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Batch mode command line parameters
SudokuMonster edited this page Jul 17, 2020
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To see command line syntax for your version, run the following command
java -cp SukakuExplainer.jar diuf.sudoku.test.serate --man
At the time of writing this manual, the following parameters are supported. At the end, an example command that demonstrates formatting syntax is given.
NAME
serate - Sukaku Explainer / Sudoku Explainer command line rating
SYNOPSIS
serate [--after=FORMAT] [--before=FORMAT] [--format=FORMAT]
[--techs=TECHSTRING] [--showArguments] [--start=FORMAT]
[--revisedRating=N] [--threads=N] [--totalTime] [--batch=N]
[--isBlocks=N] [--isDG=N] [--isWindows=N] [--isX=N]
[--isGirandola=N] [--isAsterisk=N] [--isCD=N]
[--isAntiKnight=N] [--isAntiKing=N] [--isToroidal=N] [--isNC=N]
[--input=FILE] [--output=FILE] [--pearl] [--diamond] [puzzle ...]
DESCRIPTION
serate is a Sukaku Explainer command line entry point that rates one or more
input puzzles. It is currently backward-compatible with serate v1.2.1
If an --input=FILE option is specified then 81-character puzzle
strings are read from that file, otherwise if 81-character puzzle operands are
not specified the puzzles are read from the standard input. If an --output=FILE
option is specified then the output is written to that file, otherwise output
is written to the standard output. The output is controlled by the
--format=FORMAT option (F) as well as --start (S), --before (B), and --after (A) options.
Ratings are floating point numbers in the range 0.0 - 20.0, rounded to the
tenths digit. 0.0 indicates a processing error and 20.0 indicates an valid
but otherwise unsolvable input puzzle.
OPTIONS
-a, --after=FORMAT
Format the output after each step according to FORMAT. Default is empty.
-b, --before=FORMAT
Format the output before each step according to FORMAT. Default is empty.
-B, --batch=N
Batch solving. Default 0=disabled.
1=Apply all available hints that have the lowest rating
2=Apply all available hints with rating lower than maximum puzzle rating
-c, --isNC=N
Control Non-Consecutive constraints 0: disable (default)
1: NC (1,9 not included)
2: NC+ (1,9 included)
3: FNC (1,9 not included)
4: FNC+ (1,9 included)
-d, --diamond
Terminate rating if the puzzle is not a diamond.
-D, --isDG=N
Enable/disable Disjoint Group constraints. 0:disable (default), 1:enabled
-E, --isCD=N
Enable/disable Center Dot group constraints. 0:disable (default), 1:enabled
-f, --format=FORMAT
Format the output for each input puzzle according to FORMAT. Format
conversion are %CHARACTER; all other characters are output unchanged.
The default format is %r/%p/%d. The format conversions are:
%d The diamond rating. This is the highest ER of the methods leading
to the first candidate elimination. (F)
%D The diamond rating technique name. This is the name of technique with highest rating
of the methods leading to the first candidate elimination. (F)
%e The elapsed time to rate the puzzle. (AF)
%h The long step description in multi-line HTML format. (A)
%g The input puzzle line. (SBAF)
%i The puzzle grid in 81-character [0-9] form. (SBAF)
%l The new line. (SBAF)
%m The input puzzle pencilmarks in 729-char format. (SBA)
%M The input puzzle pencilmarks in multi-line format. (SBA)
%n The input puzzle ordinal, counting from 1. (SF)
%p The pearl rating. This is the highest ER of the methods leading
to the first cell placement. (F)
%P The pearl rating technique name. This is the name of 1st technique with highest
rating of the methods leading to the first cell placement. (F)
%r The puzzle rating. This is the highest ER of the methods leading
to the puzzle solution. (AF)
%R The puzzle highest rating technique name. This is the name of 1st technique with
highest ER of the methods leading to the puzzle solution. (F)
%s The short step description. (A)
%S The puzzle highest rating technique shortened name. This is the SHORT name of 1st technique with
highest ER of the methods leading to the puzzle solution. (AF)
%t The tab character. (SBAF)
%T The pearl rating technique shortened name. This is the SHORT name of 1st technique with highest
rating of the methods leading to the first cell placement. (F)
%U The diamond rating technique shortened name. This is the SHORT name of technique with highest
rating of the methods leading to the first candidate elimination. (F)
%% The % character.
-G, --islkSudokuBUG=N
Fix to BUG algorithm by lkSudoku. 0=disabled 1=enabled (default)
-h, --html
List detailed info in html.
-i, --input=FILE
Read 81-character puzzle strings, one per line, from FILE. By default
operands are treated as 81-character puzzle strings. If no operands are
specified then the standard input is read.
-k, --isAntiKing=N
Enable/disable Anti-King constraints. 0:disable (default), 1:enabled
-K, --isAsterisk=N
Enable/disable Asterisk group constraints. 0:disable (default), 1:enabled
-m, --man
List detailed info in displayed man page form.
-n, --isAntiKnight=N
Enable/disable Anti-kNight constraints. 0:disable (default), 1:enabled
-N, --revisedRating=N
Revised rating scheme. Default 0=disabled. 1=enabled
-o, --output=FILE
Write output to FILE instead of the standard output.
-O, --isToroidal=N
Enable/disable Toroidal board. 0:disable (default), 1:enabled
-p, --pearl
Terminate rating if the puzzle is not a pearl.
-P, --FCPlus=N
Control non-trivial implications in FC+ and nested chains 0:default (similar to SE121)
1:More techniques added
2:More techniques added
-Q, --isBlocks=N
Enable/disable block(box) constraints. 0:disable (For Latin Square), 1:enabled (default)
-R, --isGirandola=N
Enable/disable Girandola group constraints. 0:disable (default), 1:enabled
-s, --start=FORMAT
Format the output before each puzzle according to FORMAT. Default is empty.
-S, --showArguments
Show parameters used
-t, --threads=N
Maximal degree of parallelism. Default 0=auto. 1=no parallelism; -1=unlimited
-T, --totalTime
The time required to process all puzzles parsed to standard output
-U, --islkSudokuURUL=NAME
Fix to UR and UL algorithm by lkSudoku. 0=disabled 1=enabled (default)
-~, --techs=TECHSTRING
Specific techniques only, set which techniques to use
the techniques string TECHSTRING is a string consisting of the letters '0' and '1',
where '1' means the technique should be used and '0' means it should not be used
To see which technique is in which letter, and how many techniques are
there, just type --techs= without any string after the = in TECHSTRING
-V, --version
Print the Sudoku Explainer (serate) version and exit.
-W, --isWindows=N
Enable/disable Windows constraints. 0:disable (default), 1:enabled
-X, --isX=N
Enable/disable X diagonal constraints. 0:disable (default), 1:enabled
INVOCATION
java -Xrs -Xmx500m -cp SudokuExplainer.jar diuf.sudoku.test.serate ...
EXAMPLES
Note: % must be entered as %% in windows .bat files and shortcut commands.
To rate a single or a group of puzzle(s):
java.exe -Xrs -Xmx500m -cp SukakuExplainer.jar diuf.sudoku.test.serate --format="%g ED=%r/%p/%d" --input=puzzles.txt --output=puzzles.rated.txt
To display all supported format parameters (at the time of writing this document):
java -Xrs -Xmx1g -cp SukakuExplainer.jar diuf.sudoku.test.serate \
--format="--format%l%%d: %d%l%%D: %D%l%%e: %e%l%%g: %g%l%%i: %i%l%%n: %n%l%%p: %p%l%%P: %P%l%%r: %r%l%%R: %R%l%%S: %S%l%%T: %T%l%%U: %U%l--- end of final section ---" \
--start="--start%l%%g: %g%l%%i: %i%l%%m: %m%l%%M:%l%M%l%%n: %n%l--- end of start section ---" \
--before="--before%l%%g: %g%l%%i: %i%l%%m: %m%l%%M:%l%M%l--- end of before section ---" \
--after="--after%l%%e: %e%l%%h:%l%h%l%%g: %g%l%%i: %i%l%%m: %m%l%%M:%l%M%l%%r: %r%l%%s: %s%l--- end of after section ---" \
--input=my_input_file.txt --output=- --threads=0 > my_output_file.txt
To display man document:
java -cp SukakuExplainer/SukakuExplainer.jar diuf.sudoku.test.serate --man
To use Sukaku Explainer to rate puzzles similar to Sudoku Explainer v1.2.1:
java.exe -Xrs -Xmx500m -cp SukakuExplainer.jar diuf.sudoku.test.serate
--techs=1111000011010111011011011011000010100010111111 -U0 -G0 -t0 --format="%g ED=%r/%p/%d"
--input=puzzles.txt --output=puzzles.rated.txt
SEE ALSO
SudokuExplainer(1), sudoku(1),
https://github.com/SudokuMonster/SukakuExplainer/wiki/Batch-mode-command-line-parameters
https://github.com/SudokuMonster/SukakuExplainer
IMPLEMENTATION
version serate 1.17.7 (Sukaku Explainer) 2020-07-15
author Nicolas Juillerat
copyright Copyright (c) 2006-2020 Nicolas Juillerat
license Lesser General Public License (LGPL)
The following command demonstrates all supported format parameters (at the time of writing this document).
