- Code: Select all
*-----------*
|4.2|8..|7.9|
|.91|...|68.|
|78.|...|.21|
|---+---+---|
|...|.1.|..5|
|...|372|...|
|2..|.4.|...|
|---+---+---|
|65.|...|.92|
|.27|...|83.|
|9.8|..6|5.7|
*-----------*
Play/Print this puzzle online
*-----------*
|4.2|8..|7.9|
|.91|...|68.|
|78.|...|.21|
|---+---+---|
|...|.1.|..5|
|...|372|...|
|2..|.4.|...|
|---+---+---|
|65.|...|.92|
|.27|...|83.|
|9.8|..6|5.7|
*-----------*
*--------------------------------------------------------------------------------*
| 4 36 2 | 8 36 1 | 7 5 9 |
|a35 9 1 |b27 a235 3457 | 6 8 a34 |
| 7 8 356 | 459 3569 3459 | 3-4 2 1 |
|--------------------------+--------------------------+--------------------------|
| 38 3467 3469 | 69 1 89 | 2 467 5 |
| 58 146 4569 | 3 7 2 | 149 146 48 |
| 2 167 69 | 569 4 589 | 139 167 38 |
|--------------------------+--------------------------+--------------------------|
| 6 5 34 |c17 8 37 |c14 9 2 |
| 1 2 7 | 459 59 459 | 8 3 6 |
| 9 34 8 | 12 23 6 | 5 14 7 |
*--------------------------------------------------------------------------------*
*--------------------------------------------------------------------------------*
| 4 36 2 | 8 36 1 | 7 5 9 |
| 35 9 1 | 27 235 3457 | 6 8 34 |
| 7 8 356 | 459 3569 459-3 |a34 2 1 |
|--------------------------+--------------------------+--------------------------|
| 38 3467 3469 | 69 1 89 | 2 467 5 |
| 58 146 4569 | 3 7 2 | 149 146 48 |
| 2 167 69 | 569 4 589 | 139 167 38 |
|--------------------------+--------------------------+--------------------------|
| 6 5 c34 | 17 8 d37 |b14 9 2 |
| 1 2 7 | 459 59 459 | 8 3 6 |
| 9 34 8 | 12 23 6 | 5 14 7 |
*--------------------------------------------------------------------------------*
+--------------+---------------+------------+
| 4 36 2 | 8 36 1 | 7 5 9 |
| 35 9 1 | 27 235 3457 | 6 8 34 |
| 7 8 356 | 459 3569 3459 | 34 2 1 |
+--------------+---------------+------------+
| 38 3467 3469 | 69 1 89 | 2 467 5 |
| 58 146 4569 | 3 7 2 | 149 146 48 |
| 2 167 69 | 569 4 589 | 139 167 38 |
+--------------+---------------+------------+
| 6 5 34 | 17 8 37 | 14 9 2 |
| 1 2 7 | 459 59 459 | 8 3 6 |
| 9 34 8 | 12 23 6 | 5 14 7 |
+--------------+---------------+------------+
Marty R. wrote:
- Code: Select all
+--------------+---------------+------------+
| 4 36 2 | 8 36 1 | 7 5 9 |
| 35 9 1 | 27 235 3457 | 6 8 34 |
| 7 8 356 | 459 3569 3459 | 34 2 1 |
+--------------+---------------+------------+
| 38 3467 3469 | 69 1 89 | 2 467 5 |
| 58 146 4569 | 3 7 2 | 149 146 48 |
| 2 167 69 | 569 4 589 | 139 167 38 |
+--------------+---------------+------------+
| 6 5 34 | 17 8 37 | 14 9 2 |
| 1 2 7 | 459 59 459 | 8 3 6 |
| 9 34 8 | 12 23 6 | 5 14 7 |
+--------------+---------------+------------+
Play this puzzle online at the Daily Sudoku site
Same as leren's first, but with a longer path.
