## Almost ER?

Advanced methods and approaches for solving Sudoku puzzles
Steve K wrote:Denis, further down the page is the TM definition. It is unclear what you think is undefined. Everything that needs to be defined is defined.

Steve K wrote:Tri-angular matrix definition:
nxn
Each row contains at least one truth
The top entry of each column is in conflict with each item below it.
For row i, items i+2 and greater are empty. This can be translated, in Booleans, as False.

Same remarks as for the PM's
[Two lines deleted. They were the result of a careless reading on my part.]

To repeat and extend one of my previous posts:
the definition is not given in factual terms, but in terms of weak and strong inference sets. The way these inference sets are related to facts on the grid is undefined. E.g. do these strong inference sets allow ALSs?

What is clear is that PMs and TMs, like AICs, are tools to combine "weak" and "strong" inferences.
In the case of AICs, "strong links" have received successively several interpretations in terms of factual patterns (bilocation, + bivalue, + ALSs). In the philosophy of AICs, one insists on the trivial alternance between "weak" and "strong" inferences and considers the nature of the patterns allowing "strong links" as secondary. Unfortunately, the 3 patterns mentioned above correspond to wildly different complexities and neglecting this amounts to cheating with a major aspect of chains.

PMs, TMs and AICs are general logical means of combining truth values. Unless the basic building blocks corresponding to these truth values are defined, PMs, TMs and AICs do not specify patterns on a grid. In this sense, yes, I repeat it, PMs and TMs are largely undefined. (And the same could be said of AICs if usage hadn't established bilocation + bivalue + ALSs as the supports for "strong links").
Last edited by denis_berthier on Tue Aug 12, 2008 10:14 am, edited 1 time in total.
denis_berthier
2010 Supporter

Posts: 1261
Joined: 19 June 2007
Location: Paris

Hi All,
A deduction by human !
On Sudoku Land, I’m not Inventors or Experts I’m a Worker . I always try to solve puzzles by myself (or can call by hand), I like that… I think that human can solve all puzzles if they have time-patient-smart (and for me need a bit lucky ). Below is a deduction by myself – human, I spent all this weekend for this that most of time for drawing. I found this deduction around 2 hours but drawing it 2 days… Later one maybe faster. I like to know SE rating for this deduction but my computer can’t count SE rating for this.

Code: Select all
`*-----------*    dml13 (on Ravel : Hardest Thread – first page) |..2|1..|7..| |.3.|.5.|...| |4..|..6|...| |---+---+---| |..1|9..|..2| |.8.|...|.3.| |7..|...|4..| |---+---+---| |...|..8|..6| |...|.3.|.5.| |9..|4..|1..| *-----------*After SSTS *-----------------------------------------------------------------------------* | 568     569     2       | 1       489     349     | 7       4689    34589   | | 168     3       6789    | 278     5       2479    | 2689    124689  1489    | | 4       1579    5789    | 2378    2789    6       | 23589   1289    13589   | |-------------------------+-------------------------+-------------------------| | 3       456     1       | 9       4678    457     | 568     678     2       | | 256     8       4569    | 2567    12467   12457   | 569     3       1579    | | 7       2569    569     | 23568   1268    1235    | 4       1689    1589    | |-------------------------+-------------------------+-------------------------| | 125     12457   3457    | 257     19      8       | 239     2479    6       | | 1268    12467   4678    | 267     3       19      | 289     5       4789    | | 9       2567    35678   | 4       267     257     | 1       278     378     | *-----------------------------------------------------------------------------*`

Elimination r3c2=5
Some explanation :
1- If r1c12=5 => r3c2<>5
2- If r1c12<>5 => r1c9=5 after some steps => r1c59<>8
2.1- If r1c1=8 : drawing No.1 => r3c2<>5
2.2- If r1c8=8 : drawing No.2 => r3c2<>5