java -Xrs -Xmx1g -cp SukakuExplainer.jar diuf.sudoku.test.serate \
--format="--format%l%%d: %d%l%%D: %D%l%%e: %e%l%%g: %g%l%%i: %i%l%%n: %n%l%%p: %p%l%%P: %P%l%%r: %r%l%%R: %R%l%%S: %S%l%%T: %T%l%%U: %U%l--- end of final section ---" \
--start="--start%l%%g: %g%l%%i: %i%l%%m: %m%l%%M:%l%M%l%%n: %n%l--- end of start section ---" \
--before="--before%l%%g: %g%l%%i: %i%l%%m: %m%l%%M:%l%M%l--- end of before section ---" \
--after="--after%l%%e: %e%l%%h:%l%h%l%%g: %g%l%%i: %i%l%%m: %m%l%%M:%l%M%l%%r: %r%l%%R: %R%l%%s: %s%l--- end of after section ---" \
--input=my_input_file.txt --output=- --threads=0 > my_output_file.txt
An example output of the above command.
--start
%g: 98.7.....7.....6....6.5.....4...5.3...79..5......2...1..85..9......1...4.....3.2.;11.90;11.90;11.80;GP;champagne dry;1;22;
%i: 98.7.....7.....6....6.5.....4...5.3...79..5......2...1..85..9......1...4.....3.2.
%m: ........9......7..1234.....12...6.8.123..6.8...3.56.8.1234.6....23.56...1..456..........8.123.5....123.........4.....123..6.....3.56..9123..67...23.567.91...567.912345....12345.........6...12......9......7....3.5...9.......8..23.5...91..45...9......7..1234...8.1234...8.1....6.8.........9..34.6.8.....5.....2...6.8....4.6.8...34.6.....34...89....5.........678...34.6.8..2..........4.67..1...........4.678912.4.6...12.4...8912.4...89....5....1..4.6.8....4.678..2.4.67...2...6789..3......1234..........6...1234..78..2....78.....5.......4..78.........9..3...78.1.....78.1..45....1..45..891..4..789..3.........4.6.8....4.67891....67......5678..2........23.5.....23.5..89.23...789.2...6789.2...6.8.1..........3..67.....4.........5678.
%M:
+----------------------+----------------------+----------------------+
| 9 8 12345 | 7 346 1246 | 1234 145 235 |
| 7 1235 12345 | 12348 3489 12489 | 6 14589 23589 |
| 1234 123 6 | 12348 5 12489 | 123478 14789 23789 |
+----------------------+----------------------+----------------------+
| 1268 4 129 | 168 678 5 | 278 3 26789 |
| 12368 1236 7 | 9 3468 1468 | 5 468 268 |
| 3568 3569 359 | 3468 2 4678 | 478 46789 1 |
+----------------------+----------------------+----------------------+
| 12346 12367 8 | 5 467 2467 | 9 167 367 |
| 2356 235679 2359 | 268 1 26789 | 378 5678 4 |
| 1456 15679 1459 | 468 46789 3 | 178 2 5678 |
+----------------------+----------------------+----------------------+
%n: 1
--- end of start section ---
--before
%g: 98.7.....7.....6....6.5.....4...5.3...79..5......2...1..85..9......1...4.....3.2.;11.90;11.90;11.80;GP;champagne dry;1;22;
%i: 98.7.....7.....6....6.5.....4...5.3...79..5......2...1..85..9......1...4.....3.2.
%m: ........9......7..1234.....12...6.8.123..6.8...3.56.8.1234.6....23.56...1..456..........8.123.5....123.........4.....123..6.....3.56..9123..67...23.567.91...567.912345....12345.........6...12......9......7....3.5...9.......8..23.5...91..45...9......7..1234...8.1234...8.1....6.8.........9..34.6.8.....5.....2...6.8....4.6.8...34.6.....34...89....5.........678...34.6.8..2..........4.67..1...........4.678912.4.6...12.4...8912.4...89....5....1..4.6.8....4.678..2.4.67...2...6789..3......1234..........6...1234..78..2....78.....5.......4..78.........9..3...78.1.....78.1..45....1..45..891..4..789..3.........4.6.8....4.67891....67......5678..2........23.5.....23.5..89.23...789.2...6789.2...6.8.1..........3..67.....4.........5678.
%M:
+----------------------+----------------------+----------------------+
| 9 8 12345 | 7 346 1246 | 1234 145 235 |
| 7 1235 12345 | 12348 3489 12489 | 6 14589 23589 |
| 1234 123 6 | 12348 5 12489 | 123478 14789 23789 |
+----------------------+----------------------+----------------------+
| 1268 4 129 | 168 678 5 | 278 3 26789 |
| 12368 1236 7 | 9 3468 1468 | 5 468 268 |
| 3568 3569 359 | 3468 2 4678 | 478 46789 1 |
+----------------------+----------------------+----------------------+
| 12346 12367 8 | 5 467 2467 | 9 167 367 |
| 2356 235679 2359 | 268 1 26789 | 378 5678 4 |
| 1456 15679 1459 | 468 46789 3 | 178 2 5678 |
+----------------------+----------------------+----------------------+
--- end of before section ---
--after%e: 45.52s
%h:
<html>
<body>
<h2>Dynamic Contradiction Forcing Chains</h2>
<p>
With this solving technique, we will prove the two following assertions:
<ul>
<li>If E9 contains the value 4, then D6 must contain the value 6
<li>If E9 contains the value 4, then D6 cannot contain the value 6
</ul>
Because the same assumption yields to contradictory results, we can conclude that the
assumption is false, that is, <b><font color="#00AAAA">E9 cannot contain the value 4</font></b>.
</p><p>
Each assertion is proved by a different chain of simple rules. The chains can be dynamic,
which means that the conclusions of multiple sub-chains must be combined in some cases.
</p><p>
The details of each chain are given below. Use the view selector below the grid
to switch between the <font color="#E08000">graphical illustrations</font> of the two different chains.
