Analysis of zz-www.sudokuoftheday.co.uk-20190412-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019

position: ..87..6...61.........14.....5...73.93..9....7.9.....2.7..6....49.5...8...1...3... initial

Autosolve

position: .387..6.1.61.......79146....5...73.93..9....7.97....2.7.36....49.5.718...1...3... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 2,5 => CTR => A1: 4
* DIS # H2: 4,9 => CTR => H2: 7
* DIS # D2: 2,5 => CTR => D2: 3,8
* DIS # E2: 2,5 => CTR => E2: 3,8,9
* DIS # F2: 2,5 => CTR => F2: 8,9
* DIS # G7: 2,5 => CTR => G7: 1,9
* DIS # G9: 2,5 => CTR => G9: 7,9
* DIS # D2: 2,8 => CTR => D2: 3,5
* DIS # D9: 2,8 => CTR => D9: 4,5
* DIS # H4: 6,8 => CTR => H4: 1,4
* DIS # B5: 4 => CTR => B5: 2,8
* DIS # D9: 5,8 => CTR => D9: 2,4
* DIS # G7: 2,5 => CTR => G7: 1,9
* DIS # G9: 2,5 => CTR => G9: 7,9
* DIS # D9: 2,5 => CTR => D9: 4,8
* DIS # E9: 2,5 => CTR => E9: 8,9
* CNT  16 HDP CHAINS /  49 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # A1: 2,5 => CTR => A1: 4
* DIS A1: 4 # G7: 2,5 => CTR => G7: 1,9
* DIS A1: 4 + G7: 1,9 # G9: 2,5 => CTR => G9: 7,9
* DIS A1: 4 + G7: 1,9 + G9: 7,9 # E4: 2,8 => CTR => E4: 1,6
* DIS A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 # E5: 2,8 => CTR => E5: 1,5,6
* DIS A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 # F5: 4,5 => CTR => F5: 2,8
* DIS A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 + F5: 2,8 # H4: 6,8 => CTR => H4: 1,4
* PRF A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 + F5: 2,8 + H4: 1,4 => SOL
* STA A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 + F5: 2,8 + H4: 1,4
* CNT   8 HDP CHAINS /   9 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Details