Let A : (3)r1c9=(3)r1c6-(3)r3c4=(3)r6c4

Code: Select all
`Drawing No.1(5)r1c12 || ||      --------------------------(8)r1c9 ||     |                           || ||     |     -(8)r6c4=(8)r23c4 ---(8)r1c5  ||     |    |                      ||     -----------------------------------(8)r3c3 ||     |    |                      ||    |                                    ||  ||     |    |                      ||     -------------------------(8)r2c3    || ||     |    |                      ||    |                          ||        || ||     |    |                     (8)r1c1--(6)r1c1                  ||        ||  ||     |    |                               ||                      ||        || (5)r1c9 -- A -------------------------------(6)r6c4                  ||        ||        |    |                               ||                      ||        ||         |    |                       -------(6)r4c7                  ||        ||        |    |                      |        ||   ------------------(6)r2c3    ||         |     -(5)r6c4              |        ||  /                   ||        ||        |       ||           (Swf 6’s: r258c147) --(6)r5c3=(49)r5c3  ||        ||         |       ||                  |                       ||       ||        ||        ----- (5)r1c1/r56c9         |                       ||       ||        ||        |       ||                  |                       ||       ||        ||   (Xw 5’s r57c14)-(5)r5c37=(5)r4c7 ---------------(5)r4c2=(46)r4c2  ||        ||        |                                                   ||       ||        ||                ------------------------------------------(5)r1c2=(69)r1c2  ||        ||                                                            ||       ||        ||                                                       (XY wing)----(9)r2c3    ||                                                                |    ||        ||                                                                  |    (7)r2c3---(7)r3c3                                                                                 |              ||                                                                   ------------(9)r3c3                                                                                 ||                                                                                  (5)r3c3`

Code: Select all
`Drawing No.2(5)r1c12 || ||      ------------------------------------------------(5)r1c2 ||     |                                                 ||     ||     |                                    (6)r1c1 ----(6)r1c2   ||     |                                     ||     |    ||     ----------(9)r3c3 ||     |                                     ||     |    ||    /           || ||      ------------------------------------(5)r1c1 |  (9)r1c2--(9)r2c3    || ||     |                                     ||     |            ||        ||   ||      --------------------------(8)r1c9    ||      -----------(6)r2c3    || ||     |                           ||        ||                  ||        || (5)r1c9 -- A --(8)r6c4=(8)r23c4 --(8)r1c5    ||                  ||        ||        |    |                      ||        ||                  ||        ||        |     -(5)r6c4             (8)r1c8---(8)r1c1              ||        ||        |       ||                         |                      ||        ||        |       ||                          -----------(8)r9c8    ||        ||          |       ||                         |            ||        ||        ||         ----- (5)r1c1/r56c9                -(8)r46c8   ||        ||        ||                ||                            ||        ||        ||        ||          (Xw 5’s r57c14)-(5)r5c37=(5)r4c7---(8)r4c7    ||        ||        ||                                              ||        ||        ||        ||                                             (8)r6c9 --(8)r9c9    ||        ||                                                    |   ||        ||        ||                                                    |   (8)r9c3---(8)r2c3   ||                                                    |              ||       ||                                                    |             (7)r2c3--(7)r3c3                                                    |                       ||                                                     ----------------------(8)r3c3                                                                            ||                                                                             (5)r3c3`

Please correct me if something’s wrong or typos.
Thanks to all
ttt
ttt

Posts: 185
Joined: 20 October 2006
Location: vietnam

Hi ttt,
ttt wrote:
I like to know SE rating for this deduction but my computer can't count SE rating for this.

Maybe one way to rate the elimination is compare to other puzzles using sets. The partial logic in diagram 1 has 35 sets (strong & weak). The smallest elimination for 5r3c2 that my solver finds with similar logic is 45 sets, so you can rate your complete elimination as about 45 sets. From earlier work I have found:

Code: Select all
`Top 1465 #3 (once toughest)         Largest elim. ~41 sets.This elimination                                   45 sets.Easter Monster (recent toughest)    Largest elim. ~48 sets.`

I entered diagram 1 into my solver and get the same results. In terms of sets, it looks like this (click):

I always try to solve puzzles by myself (or can call by hand),..… I think that human can solve all puzzles if they have time-patient-smart (and for me need a bit lucky)

I think my luck is missing but, ... I wrote my solver by hand.
Allan Barker

Posts: 266
Joined: 20 February 2008

I'd already informed ttt in a PM
SE applied a Dynamic Contradiction Forcing Chain
If r3c2=5 => r8c1=6 and r8c1<>6. Tariff ER 10.7
Glyn

Posts: 357
Joined: 26 April 2007

Previous