</p><p>
Chain 1: <b>If E9 contains the value 4, then D6 cannot contain the value 6</b> (View 1):<br>
(1) If E9 contains the value 4, then E9 cannot contain the value 9 (the cell can contain only one value)<br>(2) If E9 does not contain the value 9, then E2 must contain the value 9 (only remaining possible position in the column)<br>(3) If E2 contains the value 9, then H2 cannot contain the value 9 (the value can occur only once in the row)<br>(4) If E9 does not contain the value 9 (1), then F8 must contain the value 9 (only remaining possible position in the block)<br>(5) If F8 contains the value 9, then F8 cannot contain the value 7 (the cell can contain only one value)<br>(6) If E9 contains the value 4 (initial assumption), then E9 cannot contain the value 7 (the cell can contain only one value)<br>(7) If E9 does not contain the value 7 and F8 does not contain the value 7 (5), then H7 cannot contain the value 7 (Pointing: Cells E7,F7: 7 in block and row)<br>(8) If E2 contains the value 9 (2), then E2 cannot contain the value 3 (the cell can contain only one value)<br>(9) If F8 contains the value 9 (4), then F8 cannot contain the value 8 (the cell can contain only one value)<br>(10) If E9 contains the value 4 (initial assumption), then E9 cannot contain the value 8 (the cell can contain only one value)<br>(11) If E9 does not contain the value 8 and F8 does not contain the value 8 (9), then D4 cannot contain the value 8 (Pointing: Cells D8,D9: 8 in block and column)<br>(12) If E2 contains the value 9 (2), then E2 cannot contain the value 8 (the cell can contain only one value)<br>(13) If E9 does not contain the value 8 (10) and E2 does not contain the value 8, then F5 cannot contain the value 8 (Claiming: Cells E4,E5: 8 in column and block)<br>(14) If E9 does not contain the value 8 (10) and F8 does not contain the value 8 (9), then D6 cannot contain the value 8 (Pointing: Cells D8,D9: 8 in block and column)<br>(15) If E9 does not contain the value 8 (10) and E2 does not contain the value 8 (12), then F6 cannot contain the value 8 (Claiming: Cells E4,E5: 8 in column and block)<br>(16) If E9 contains the value 4 (initial assumption), then C9 cannot contain the value 4 (the value can occur only once in the row)<br>(17) If E2 contains the value 9 (2), then I2 cannot contain the value 9 (the value can occur only once in the row)<br>(18) If I2 does not contain the value 9, C9 does not contain the value 4 (16), F6 does not contain the value 8 (15), D6 does not contain the value 8 (14), F5 does not contain the value 8 (13), D4 does not contain the value 8 (11), E2 does not contain the value 3 (8), H7 does not contain the value 7 (7) and H2 does not contain the value 9 (3), then E5 cannot contain the value 6 (Contradiction Forcing Chain: E5.6 on ==> G9.1 both on & off)<br>(19) If E9 contains the value 4 (initial assumption), then E5 cannot contain the value 4 (the value can occur only once in the column)<br>(20) If E9 contains the value 4 (initial assumption), then F7 cannot contain the value 4 (the value can occur only once in the block)<br>(21) If E9 contains the value 4 (initial assumption), then E7 cannot contain the value 4 (the value can occur only once in the block)<br>(22) If E7 does not contain the value 4 and F7 does not contain the value 4 (20), then A7 must contain the value 4 (only remaining possible position in the row)<br>(23) If A7 contains the value 4, then A7 cannot contain the value 3 (the cell can contain only one value)<br>(24) If A7 contains the value 4 (22), then A7 cannot contain the value 1 (the cell can contain only one value)<br>(25) If A7 contains the value 4 (22), then A7 cannot contain the value 2 (the cell can contain only one value)<br>(26) If E9 contains the value 4 (initial assumption), then D9 cannot contain the value 4 (the value can occur only once in the block)<br>(27) If D9 does not contain the value 4, A7 does not contain the value 2 (25), E9 does not contain the value 8 (10), F8 does not contain the value 8 (9), A7 does not contain the value 1 (24), A7 does not contain the value 3 (23) and E5 does not contain the value 4 (19), then D4 cannot contain the value 6 (Cell Forcing Chains: D8 ==> D4.6 off)<br>(28) If E9 contains the value 4 (initial assumption), then E1 cannot contain the value 4 (the value can occur only once in the column)<br>(29) If A7 contains the value 4 (22), then A3 cannot contain the value 4 (the value can occur only once in the column)<br>(30) If A3 does not contain the value 4, F6 does not contain the value 8 (15), D6 does not contain the value 8 (14), F5 does not contain the value 8 (13), D4 does not contain the value 8 (11), H7 does not contain the value 7 (7), H2 does not contain the value 9 (3), E1 does not contain the value 4 (28) and I2 does not contain the value 9 (17), then E4 cannot contain the value 6 (Contradiction Forcing Chain: E4.6 on ==> G8.3 both on & off)<br>(31) If F6 does not contain the value 8 (15), D6 does not contain the value 8 (14), F5 does not contain the value 8 (13), D4 does not contain the value 8 (11), E7 does not contain the value 4 (21), E5 does not contain the value 4 (19), F8 does not contain the value 7 (5), E2 does not contain the value 3 (8) and A7 does not contain the value 1 (24), then F5 cannot contain the value 6 (Contradiction Forcing Chain: F5.6 on ==> H7.1 both on & off)<br>(32) If F8 does not contain the value 7 (5) and E7 does not contain the value 4 (21), then F6 cannot contain the value 6 (Cell Forcing Chains: E7 ==> F6.6 off)<br>(33) If F6 does not contain the value 6, F5 does not contain the value 6 (31), E4 does not contain the value 6 (30), D4 does not contain the value 6 (27) and E5 does not contain the value 6 (18), then D6 must contain the value 6 (only remaining possible position in the block)<br>
</p><p>
Chain 2: <b>If D6 must contain the value 6, then D6 cannot contain the value 6</b> (View 2):<br>
(1) If E9 contains the value 4, then F7 cannot contain the value 4 (the value can occur only once in the block)<br>(2) If E9 contains the value 4 (initial assumption), then E7 cannot contain the value 4 (the value can occur only once in the block)<br>(3) If E7 does not contain the value 4 and F7 does not contain the value 4 (1), then A7 must contain the value 4 (only remaining possible position in the row)<br>(4) If A7 contains the value 4, then A7 cannot contain the value 2 (the cell can contain only one value)<br>(5) If E9 contains the value 4 (initial assumption), then E9 cannot contain the value 9 (the cell can contain only one value)<br>(6) If E9 does not contain the value 9, then E2 must contain the value 9 (only remaining possible position in the column)<br>(7) If E2 contains the value 9, then H2 cannot contain the value 9 (the value can occur only once in the row)<br>(8) If E2 contains the value 9 (6), then I2 cannot contain the value 9 (the value can occur only once in the row)<br>(9) If E9 contains the value 4 (initial assumption), then D9 cannot contain the value 4 (the value can occur only once in the block)<br>(10) If E9 does not contain the value 9 (5), then F8 must contain the value 9 (only remaining possible position in the block)<br>(11) If F8 contains the value 9, then F8 cannot contain the value 8 (the cell can contain only one value)<br>(12) If E9 contains the value 4 (initial assumption), then E9 cannot contain the value 8 (the cell can contain only one value)<br>(13) If E9 does not contain the value 8 and F8 does not contain the value 8 (11), then D4 cannot contain the value 8 (Pointing: Cells D8,D9: 8 in block and column)<br>(14) If E2 contains the value 9 (6), then E2 cannot contain the value 8 (the cell can contain only one value)<br>(15) If E9 does not contain the value 8 (12) and E2 does not contain the value 8, then F5 cannot contain the value 8 (Claiming: Cells E4,E5: 8 in column and block)<br>(16) If E9 does not contain the value 8 (12) and F8 does not contain the value 8 (11), then D6 cannot contain the value 8 (Pointing: Cells D8,D9: 8 in block and column)<br>(17) If E9 does not contain the value 8 (12) and E2 does not contain the value 8 (14), then F6 cannot contain the value 8 (Claiming: Cells E4,E5: 8 in column and block)<br>(18) If F8 contains the value 9 (10), then F8 cannot contain the value 7 (the cell can contain only one value)<br>(19) If E9 contains the value 4 (initial assumption), then E9 cannot contain the value 7 (the cell can contain only one value)<br>(20) If E9 does not contain the value 7 and F8 does not contain the value 7 (18), then H7 cannot contain the value 7 (Pointing: Cells E7,F7: 7 in block and row)<br>(21) If F8 contains the value 9 (10), then F8 cannot contain the value 6 (the cell can contain only one value)<br>(22) If E9 contains the value 4 (initial assumption), then E1 cannot contain the value 4 (the value can occur only once in the column)<br>(23) If E9 does not contain the value 8 (12) and F8 does not contain the value 8 (11), then D3 cannot contain the value 8 (Pointing: Cells D8,D9: 8 in block and column)<br>(24) If E9 does not contain the value 7 (19) and F8 does not contain the value 7 (18), then I7 cannot contain the value 7 (Pointing: Cells E7,F7: 7 in block and row)<br>(25) If I7 does not contain the value 7, D3 does not contain the value 8 (23), E1 does not contain the value 4 (22), F8 does not contain the value 6 (21), H7 does not contain the value 7 (20), F6 does not contain the value 8 (17), D6 does not contain the value 8 (16), F5 does not contain the value 8 (15), D4 does not contain the value 8 (13), D9 does not contain the value 4 (9), I2 does not contain the value 9 (8), H2 does not contain the value 9 (7) and A7 does not contain the value 2 (4), then D6 cannot contain the value 6 (Contradiction Forcing Chain: D6.6 on ==> F3.2 both on & off)<br>