(4=352)r2c195-(2=3)r9c5-(3=7)r7c6-(7=1)r7c4-(1=4)r7c7=>r3c7<>4
Marty R. wrote:Marty R. wrote:
- Code: Select all
+--------------+---------------+------------+
| 4 36 2 | 8 36 1 | 7 5 9 |
| 35 9 1 | 27 235 3457 | 6 8 34 |
| 7 8 356 | 459 3569 3459 | 34 2 1 |
+--------------+---------------+------------+
| 38 3467 3469 | 69 1 89 | 2 467 5 |
| 58 146 4569 | 3 7 2 | 149 146 48 |
| 2 167 69 | 569 4 589 | 139 167 38 |
+--------------+---------------+------------+
| 6 5 34 | 17 8 37 | 14 9 2 |
| 1 2 7 | 459 59 459 | 8 3 6 |
| 9 34 8 | 12 23 6 | 5 14 7 |
+--------------+---------------+------------+
Play this puzzle online at the Daily Sudoku site
Same as leren's first, but with a longer path.
(4=352)r2c195-(2=3)r9c5-(3=7)r7c6-(7=1)r7c4-(1=4)r7c7=>r3c7<>4
Just a quick notation question about the first term. Would (435=2) be any more or less correct than the (4=352) that I used?
Marty R. wrote:Just a quick notation question about the first term. Would (435=2) be any more or less correct than the (4=352) that I used?Marty R. wrote:Same as leren's first, but with a longer path.
(4=352)r2c195-(2=3)r9c5-(3=7)r7c6-(7=1)r7c4-(1=4)r7c7=>r3c7<>4
Marty R. wrote:Marty R. wrote:
- Code: Select all
+--------------+---------------+------------+
| 4 36 2 | 8 36 1 | 7 5 9 |
| 35 9 1 | 27 235 3457 | 6 8 34 |
| 7 8 356 | 459 3569 3459 | 34 2 1 |
+--------------+---------------+------------+
| 38 3467 3469 | 69 1 89 | 2 467 5 |
| 58 146 4569 | 3 7 2 | 149 146 48 |
| 2 167 69 | 569 4 589 | 139 167 38 |
+--------------+---------------+------------+
| 6 5 34 | 17 8 37 | 14 9 2 |
| 1 2 7 | 459 59 459 | 8 3 6 |
| 9 34 8 | 12 23 6 | 5 14 7 |
+--------------+---------------+------------+
Same as leren's first, but with a longer path.
(4=352)r2c195-(2=3)r9c5-(3=7)r7c6-(7=1)r7c4-(1=4)r7c7=>r3c7<>4
Just a quick notation question about the first term. Would (435=2) be any more or less correct than the (4=352) that I used?
MartyR wrote:Just a quick notation question about the first term. Would (435=2) be any more or less correct than the (4=352) that I used?
Marty R. wrote:Marty R. wrote:
- Code: Select all
+--------------+---------------+------------+
| 4 36 2 | 8 36 1 | 7 5 9 |
| 35 9 1 | 27 235 3457 | 6 8 34 |
| 7 8 356 | 459 3569 3459 | 34 2 1 |
+--------------+---------------+------------+
| 38 3467 3469 | 69 1 89 | 2 467 5 |
| 58 146 4569 | 3 7 2 | 149 146 48 |
| 2 167 69 | 569 4 589 | 139 167 38 |
+--------------+---------------+------------+
| 6 5 34 | 17 8 37 | 14 9 2 |
| 1 2 7 | 459 59 459 | 8 3 6 |
| 9 34 8 | 12 23 6 | 5 14 7 |
+--------------+---------------+------------+
Play this puzzle online at the Daily Sudoku site
Same as leren's first, but with a longer path.
(4=352)r2c195-(2=3)r9c5-(3=7)r7c6-(7=1)r7c4-(1=4)r7c7=>r3c7<>4
Just a quick notation question about the first term. Would (435=2) be any more or less correct than the (4=352) that I used?
