     4     2 │  13     9   137 │ 178     5     6 │
├─────────────────┼─────────────────┼─────────────────┤
│ 138     5    18 │ 138     7     2 │   4     6     9 │
│                 │                 │                 │
│   4     9     7 │  18     5     6 │   3    18     2 │
│                 │                 │                 │
│   2   138     6 │   9    34   134 │  17   178     5 │
└─────────────────┴─────────────────┴─────────────────┘

Kite (1) hingedb6
1r1c9=r4c3
1r1c9-(1=3)r1c8
1r4c3-(1=8)r7c3-r7c4=r8c4-(8=13)r81c8=> 3r1c8

[Marty R.]

Almost UR(34)r29c56, using internals

Can't we drop the "almost" and say it IS a UR, as in Type 3?

[Cenoman]

Code: Select all

 +-------------------+-------------------+-------------------+
 |  6    D38    4    |  7     2    9     |  5     13   C18   |
 |  138   138   5    |  6     34   348   |  2     9     7    |
 |  7     2     9    |  5     1    38    |  6     34    48   |
 +-------------------+-------------------+-------------------+
 |  9     7     18y  |  4     6    5     | A18x   2     3    |
 |  5     6     3    |  2     8    17*   |  9     147* B14w  |
 |  18    4     2    |  13    9    137*  |  178*  5     6    |
 +-------------------+-------------------+-------------------+
 |  138   5     18z  |  138   7    2     |  4     6     9    |
 |  4     9     7    |  18    5    6     |  3     18Y   2    |
 |  2     13-8  6    |  9     34  a134   | b17*  b178Z* 5    |
 +-------------------+-------------------+-------------------+

DP(17)r56c6,b6p57,r9c78 using externals (c6, b6, b9)
(1)r9c6 - (17=8)r9c78 (a, b)
(1)r4c7 - r5c9 = (1-8)r1c9 = (8)r1c2 (A, B, C, D)
(1)r5c9 - r4c7 = r4c3 - (1=8)r7c3 (w, x, y ,z)
(1-8)r8c8 = (8)r9c8 (Y, Z)
=> -8 r9c2; stte

[Sudtyro2]

Almost UR(34)r29c56, using internals

Can't we drop the "almost" and say it IS a UR, as in Type 3?

Good question, Marty!
What I've seen in the past is:
UR(34)r29c56
AUR(34)r29c56
DP(34)r29c56
ADP(34)r29c56
etc.

Seems like a DP or a UR wouldn't have any extra candidates.
Sorta like an ALS is really an "Almost" LS.

But, I'm game for the truly "proper" notation...

SteveC

[pjb]

Code: Select all

 6       38      4      | 7      2      9      | 5      13     18     
 138     138     5      | 6      34     348    | 2      9      7     
 7       2       9      | 5      1      38     | 6      34     48     
------------------------+----------------------+---------------------
 9       7      b18     | 4      6      5      |a18     2      3     
 5       6       3      | 2      8      17     | 9      47-1   14     
 18      4       2      | 13     9      137    | 178    5      6     
------------------------+----------------------+---------------------
 138     5      c18     |d138    7      2      | 4      6      9     
 4       9       7      |e18     5      6      | 3     f18     2     
 2       138     6      | 9      34     134    | 7-1    178    5     


(1=8)r4c7 - (8=1)r4c3 - (1=8)r7c3 - r7c4 = r8c4 - (8=1)r8c8 => -1 r5c8, r9c7; stte

Phil

[SpAce]

Almost UR(34)r29c56, using internals

Can't we drop the "almost" and say it IS a UR, as in Type 3?

Good question, Marty!
What I've seen in the past is:
UR(34)r29c56
AUR(34)r29c56
DP(34)r29c56
ADP(34)r29c56
etc.

Seems like a DP or a UR wouldn't have any extra candidates.
Sorta like an ALS is really an "Almost" LS.

But, I'm game for the truly "proper" notation...

Yes, that is a good question! I'd like to see a definitive answer to it as well. I think there's a good argument for both notations.

On the one hand, my intuition would be in line with SteveC's, as I would think of a Unique Rectangle as a realized Deadly Pattern. Thus, the only form of it that we can have in a valid grid and as part of chains is the almost form of it (unless it appears as a produced contradiction in a forcing chain). It's just like BUG+1 is an almost-BUG (and BUG+2 would be an almost-almost-BUG). Why wouldn't we use the same logic here? This case would be a UR+2 (or AAUR).

On the other hand, "Unique Rectangle" refers to several techniques that use almost-deadly-patterns (Type 1..N, Hidden, Extended...) which have their own elimination rules in order to avoid the deadly pattern. That's the argument for using just UR instead of AUR when we have such situations on the board. AUR would logically mean an almost-form of any such known UR-pattern.

So, UR can actually mean two different things, which makes it a bit confusing. If we think about its name, the latter definition above makes a bit more sense as "unique" does not imply "deadly". Maybe the UR is better thought of as NOT a deadly pattern per se, but a collection of solving patterns that depend on the avoidance of a particular deadly pattern. In that case, I think we need a name for the rectangular deadly pattern itself. How about simply: Deadly Rectangle (DR)? Then any UR could be described as an Almost-Deadly-Rectangle, or ADR, or more generally as an ADP -- and AUR would logically mean what it should.

[Cenoman]

In the list of uniqueness patterns you forgot the BUG and the BUG-lite...
How many "A" according to the configuration of the guardians: as many "A" as guardians. E.g. my deadly pattern (solution to this puzzle) would be an AAAADP ???
A BUG+10 would be AAAAAAAAAABUG ?