</p>
<br><br>
<b>Nested Forcing Chains details</b> (Note that each Nested Forcing Chain relies on the fact that some <font color="blue">candidates</font> have been excluded by the main Forcing Chain): <br><br>
<i>Nested <b>Contradiction Forcing Chain: E5.6 on ==> G9.1 both on & off</b></i><br>
Chain 3: <b>If E5 contains the value 6, then G9 must contain the value 1</b> (View 3):<br>
(1) If E5 contains the value 6, then D4 cannot contain the value 6 (the value can occur only once in the block)<br>(2) If D4 does not contain the value 6, then D4 must contain the value 1 (only remaining possible value in the cell)<br>(3) If D4 contains the value 1, then F5 cannot contain the value 1 (the value can occur only once in the block)<br>(4) If E5 contains the value 6 (initial assumption), then F5 cannot contain the value 6 (the value can occur only once in the block)<br>(5) If F5 does not contain the value 6 and F5 does not contain the value 1 (3), then F5 must contain the value 4 (only remaining possible value in the cell)<br>(6) If F5 contains the value 4, then H5 cannot contain the value 4 (the value can occur only once in the row)<br>(7) If E5 contains the value 6 (initial assumption), then H5 cannot contain the value 6 (the value can occur only once in the row)<br>(8) If H5 does not contain the value 6 and H5 does not contain the value 4 (6), then H5 must contain the value 8 (only remaining possible value in the cell)<br>(9) If H5 contains the value 8, then I5 cannot contain the value 8 (the value can occur only once in the block)<br>(10) If E5 contains the value 6 (initial assumption), then I5 cannot contain the value 6 (the value can occur only once in the row)<br>(11) If I5 does not contain the value 6 and I5 does not contain the value 8 (9), then I5 must contain the value 2 (only remaining possible value in the cell)<br>(12) If I5 contains the value 2, then I1 cannot contain the value 2 (the value can occur only once in the column)<br>(13) If E5 contains the value 6 (initial assumption), then E5 cannot contain the value 3 (the cell can contain only one value)<br>(14) If E5 does not contain the value 3, then E1 must contain the value 3 (only remaining possible position in the column)<br>(15) If E1 contains the value 3, then I1 cannot contain the value 3 (the value can occur only once in the row)<br>(16) If I1 does not contain the value 3 and I1 does not contain the value 2 (12), then I1 must contain the value 5 (only remaining possible value in the cell)<br>(17) If I1 contains the value 5, then H2 cannot contain the value 5 (the value can occur only once in the block)<br>(18) If I1 contains the value 5 (16), then H1 cannot contain the value 5 (the value can occur only once in the block)<br>(19) If H1 does not contain the value 5 and H2 does not contain the value 5 (17), then H8 must contain the value 5 (only remaining possible position in the column)<br>(20) If H8 contains the value 5, then H8 cannot contain the value 7 (the cell can contain only one value)<br>(21) If E5 contains the value 6 (initial assumption), then E5 cannot contain the value 8 (the cell can contain only one value)<br>(22) If E5 does not contain the value 8, then E4 must contain the value 8 (only remaining possible position in the block)<br>(23) If E4 contains the value 8, then E4 cannot contain the value 7 (the cell can contain only one value)<br>(24) If E4 does not contain the value 7, then F6 must contain the value 7 (only remaining possible position in the block)<br>(25) If F6 contains the value 7, then H6 cannot contain the value 7 (the value can occur only once in the row)<br>(26) If H6 does not contain the value 7 and H8 does not contain the value 7 (20), then H3 must contain the value 7 (only remaining possible position in the column)<br>(27) If H3 contains the value 7, then H3 cannot contain the value 9 (the cell can contain only one value)<br>(28) If H3 does not contain the value 9, then H6 must contain the value 9 (only remaining possible position in the column)<br>(29) If H6 contains the value 9, then H6 cannot contain the value 6 (the cell can contain only one value)<br>(30) If H8 contains the value 5 (19), then H8 cannot contain the value 6 (the cell can contain only one value)<br>(31) If H8 does not contain the value 6, H5 does not contain the value 6 (7) and H6 does not contain the value 6 (29), then H7 must contain the value 6 (only remaining possible position in the column)<br>(32) If H7 contains the value 6, then H7 cannot contain the value 1 (the cell can contain only one value)<br>(33) If H7 does not contain the value 1, then G9 must contain the value 1 (only remaining possible position in the block)<br><br>
Chain 4: <b>If E5 contains the value 6, then G9 cannot contain the value 1</b> (View 4):<br>
(1) If E5 contains the value 6, then D4 cannot contain the value 6 (the value can occur only once in the block)<br>(2) If D4 does not contain the value 6, then D4 must contain the value 1 (only remaining possible value in the cell)<br>(3) If D4 contains the value 1, then F5 cannot contain the value 1 (the value can occur only once in the block)<br>(4) If E5 contains the value 6 (initial assumption), then F5 cannot contain the value 6 (the value can occur only once in the block)<br>(5) If F5 does not contain the value 6 and F5 does not contain the value 1 (3), then F5 must contain the value 4 (only remaining possible value in the cell)<br>(6) If F5 contains the value 4, then H5 cannot contain the value 4 (the value can occur only once in the row)<br>(7) If E5 contains the value 6 (initial assumption), then H5 cannot contain the value 6 (the value can occur only once in the row)<br>(8) If H5 does not contain the value 6 and H5 does not contain the value 4 (6), then H5 must contain the value 8 (only remaining possible value in the cell)<br>(9) If H5 contains the value 8, then I5 cannot contain the value 8 (the value can occur only once in the block)<br>(10) If E5 contains the value 6 (initial assumption), then I5 cannot contain the value 6 (the value can occur only once in the row)<br>(11) If I5 does not contain the value 6 and I5 does not contain the value 8 (9), then I5 must contain the value 2 (only remaining possible value in the cell)<br>(12) If I5 contains the value 2, then I1 cannot contain the value 2 (the value can occur only once in the column)<br>(13) If E5 contains the value 6 (initial assumption), then E5 cannot contain the value 3 (the cell can contain only one value)<br>(14) If E5 does not contain the value 3, then E1 must contain the value 3 (only remaining possible position in the column)<br>(15) If E1 contains the value 3, then I1 cannot contain the value 3 (the value can occur only once in the row)<br>(16) If I1 does not contain the value 3 and I1 does not contain the value 2 (12), then I1 must contain the value 5 (only remaining possible value in the cell)<br>(17) If I1 contains the value 5, then H2 cannot contain the value 5 (the value can occur only once in the block)<br>(18) If I1 contains the value 5 (16), then H1 cannot contain the value 5 (the value can occur only once in the block)<br>(19) If H1 does not contain the value 5 and H2 does not contain the value 5 (17), then H8 must contain the value 5 (only remaining possible position in the column)<br>(20) If H8 contains the value 5, then H8 cannot contain the value 7 (the cell can contain only one value)<br>(21) If E5 contains the value 6 (initial assumption), then E5 cannot contain the value 8 (the cell can contain only one value)<br>(22) If E5 does not contain the value 8, then E4 must contain the value 8 (only remaining possible position in the block)<br>(23) If E4 contains the value 8, then E4 cannot contain the value 7 (the cell can contain only one value)<br>(24) If E4 does not contain the value 7, then F6 must contain the value 7 (only remaining possible position in the block)<br>(25) If F6 contains the value 7, then H6 cannot contain the value 7 (the value can occur only once in the row)<br>(26) If H6 does not contain the value 7 and H8 does not contain the value 7 (20), then H3 must contain the value 7 (only remaining possible position in the column)<br>(27) If H3 contains