As others have said, the single and the tuple can be written either way round in the ANS (or AHS) expression. For checking purposes, I personally prefer the digits in the tuple to be in ascending order.
David P Bird wrote:A Forcing Chain assumes a starting node to be true or false and looks for a contradiction.
An AIC observes that two strongly linked nodes must hold at least one truth, and without assuming anything, looks for candidates that can't be true as a result.
From a practical viewpoint AICs are generally more productive. Unlike for Forcing Chains, once AIC segments are found, they can be re-used freely as they don't depend on any assumption (or guess as some would say). The solutions to multiple step puzzles often demonstrate this.
Jeff wrote:Implication Stream - a sequence of nodes and links where strong or weak inferences are made from one node to the other(s) unidirectionally from left to right. (Refer definitions for "node", "link", "strong inference" and "weak inferences" below)
Forcing Chain - a chain that has 2 or more implication streams that start from one node and end in another node where the outcomes of inferences merge from the 2 implication streams. In a forcing chain, a node can only infer the next successive node downstream.
Forcing Net - same as a forcing chain, except that in a forcing net, a node could infer 2 or more nodes downstream. Such inference is regarded as a multiple inference. (Refer definition of "multiple inference" below)
Jeff wrote:Error Net or SIN (Single Implication Network) - a network with one implication stream that starts with a candidate selected in one node and propagates with or without multiple inferences until a contradiction is revealed. Due to this contradiction, such as 'empty cell', 'one digit appears 2 times in a unit' and 'no place for a digit in a unit', it can be concluded that the candidate selected at the start is invalid. This is also the principle of a "backtest" (Refer definition of a backtest below).
daj95376 wrote:When Jeff wrote his thread on Forcing Chains, he included numerous definitions and scenarios. Among his definitions are:Jeff wrote:Implication Stream - a sequence of nodes and links where strong or weak inferences are made from one node to the other(s) unidirectionally from left to right. (Refer definitions for "node", "link", "strong inference" and "weak inferences" below)
Forcing Chain - a chain that has 2 or more implication streams that start from one node and end in another node where the outcomes of inferences merge from the 2 implication streams. In a forcing chain, a node can only infer the next successive node downstream.
Forcing Net - same as a forcing chain, except that in a forcing net, a node could infer 2 or more nodes downstream. Such inference is regarded as a multiple inference. (Refer definition of "multiple inference" below)
These definitions seem to match eleven's comments above. However, Jeff also includes:Jeff wrote:Error Net or SIN (Single Implication Network) - a network with one implication stream that starts with a candidate selected in one node and propagates with or without multiple inferences until a contradiction is revealed. Due to this contradiction, such as 'empty cell', 'one digit appears 2 times in a unit' and 'no place for a digit in a unit', it can be concluded that the candidate selected at the start is invalid. This is also the principle of a "backtest" (Refer definition of a backtest below).
This provides the contradiction that DPB mentioned, but only when a single implication stream is involved. I have a SIN module in my solver, and its output is often difficult to translate into chain notation. However, it's common that I can translate the output into a Kraken Cell/Column/Row.
I've been in several discussions on AIC vs. Forcing Chains. Myth Jellies tried to explain their difference in another forum, but I was unable to understand his position. Finally, aran convinced me that any candidate that forces both ends of an AIC to be false must itself be false ... and can be eliminated. Bottom Line: a Forcing Chain can be constructed from any AIC strong inference and produce identical eliminations (mentioned by eleven), but the underlying principles are different.
DonM wrote:However, as a manual solving method, a forcing chain is quite different from an AIC.
When it comes to more difficult puzzles with few, if any, bivalue cells, the weakness in the forcing chain method for manual solvers becomes more apparent
SINs were interesting from a theoretical point-of-view, but in practice the concept, not the least of which when it came to notation, was unwieldy for manual solvers and was never picked up as a practical manual method