The solution retained for ALS's, AALS's, AAALS's should be avoided for DP's.

I will stick to UR, DP, BUG, ... This is unambiguous. If I find in my PM grid such a pattern which is not almost or almost-almost or ..., then I restart my search of a solution. I must have been wrong somewhere.

[pjb]

wrong puzzle

[SpAce]

In the list of uniqueness patterns you forgot the BUG and the BUG-lite...
How many "A" according to the configuration of the guardians: as many "A" as guardians. E.g. my deadly pattern (solution to this puzzle) would be an AAAADP ???
A BUG+10 would be AAAAAAAAAABUG ?

The solution retained for ALS's, AALS's, AAALS's should be avoided for DP's.

I will stick to UR, DP, BUG, ... This is unambiguous. If I find in my PM grid such a pattern which is not almost or almost-almost or ..., then I restart my search of a solution. I must have been wrong somewhere.

With all due respect, I think you're missing the point a bit. The definition of UR is NOT unambiguous, unlike the definition of BUG or any generic DP. BUG is a DP by definition, but UR is not necessarily. The real question is what definition of UR should be used within chaining logic. That is not unambiguous, as it can mean two different things as I tried to explain. Adopting DR to represent the DP-definition, and reserving UR to mean the various solving patterns, would remove the ambiguity. Then, one could say DR+1 and it would clearly translate into UR Type 1, for example. UR+1 or AUR don't have unambiguous meanings, because UR itself doesn't.

You can have a UR on a valid grid but you can't have a BUG or any other DP except in their almost-forms! That's a huge difference, I think. I'd prefer to have a way to make URs work like other DPs, but it's not possible with the current nomenclature without ambiguity (unless you stick to using the generic DP to refer to them, which is less informative). Or... perhaps the definition of UR is already unambiguous but some of us have gotten confused along the way. I don't know.

PS. BUG+1 is an almost-BUG by definition, and BUG+2 is almost-almost-BUG. Still, I don't see anyone suggesting they should be called ABUG or AABUG, thank goodness. I don't know where you got that. In fact, I don't think the A-prefix or the almost-term should be used for DP patterns. It's clearer if it's reserved for almost- elimination patterns (not just ALSs, though -- I think almost-fishes, almost-AICs, and yes, almost-URs with the right definition, are useful concepts).

[Cenoman]

http://sudopedia.enjoysudoku.com/Deadly_Pattern.html

and

http://forum.enjoysudoku.com/forming-mugs-from-bug-lite-composites-t3210-60.html

Last message from Cenoman in this thread.

[SpAce]

(two links without comments)

Sorry, but I don't think anything behing those links invalidates my point. Why don't you try to argue your point? I respect your opinions, and I'm quite capable of conceding when demonstrably wrong, but I'm equally incapable of it when not shown where and why I'm wrong (or unless I figure it out myself). In this case I still stand by my original points: the definition of UR is ambiguous and therefore so is the definition of AUR. I also think the pattern in SteveC's solution is an AUR by any definition, as it's not a complete UR pattern:

Can't we drop the "almost" and say it IS a UR, as in Type 3?

Is it? It has partially the pattern of a UR Type 3, namely the rectangle itself, but it lacks the other components of a locked set needed for eliminations. Therefore I see it as an almost-UR (Type 3 or Type 1, at least), because it's incapable of doing anything by itself.

About the definitions themselves, let's look at what Sudopedia says about the UR:

A Unique Rectangle is a Deadly Pattern ... The name is not well chosen. The pattern causes the puzzle to have at least 2 solutions, so a better name would be non-unique rectangle.

http://sudopedia.enjoysudoku.com/Unique_Rectangle.html

It's clear that Sudopedia treats the UR as a DP (not almost-DP), which means that by that definition any pattern that includes such a pattern is an almost-UR. Hodoku uses the same definition (refers to Sudopedia, in fact). However, that is not the definition everyone else uses. In fact, it's pretty stupid if you think about it. If the UR were a DP itself, then pattern names like UR Type 1 etc. should logically mean different kinds of DP patterns. That's not the case. The DP is the same in all URs -- it's the extra parts which make it an almost-DP that differ. Therefore UR-patterns are almost-DPs. We have a clear source of confusion and ambiguity here.

Here I found a definition of AUR (agreeing with my preferred one, I think) and its use in chains:

Almost Unique Rectangle (AUR): a set of four cells populated in such a way that if one or two of them does not have a specific candidate 'x', then those four cells form a unique rectangle.

http://forum.enjoysudoku.com/almost-unique-rectangles-description-and-use-in-nice-loops-t2751.html

If I understand that correctly, it does not use the Sudopedia definition of UR. More of the same here:

Some Almost Unique Rectangles and Almost Almost Unique Rectangles allow some interesting aplications of Almost Nice Loops.

http://forum.enjoysudoku.com/almost-nice-loops-t3681.html

Here I interpret Leren's use of UR to mean the Sudopedia definition (UR=DP):

Just to make the question more concrete consider a puzzle with a 4 cell UR plus one guard digit (that prevents the UR from being exposed).

http://forum.enjoysudoku.com/uniqueness-question-t32588.html

Unambiguous? Really?

[Sudtyro2]

We have a clear source of confusion and ambiguity here.

On this Forum, a quick search of the AUR term as used by any author extends back to 2006 and totals 13 pages of hits. Of those, my own use extends back to 2015. As far as I know, there have been no objections to the "A" in AUR meaning "Almost." Yet, for some unknown reason, in my own posting above, I elected to explicitly write the AUR term as "Almost UR". Huge mistake!!

SteveC