the value 7, then H3 cannot contain the value 9 (the cell can contain only one value)<br>(28) If H3 does not contain the value 9, then I3 must contain the value 9 (only remaining possible position in the block)<br>(29) If I3 contains the value 9, then I4 cannot contain the value 9 (the value can occur only once in the column)<br>(30) If I4 does not contain the value 9, then C4 must contain the value 9 (only remaining possible position in the row)<br>(31) If C4 contains the value 9, then C9 cannot contain the value 9 (the value can occur only once in the column)<br>(32) If H8 contains the value 5 (19), then A8 cannot contain the value 5 (the value can occur only once in the row)<br>(33) If H5 contains the value 8 (8), then H6 cannot contain the value 8 (the value can occur only once in the block)<br>(34) If H5 contains the value 8 (8), then G6 cannot contain the value 8 (the value can occur only once in the block)<br>(35) If G6 does not contain the value 8 and H6 does not contain the value 8 (33), then A6 must contain the value 8 (only remaining possible position in the row)<br>(36) If A6 contains the value 8, then A6 cannot contain the value 5 (the cell can contain only one value)<br>(37) If A6 does not contain the value 5 and A8 does not contain the value 5 (32), then A9 must contain the value 5 (only remaining possible position in the column)<br>(38) If A9 contains the value 5, then C9 cannot contain the value 5 (the value can occur only once in the block)<br>(39) If C9 does not contain the value 5 and C9 does not contain the value 9 (31), then C9 must contain the value 1 (only remaining possible value in the cell)<br>(40) If C9 contains the value 1, then G9 cannot contain the value 1 (the value can occur only once in the row)<br><br>
<i>Nested <b>Cell Forcing Chains: D8 ==> D4.6 off</b></i><br>
Chain 5: <b>If D8 contains the value 2, then D4 cannot contain the value 6</b> (View 5):<br>
(1) If D8 contains the value 2, then F7 cannot contain the value 2 (the value can occur only once in the block)<br>(2) If F7 does not contain the value 2, then B7 must contain the value 2 (only remaining possible position in the row)<br>(3) If B7 contains the value 2, then B7 cannot contain the value 1 (the cell can contain only one value)<br>(4) If B7 does not contain the value 1, then H7 must contain the value 1 (only remaining possible position in the row)<br>(5) If H7 contains the value 1, then G9 cannot contain the value 1 (the value can occur only once in the block)<br>(6) If D8 contains the value 2 (initial assumption), then D8 cannot contain the value 8 (the cell can contain only one value)<br>(7) If D8 does not contain the value 8, then D9 must contain the value 8 (only remaining possible position in the block)<br>(8) If D9 contains the value 8, then G9 cannot contain the value 8 (the value can occur only once in the row)<br>(9) If G9 does not contain the value 8 and G9 does not contain the value 1 (5), then G9 must contain the value 7 (only remaining possible value in the cell)<br>(10) If G9 contains the value 7, then G8 cannot contain the value 7 (the value can occur only once in the block)<br>(11) If B7 contains the value 2 (2), then B7 cannot contain the value 3 (the cell can contain only one value)<br>(12) If B7 does not contain the value 3, then I7 must contain the value 3 (only remaining possible position in the row)<br>(13) If I7 contains the value 3, then G8 cannot contain the value 3 (the value can occur only once in the block)<br>(14) If G8 does not contain the value 3 and G8 does not contain the value 7 (10), then G8 must contain the value 8 (only remaining possible value in the cell)<br>(15) If G8 contains the value 8, then G6 cannot contain the value 8 (the value can occur only once in the column)<br>(16) If G9 contains the value 7 (9), then G6 cannot contain the value 7 (the value can occur only once in the column)<br>(17) If G6 does not contain the value 7 and G6 does not contain the value 8 (15), then G6 must contain the value 4 (only remaining possible value in the cell)<br>(18) If G6 contains the value 4, then H5 cannot contain the value 4 (the value can occur only once in the block)<br>(19) If H5 does not contain the value 4, then F5 must contain the value 4 (only remaining possible position in the row)<br>(20) If F5 contains the value 4, then F5 cannot contain the value 1 (the cell can contain only one value)<br>(21) If F5 does not contain the value 1, then D4 must contain the value 1 (only remaining possible position in the block)<br>(22) If D4 contains the value 1, then D4 cannot contain the value 6 (the cell can contain only one value)<br><br>
Chain 6: <b>If D8 contains the value 6, then D4 cannot contain the value 6</b> (View 6):<br>
(1) If D8 contains the value 6, then D4 cannot contain the value 6 (the value can occur only once in the column)<br><br>
Chain 7: <b>If D8 contains the value 8, then D4 cannot contain the value 6</b> (View 7):<br>
(1) If D8 contains the value 8, then D9 cannot contain the value 8 (the value can occur only once in the block)<br>(2) If D9 does not contain the value 8, then D9 must contain the value 6 (only remaining possible value in the cell)<br>(3) If D9 contains the value 6, then D4 cannot contain the value 6 (the value can occur only once in the column)<br><br>
<i>Nested <b>Contradiction Forcing Chain: E4.6 on ==> G8.3 both on & off</b></i><br>
Chain 8: <b>If E4 contains the value 6, then G8 must contain the value 3</b> (View 8):<br>
(1) If E4 contains the value 6, then D4 cannot contain the value 6 (the value can occur only once in the block)<br>(2) If D4 does not contain the value 6, then D4 must contain the value 1 (only remaining possible value in the cell)<br>(3) If D4 contains the value 1, then F5 cannot contain the value 1 (the value can occur only once in the block)<br>(4) If E4 contains the value 6 (initial assumption), then F5 cannot contain the value 6 (the value can occur only once in the block)<br>(5) If F5 does not contain the value 6 and F5 does not contain the value 1 (3), then F5 must contain the value 4 (only remaining possible value in the cell)<br>(6) If F5 contains the value 4, then H5 cannot contain the value 4 (the value can occur only once in the row)<br>(7) If E4 contains the value 6 (initial assumption), then E4 cannot contain the value 8 (the cell can contain only one value)<br>(8) If E4 does not contain the value 8, then E5 must contain the value 8 (only remaining possible position in the block)<br>(9) If E5 contains the value 8, then H5 cannot contain the value 8 (the value can occur only once in the row)<br>(10) If H5 does not contain the value 8 and H5 does not contain the value 4 (6), then H5 must contain the value 6 (only remaining possible value in the cell)<br>(11) If H5 contains the value 6, then I5 cannot contain the value 6 (the value can occur only once in the block)<br>(12) If E5 contains the value 8 (8), then I5 cannot contain the value 8 (the value can occur only once in the row)<br>(13) If I5 does not contain the value 8 and I5 does not contain the value 6 (11), then I5 must contain the value 2 (only remaining possible value in the cell)<br>(14) If I5 contains the value 2, then I1 cannot contain the value 2 (the value can occur only once in the column)<br>(15) If E4 contains the value 6 (initial assumption), then E1 cannot contain the value 6 (the value can occur only once in the column)<br>(16) If E1 does not contain the value 6, then E1 must contain the value 3 (only remaining possible value in the cell)<br>(17) If E1 contains the value 3, then I1 cannot contain the value 3 (the value can occur only once in the row)<br>(18) If I1 does not contain the value 3 and I1 does not contain the value 2 (14), then I1 must contain the value 5 (only remaining possible value in the cell)<br>(19) If I1 contains the value 5, then H1 cannot contain the value 5 (the value can occur only once in the block)<br>(20) If H5 contains the value 6 (10), then H7 cannot contain the value 6 (the value can occur only once in the column)<br>(21) If H7 does not contain the value 6, then H7 must contain the value 1 (only remaining possible value in the cell)<br>(22) If H7 contains the value 1, then H1 cannot contain the value 1 (the value can occur only once in the column)<br>(23) If H1 does not contain the value 1 and H1 does not contain the value 5 (19), then H1 must contain the value 4 (only remaining possible value in the cell)<br>(24) If H1 contains the value 4, then H2 cannot contain the value 4 (the value can occur only once in the block)<br>(25) If H7 contains the value 1 (21), then H2 cannot contain the value 1 (the value can occur only once in the column)<br>(26) If I1 contains the value 5 (18), then H2 cannot contain the value 5 (the value can occur only once in the block)<br>(27) If H2 does not contain the value 5, H2 does not contain the value 1 (25) and H2 does not contain the value 4 (24), then H2 must contain the value 8 (only remaining possible value in the cell)<br>(28) If H2 contains the value 8, then I2 cannot contain the value 8 (the value can occur only once in the block)<br>(29) If I5 contains the value 2 (13), then I2 cannot contain the value 2 (the value can occur only once in the column)<br>(30) If I1 contains the value 5 (18), then I2 cannot contain the value 5 (the value can occur only once in the block)<br>(31) If I2 does not contain the value 5, I2 does not contain the value 2 (29) and I2 does not contain the value 8 (28), then I2 must contain the value 3 (only remaining possible value in the cell)<br>(32) If I2 contains the value 3, then G3 cannot contain the value 3 (the value can occur only once in the block)<br>(33) If E1 contains the value 3 (16), then G1 cannot contain the value 3 (the value can occur only once in the row)<br>(34) If G1 does not contain the value 3 and G3 does not contain the value 3 (32), then G8 must contain the value 3 (only remaining possible position in the column)<br><br>
Chain 9: <b>If E4 contains the value 6, then G8 cannot contain the value 3</b> (View 9):<br>
(1) If E4 contains the value 6, then D4 cannot contain the value 6 (the value can occur only once in the block)<br>(2) If D4 does not contain the value 6, then D4 must contain the value 1 (only remaining possible value in the cell)<br>(3) If D4 contains the value 1, then F5 cannot contain the value 1 (the value can occur only once in the block)<br>(4) If E4 contains the value 6 (initial assumption), then F5 cannot contain the value 6 (the value can occur only once in the block)<br>(5) If F5 does not contain the value 6 and F5 does not contain the value 1 (3), then F5 must contain the value 4 (only remaining possible value in the cell)<br>(6) If F5 contains the value 4, then H5 cannot contain the value 4 (the value can occur only once in the row)<br>(7) If E4 contains the value 6 (initial assumption), then E4 cannot contain the value 8 (the cell can contain only one value)<br>(8) If E4 does not contain the value 8, then E5 must contain the value 8 (only remaining possible position in the block)<br>(9) If E5 contains the value 8, then H5 cannot contain the value 8 (the value can occur only once in the row)<br>(10) If H5 does not contain the value 8 and H5 does not contain the value 4 (6), then H5 must contain the value 6 (only remaining possible value in the cell)<br>(11) If H5 contains the value 6, then I5 cannot contain the value 6 (the value can occur only once in the block)<br>(12) If E5 contains the value 8 (8), then I5 cannot contain the value 8 (the value can occur only once in the row)<br>(13) If I5 does not contain the value 8 and I5 does not contain the value 6 (11), then I5 must contain the value 2 (only remaining possible value in the cell)<br>(14) If I5 contains the value 2, then I1 cannot contain the value 2 (the value can occur only once in the column)<br>(15) If E4 contains the value 6 (initial assumption), then E1 cannot contain the value 6 (the value can occur only once in the column)<br>(16) If E1 does not contain the value 6, then E1 must contain the value 3 (only remaining possible value in the cell)<br>(17) If E1 contains the value 3, then I1 cannot contain the value 3 (the value can occur only once in the row)<br>(18) If I1 does not contain the value 3 and I1 does not contain the value 2 (14), then I1 must contain the value 5 (only remaining possible value in the cell)<br>(19) If I1 contains the value 5, then H1 cannot contain the value 5 (the value can occur only once in the block)<br>(20) If H5 contains the value 6 (10), then H7 cannot contain the value 6 (the value can occur only once in the column)<br>(21) If H7 does not contain the value 6, then H7 must contain the value 1 (only remaining possible value in the cell)<br>(22) If H7 contains the value 1, then H1 cannot contain the value 1 (the value can occur only once in the column)<br>(23) If H1 does not contain the value 1 and H1 does not contain the value 5 (19), then H1 must contain the value 4 (only remaining possible value in the cell)<br>(24) If H1 contains the value 4, then C1 cannot contain the value 4 (the value can occur only once in the row)<br>(25) If C1 does not contain the value 4, then C2 must contain the value 4 (only remaining possible position in the block)<br>(26) If C2 contains the value 4, then C2 cannot contain the value 3 (the cell can contain only one value)<br>(27) If E1 contains the value 3 (16), then C1 cannot contain the value 3 (the value can occur only once in the row)<br>(28) If E5 contains the value 8 (8), then E5 cannot contain the value 3 (the cell can contain only one value)<br>(29) If E5 does not contain the value 3, then D6 must contain the value 3 (only remaining possible position in the block)<br>(30) If D6 contains the value 3, then C6 cannot contain the value 3 (the value can occur only once in the row)<br>(31) If C6 does not contain the value 3, C1 does not contain the value 3 (27) and C2 does not contain the value 3 (26), then C8 must contain the value 3 (only remaining possible position in the column)<br>(32) If C8 contains the value 3, then G8 cannot contain the value 3 (the value can occur only once in the row)<br><br>
<i>Nested <b>Contradiction Forcing Chain: F5.6 on ==> H7.1 both on & off</b></i><br>
Chain 10: <b>If F5 contains the value 6, then H7 must contain the value 1</b> (View 10):<br>
(1) If F5 contains the value 6, then F1 cannot contain the value 6 (the value can occur only once in the column)<br>(2) If F1 does not contain the value 6, then E1 must contain the value 6 (only remaining possible position in the block)<br>(3) If E1 contains the value 6, then E7 cannot contain the value 6 (the value can occur only once in the column)<br>(4) If E7 does not contain the value 6, then E7 must contain the value 7 (only remaining possible value in the cell)<br>(5) If E7 contains the value 7, then F7 cannot contain the value 7 (the value can occur only once in the block)<br>(6) If F7 does not contain the value 7, then F6 must contain the value 7 (only remaining possible position in the column)<br>(7) If F6 contains the value 7, then G6 cannot contain the value 7 (the value can occur only once in the row)<br>(8) If F5 contains the value 6 (initial assumption), then F5 cannot contain the value 4 (the cell can contain only one value)<br>(9) If F5 does not contain the value 4, then H5 must contain the value 4 (only remaining possible position in the row)<br>(10) If H5 contains the value 4, then G6 cannot contain the value 4 (the value can occur only once in the block)<br>(11) If G6 does not contain the value 4 and G6 does not contain the value 7 (7), then G6 must contain the value 8 (only remaining possible value in the cell)<br>(12) If G6 contains the value 8, then I5 cannot contain the value 8 (the value can occur only once in the block)<br>(13) If F5 contains the value 6 (initial assumption), then I5 cannot contain the value 6 (the value can occur only once in the row)<br>(14) If I5 does not contain the value 6 and I5 does not contain the value 8 (12), then I5 must contain the value 2 (only remaining possible value in the cell)<br>(15) If I5 contains the value 2, then B5 cannot contain the value 2 (the value can occur only once in the row)<br>(16) If E1 contains the value 6 (2), then E1 cannot contain the value 3 (the cell can contain only one value)<br>(17) If E1 does not contain the value 3, then E5 must contain the value 3 (only remaining possible position in the column)<br>(18) If E5 contains the value 3, then B5 cannot contain the value 3 (the value can occur only once in the row)<br>(19) If F5 contains the value 6 (initial assumption), then B5 cannot contain the value 6 (the value can occur only once in the row)<br>(20) If B5 does not contain the value 6, B5 does not contain the value 3 (18) and B5 does not contain the value 2 (15), then B5 must contain the value 1 (only remaining possible value in the cell)<br>(21) If B5 contains the value 1, then B7 cannot contain the value 1 (the value can occur only once in the column)<br>(22) If B7 does not contain the value 1, then H7 must contain the value 1 (only remaining possible position in the row)<br><br>
Chain 11: <b>If F5 contains the value 6, then H7 cannot contain the value 1</b> (View 11):<br>
(1) If F5 contains the value 6, then F1 cannot contain the value 6 (the value can occur only once in the column)<br>(2) If F1 does not contain the value 6, then E1 must contain the value 6 (only remaining possible position in the block)<br>(3) If E1 contains the value 6, then E7 cannot contain the value 6 (the value can occur only once in the column)<br>(4) If E7 does not contain the value 6, then E7 must contain the value 7 (only remaining possible value in the cell)<br>(5) If E7 contains the value 7, then F7 cannot contain the value 7 (the value can occur only once in the block)<br>(6) If F7 does not contain the value 7, then F6 must contain the value 7 (only remaining possible position in the column)<br>(7) If F6 contains the value 7, then G6 cannot contain the value 7 (the value can occur only once in the row)<br>(8) If F5 contains the value 6 (initial assumption), then F5 cannot contain the value 4 (the cell can contain only one value)<br>(9) If F5 does not contain the value 4, then H5 must contain the value 4 (only remaining possible position in the row)<br>(10) If H5 contains the value 4, then G6 cannot contain the value 4 (the value can occur only once in the block)<br>(11) If G6 does not contain the value 4 and G6 does not contain the value 7 (7), then G6 must contain the value 8 (only remaining possible value in the cell)<br>(12) If G6 contains the value 8, then I5 cannot contain the value 8 (the value can occur only once in the block)<br>(13) If F5 contains the value 6 (initial assumption), then I5 cannot contain the value 6 (the value can occur only once in the row)<br>(14) If I5 does not contain the value 6 and I5 does not contain the value 8 (12), then I5 must contain the value 2 (only remaining possible value in the cell)<br>(15) If I5 contains the value 2, then G4 cannot contain the value 2 (the value can occur only once in the block)<br>(16) If E1 contains the value 6 (2), then E1 cannot contain the value 3 (the cell can contain only one value)<br>(17) If E1 does not contain the value 3, then E5 must contain the value 3 (only remaining possible position in the column)<br>(18) If E5 contains the value 3, then E5 cannot contain the value 8 (the cell can contain only one value)<br>(19) If E5 does not contain the value 8, then E4 must contain the value 8 (only remaining possible position in the block)<br>(20) If E4 contains the value 8, then G4 cannot contain the value 8 (the value can occur only once in the row)<br>(21) If G4 does not contain the value 8 and G4 does not contain the value 2 (15), then G4 must contain the value 7 (only remaining possible value in the cell)<br>(22) If G4 contains the value 7, then G9 cannot contain the value 7 (the value can occur only once in the column)<br>(23) If G6 contains the value 8 (11), then G9 cannot contain the value 8 (the value can occur only once in the column)<br>(24) If G9 does not contain the value 8 and G9 does not contain the value 7 (22), then G9 must contain the value 1 (only remaining possible value in the cell)<br>(25) If G9 contains the value 1, then H7 cannot contain the value 1 (the value can occur only once in the block)<br><br>
<i>Nested <b>Cell Forcing Chains: E7 ==> F6.6 off</b></i><br>
Chain 12: <b>If E7 contains the value 6, then F6 cannot contain the value 6</b> (View 12):<br>
(1) If E7 contains the value 6, then E1 cannot contain the value 6 (the value can occur only once in the column)<br>(2) If E1 does not contain the value 6, then F1 must contain the value 6 (only remaining possible position in the block)<br>(3) If F1 contains the value 6, then F6 cannot contain the value 6 (the value can occur only once in the column)<br><br>
Chain 13: <b>If E7 contains the value 7, then F6 cannot contain the value 6</b> (View 13):<br>
(1) If E7 contains the value 7, then F7 cannot contain the value 7 (the value can occur only once in the block)<br>(2) If F7 does not contain the value 7, then F6 must contain the value 7 (only remaining possible position in the column)<br>(3) If F6 contains the value 7, then F6 cannot contain the value 6 (the cell can contain only one value)<br><br>
<i>Nested <b>Contradiction Forcing Chain: D6.6 on ==> F3.2 both on & off</b></i><br>
Chain 14: <b>If D6 contains the value 6, then F3 must contain the value 2</b> (View 14):<br>
(1) If D6 contains the value 6, then D6 cannot contain the value 3 (the cell can contain only one value)<br>(2) If D6 does not contain the value 3, then E5 must contain the value 3 (only remaining possible position in the block)<br>(3) If E5 contains the value 3, then E1 cannot contain the value 3 (the value can occur only once in the column)<br>(4) If E1 does not contain the value 3, then E1 must contain the value 6 (only remaining possible value in the cell)<br>(5) If E1 contains the value 6, then F1 cannot contain the value 6 (the value can occur only once in the block)<br>(6) If D6 contains the value 6 (initial assumption), then F5 cannot contain the value 6 (the value can occur only once in the block)<br>(7) If D6 contains the value 6 (initial assumption), then F6 cannot contain the value 6 (the value can occur only once in the block)<br>(8) If F6 does not contain the value 6, F5 does not contain the value 6 (6) and F1 does not contain the value 6 (5), then F7 must contain the value 6 (only remaining possible position in the column)<br>(9) If F7 contains the value 6, then H7 cannot contain the value 6 (the value can occur only once in the row)<br>(10) If H7 does not contain the value 6, then H7 must contain the value 1 (only remaining possible value in the cell)<br>(11) If H7 contains the value 1, then G9 cannot contain the value 1 (the value can occur only once in the block)<br>(12) If D6 contains the value 6 (initial assumption), then D9 cannot contain the value 6 (the value can occur only once in the column)<br>(13) If D9 does not contain the value 6, then D9 must contain the value 8 (only remaining possible value in the cell)<br>(14) If D9 contains the value 8, then G9 cannot contain the value 8 (the value can occur only once in the row)<br>(15) If G9 does not contain the value 8 and G9 does not contain the value 1 (11), then G9 must contain the value 7 (only remaining possible value in the cell)<br>(16) If G9 contains the value 7, then G4 cannot contain the value 7 (the value can occur only once in the column)<br>(17) If E5 contains the value 3 (2), then E5 cannot contain the value 8 (the cell can contain only one value)<br>(18) If E5 does not contain the value 8, then E4 must contain the value 8 (only remaining possible position in the block)<br>(19) If E4 contains the value 8, then G4 cannot contain the value 8 (the value can occur only once in the row)<br>(20) If G4 does not contain the value 8 and G4 does not contain the value 7 (16), then G4 must contain the value 2 (only remaining possible value in the cell)<br>(21) If G4 contains the value 2, then I5 cannot contain the value 2 (the value can occur only once in the block)<br>(22) If D9 contains the value 8 (13), then D8 cannot contain the value 8 (the value can occur only once in the block)<br>(23) If D6 contains the value 6 (initial assumption), then D8 cannot contain the value 6 (the value can occur only once in the column)<br>(24) If D8 does not contain the value 6 and D8 does not contain the value 8 (22), then D8 must contain the value 2 (only remaining possible value in the cell)<br>(25) If D8 contains the value 2, then F7 cannot contain the value 2 (the value can occur only once in the block)<br>(26) If F7 does not contain the value 2, then B7 must contain the value 2 (only remaining possible position in the row)<br>(27) If B7 contains the value 2, then B5 cannot contain the value 2 (the value can occur only once in the column)<br>(28) If B5 does not contain the value 2 and I5 does not contain the value 2 (21), then A5 must contain the value 2 (only remaining possible position in the row)<br>(29) If A5 contains the value 2, then A3 cannot contain the value 2 (the value can occur only once in the column)<br>(30) If B7 contains the value 2 (26), then B3 cannot contain the value 2 (the value can occur only once in the column)<br>(31) If D8 contains the value 2 (24), then D3 cannot contain the value 2 (the value can occur only once in the column)<br>(32) If G4 contains the value 2 (20), then G3 cannot contain the value 2 (the value can occur only once in the column)<br>(33) If G9 contains the value 7 (15), then H8 cannot contain the value 7 (the value can occur only once in the block)<br>(34) If E4 contains the value 8 (18), then E4 cannot contain the value 7 (the cell can contain only one value)<br>(35) If E4 does not contain the value 7, then F6 must contain the value 7 (only remaining possible position in the block)<br>(36) If F6 contains the value 7, then H6 cannot contain the value 7 (the value can occur only once in the row)<br>(37) If H6 does not contain the value 7 and H8 does not contain the value 7 (33), then H3 must contain the value 7 (only remaining possible position in the column)<br>(38) If H3 contains the value 7, then H3 cannot contain the value 9 (the cell can contain only one value)<br>(39) If H3 does not contain the value 9, then I3 must contain the value 9 (only remaining possible position in the block)<br>(40) If I3 contains the value 9, then I3 cannot contain the value 2 (the cell can contain only one value)<br>(41) If I3 does not contain the value 2, G3 does not contain the value 2 (32), D3 does not contain the value 2 (31), B3 does not contain the value 2 (30) and A3 does not contain the value 2 (29), then F3 must contain the value 2 (only remaining possible position in the row)<br><br>
Chain 15: <b>If D6 contains the value 6, then F3 cannot contain the value 2</b> (View 15):<br>
(1) If D6 contains the value 6, then D6 cannot contain the value 3 (the cell can contain only one value)<br>(2) If D6 does not contain the value 3, then E5 must contain the value 3 (only remaining possible position in the block)<br>(3) If E5 contains the value 3, then E1 cannot contain the value 3 (the value can occur only once in the column)<br>(4) If E1 does not contain the value 3, then E1 must contain the value 6 (only remaining possible value in the cell)<br>(5) If E1 contains the value 6, then F1 cannot contain the value 6 (the value can occur only once in the block)<br>(6) If D6 contains the value 6 (initial assumption), then F5 cannot contain the value 6 (the value can occur only once in the block)<br>(7) If D6 contains the value 6 (initial assumption), then F6 cannot contain the value 6 (the value can occur only once in the block)<br>(8) If F6 does not contain the value 6, F5 does not contain the value 6 (6) and F1 does not contain the value 6 (5), then F7 must contain the value 6 (only remaining possible position in the column)<br>(9) If F7 contains the value 6, then H7 cannot contain the value 6 (the value can occur only once in the row)<br>(10) If H7 does not contain the value 6, then H7 must contain the value 1 (only remaining possible value in the cell)<br>(11) If H7 contains the value 1, then G9 cannot contain the value 1 (the value can occur only once in the block)<br>(12) If D6 contains the value 6 (initial assumption), then D9 cannot contain the value 6 (the value can occur only once in the column)<br>(13) If D9 does not contain the value 6, then D9 must contain the value 8 (only remaining possible value in the cell)<br>(14) If D9 contains the value 8, then G9 cannot contain the value 8 (the value can occur only once in the row)<br>(15) If G9 does not contain the value 8 and G9 does not contain the value 1 (11), then G9 must contain the value 7 (only remaining possible value in the cell)<br>(16) If G9 contains the value 7, then H8 cannot contain the value 7 (the value can occur only once in the block)<br>(17) If E5 contains the value 3 (2), then E5 cannot contain the value 8 (the cell can contain only one value)<br>(18) If E5 does not contain the value 8, then E4 must contain the value 8 (only remaining possible position in the block)<br>(19) If E4 contains the value 8, then E4 cannot contain the value 7 (the cell can contain only one value)<br>(20) If E4 does not contain the value 7, then F6 must contain the value 7 (only remaining possible position in the block)<br>(21) If F6 contains the value 7, then H6 cannot contain the value 7 (the value can occur only once in the row)<br>(22) If H6 does not contain the value 7 and H8 does not contain the value 7 (16), then H3 must contain the value 7 (only remaining possible position in the column)<br>(23) If H3 contains the value 7, then H3 cannot contain the value 9 (the cell can contain only one value)<br>(24) If H3 does not contain the value 9, then I3 must contain the value 9 (only remaining possible position in the block)<br>(25) If I3 contains the value 9, then I3 cannot contain the value 8 (the cell can contain only one value)<br>(26) If G9 contains the value 7 (15), then G8 cannot contain the value 7 (the value can occur only once in the block)<br>(27) If F7 contains the value 6 (8), then I7 cannot contain the value 6 (the value can occur only once in the row)<br>(28) If I7 does not contain the value 6, then I7 must contain the value 3 (only remaining possible value in the cell)<br>(29) If I7 contains the value 3, then G8 cannot contain the value 3 (the value can occur only once in the block)<br>(30) If G8 does not contain the value 3 and G8 does not contain the value 7 (26), then G8 must contain the value 8 (only remaining possible value in the cell)<br>(31) If G8 contains the value 8, then G3 cannot contain the value 8 (the value can occur only once in the column)<br>(32) If H3 contains the value 7 (22), then H3 cannot contain the value 8 (the cell can contain only one value)<br>(33) If H3 does not contain the value 8, G3 does not contain the value 8 (31) and I3 does not contain the value 8 (25), then F3 must contain the value 8 (only remaining possible position in the row)<br>(34) If F3 contains the value 8, then F3 cannot contain the value 2 (the cell can contain only one value)<br><br>
</body>
</html>
%g: 98.7.....7.....6....6.5.....4...5.3...79..5......2...1..85..9......1...4.....3.2.;11.90;11.90;11.80;GP;champagne dry;1;22;
%i: 98.7.....7.....6....6.5.....4...5.3...79..5......2...1..85..9......1...4.....3.2.
%m: ........9......7..1234.....12...6.8.123..6.8...3.56.8.1234.6....23.56...1..456..........8.123.5....123.........4.....123..6.....3.56..9123..67...23.567.91...567.912345....12345.........6...12......9......7....3.5...9.......8..23.5...91..45...9......7..1234...8.1234...8.1....6.8.........9..34.6.8.....5.....2...6.8....4.6.8...34.6.....34...89....5.........678...34.6.8..2..........4.67..1.............678912.4.6...12.4...8912.4...89....5....1..4.6.8....4.678..2.4.67...2...6789..3......1234..........6...1234..78..2....78.....5.......4..78.........9..3...78.1.....78.1..45....1..45..891..4..789..3.........4.6.8....4.67891....67......5678..2........23.5.....23.5..89.23...789.2...6789.2...6.8.1..........3..67.....4.........5678.
%M:
+----------------------+----------------------+----------------------+
| 9 8 12345 | 7 346 1246 | 1234 145 235 |
| 7 1235 12345 | 12348 3489 12489 | 6 14589 23589 |
| 1234 123 6 | 12348 5 12489 | 123478 14789 23789 |
+----------------------+----------------------+----------------------+
| 1268 4 129 | 168 678 5 | 278 3 26789 |
| 12368 1236 7 | 9 3468 1468 | 5 468 268 |
| 3568 3569 359 | 3468 2 4678 | 478 46789 1 |
+----------------------+----------------------+----------------------+
| 12346 12367 8 | 5 467 2467 | 9 167 367 |
| 2356 235679 2359 | 268 1 26789 | 378 5678 4 |
| 1456 15679 1459 | 468 6789 3 | 178 2 5678 |
+----------------------+----------------------+----------------------+
%r: 11.8
%s: Contradiction Forcing Chain: E9.4 on ==> D6.6 both on & off
--- end of after section ---
... more similar records ...
--before
%g: 98.7.....7.....6....6.5.....4...5.3...79..5......2...1..85..9......1...4.....3.2.;11.90;11.90;11.80;GP;champagne dry;1;22;
%i: 98173624573549261842615839714268573936794158285932746121856497367321985459.873126
%m: ........9......7.....4.....1..........3.............8..2............6.......5...........8...3.......2..........4..........6.......5....1..............7..........91............5.........6....2.............7..........9.......8...3.........4...........7.....4.....1.............6...........9..3..........5.....2..............8...3..............9....5...........8....4......2............6...1..............7.......6....2..............8.....5....1..............7.....4.............9..3.......2............6.....3............7......5.......4.............9.......8.1...........4.....1................9..3.............8......6.........7......5.....2...........5...........8.......7..........9.2.......1..........3.........4..........6...
%M:
--- end of before section ---
--after%e: 0.00s
%h:
<html>
<body>
<h2>Single</h2>
<p>
The <font color="#00AAAA">cell <b>C9</b></font> is the only remaining empty cell of the <font color="#0000A0">block</font>.
Its only possible value is the <font color="#009000">value <b>4</b></font>.
</p>
</body>
</html>
%g: 98.7.....7.....6....6.5.....4...5.3...79..5......2...1..85..9......1...4.....3.2.;11.90;11.90;11.80;GP;champagne dry;1;22;
%i: 981736245735492618426158397142685739367941582859327461218564973673219854594873126
%m: ........9......7.....4.....1..........3.............8..2............6.......5...........8...3.......2..........4..........6.......5....1..............7..........91............5.........6....2.............7..........9.......8...3.........4...........7.....4.....1.............6...........9..3..........5.....2..............8...3..............9....5...........8....4......2............6...1..............7.......6....2..............8.....5....1..............7.....4.............9..3.......2............6.....3............7......5.......4.............9.......8.1...........4.....1................9..3.............8......6.........7......5.....2...........5...........8.......7..........9.2.......1..........3.........4..........6...
%M:
%r: 1.0
%s: Hidden Single: C9: 4 in block
--- end of after section ---
--format
%d: 11.8
%D: Dynamic Contradiction Forcing Chains (+ Dynamic Forcing Chains)
%e: 10m19s
%g: 98.7.....7.....6....6.5.....4...5.3...79..5......2...1..85..9......1...4.....3.2.;11.90;11.90;11.80;GP;champagne dry;1;22;
%i: 981736245735492618426158397142685739367941582859327461218564973673219854594873126
%n: 1
%p: 11.9
%P: Dynamic Contradiction Forcing Chains (+ Dynamic Forcing Chains)
%r: 11.9
%R: Dynamic Contradiction Forcing Chains (+ Dynamic Forcing Chains)
%S: DCFC+DFC
%T: DCFC+DFC
%U: DCFC+DFC
--- end of final section ---