Positions

..87..6...61.........14.....5...73.93..9....7.9.....2.7..6....49.5...8...1...3... initial
.387..6.1.61.......79146....5...73.93..9....7.97....2.7.36....49.5.718...1...3... autosolve
438725691261389475579146283152867349384912567697534128723658914945271836816493752 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
A3: 2,5
H1: 4,9
I2: 2,5
G3: 2,5
H3: 3,8
I3: 3,8
D4: 2,8
I6: 6,8
B7: 2,8
B8: 2,4
A9: 6,8
D8: 2,4
H8: 3,6
I8: 3,6
I9: 2,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A4,A6: 1.. / A4 = 1  => 18 pairs (_) / A6 = 1  => 17 pairs (_)
G7,H7: 1.. / G7 = 1  =>  0 pairs (X) / H7 = 1  => 15 pairs (_)
I2,G3: 2.. / I2 = 2  =>  0 pairs (X) / G3 = 2  => 15 pairs (_)
A3,G3: 2.. / A3 = 2  =>  0 pairs (X) / G3 = 2  => 15 pairs (_)
B8,D8: 2.. / B8 = 2  =>  0 pairs (X) / D8 = 2  => 18 pairs (_)
I2,I9: 2.. / I2 = 2  =>  0 pairs (X) / I9 = 2  => 15 pairs (_)
D2,E2: 3.. / D2 = 3  => 18 pairs (_) / E2 = 3  => 15 pairs (_)
H3,I3: 3.. / H3 = 3  => 11 pairs (_) / I3 = 3  => 13 pairs (_)
D6,E6: 3.. / D6 = 3  => 15 pairs (_) / E6 = 3  => 18 pairs (_)
H8,I8: 3.. / H8 = 3  => 13 pairs (_) / I8 = 3  => 11 pairs (_)
D2,D6: 3.. / D2 = 3  => 18 pairs (_) / D6 = 3  => 15 pairs (_)
E2,E6: 3.. / E2 = 3  => 15 pairs (_) / E6 = 3  => 18 pairs (_)
H3,H8: 3.. / H3 = 3  => 11 pairs (_) / H8 = 3  => 13 pairs (_)
I3,I8: 3.. / I3 = 3  => 13 pairs (_) / I8 = 3  => 11 pairs (_)
A1,A2: 4.. / A1 = 4  => 23 pairs (_) / A2 = 4  =>  0 pairs (X)
F5,F6: 4.. / F5 = 4  =>  0 pairs (X) / F6 = 4  => 16 pairs (_)
B8,C9: 4.. / B8 = 4  => 18 pairs (_) / C9 = 4  =>  0 pairs (X)
D8,D9: 4.. / D8 = 4  =>  0 pairs (X) / D9 = 4  => 18 pairs (_)
A1,H1: 4.. / A1 = 4  => 23 pairs (_) / H1 = 4  =>  0 pairs (X)
C4,H4: 4.. / C4 = 4  =>  0 pairs (X) / H4 = 4  =>  0 pairs (_)
F6,G6: 4.. / F6 = 4  => 16 pairs (_) / G6 = 4  =>  0 pairs (X)
B8,D8: 4.. / B8 = 4  => 18 pairs (_) / D8 = 4  =>  0 pairs (X)
C9,D9: 4.. / C9 = 4  =>  0 pairs (X) / D9 = 4  => 18 pairs (_)
B5,B8: 4.. / B5 = 4  =>  0 pairs (X) / B8 = 4  => 18 pairs (_)
I2,G3: 5.. / I2 = 5  => 15 pairs (_) / G3 = 5  =>  0 pairs (X)
A3,G3: 5.. / A3 = 5  => 15 pairs (_) / G3 = 5  =>  0 pairs (X)
I2,I9: 5.. / I2 = 5  => 15 pairs (_) / I9 = 5  =>  0 pairs (X)
A9,C9: 6.. / A9 = 6  => 17 pairs (_) / C9 = 6  => 13 pairs (_)
H8,I8: 6.. / H8 = 6  => 11 pairs (_) / I8 = 6  => 13 pairs (_)
I6,I8: 6.. / I6 = 6  => 11 pairs (_) / I8 = 6  => 13 pairs (_)
G2,H2: 7.. / G2 = 7  =>  0 pairs (X) / H2 = 7  => 17 pairs (_)
G9,H9: 7.. / G9 = 7  => 17 pairs (_) / H9 = 7  =>  0 pairs (X)
G2,G9: 7.. / G2 = 7  =>  0 pairs (X) / G9 = 7  => 17 pairs (_)
H2,H9: 7.. / H2 = 7  => 17 pairs (_) / H9 = 7  =>  0 pairs (X)
H3,I3: 8.. / H3 = 8  => 13 pairs (_) / I3 = 8  => 11 pairs (_)
B7,A9: 8.. / B7 = 8  => 17 pairs (_) / A9 = 8  => 13 pairs (_)
B5,B7: 8.. / B5 = 8  => 13 pairs (_) / B7 = 8  => 17 pairs (_)
I3,I6: 8.. / I3 = 8  => 11 pairs (_) / I6 = 8  => 13 pairs (_)
* DURATION: 0:00:50.389912  START: 05:14:20.085091  END: 05:15:10.475003 2019-05-01
* CP COUNT: (38)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A9,B7,B8,D4,D8,G3,H1,H3,H8,I2,I3,I6,I8,I9)
* .387..6.1.61.......79146....5...73.93..9....7.97....2.7.36....49.5.718...1...3...
* PAIR A3: 2,5 BLK 1
A1: 2,5,4                                # reduction candidate for 2,5
A1: 2,5 => CTR
* .387..641461538..22791465...548273.93..9...57.973.54287.3659.149452718.681.4.3...
A1: 4                                    # 23 pairs
A2: 2,5,4                                # reduction candidate for 2,5
A2: 2,5                                  # 23 pairs
* PAIR H1: 4,9 BLK 3
G2: 4,9,7                                # reduction candidate for 4,9
G2: 4,9                                  # 17 pairs
H2: 4,9,7                                # reduction candidate for 4,9
H2: 4,9 => CTR
* .387..6.1.615387922791465...548273.93..9...57.973.54287.3659.149452718.681.4.3.7.
H2: 7                                    # 17 pairs
* PAIR I2: 2,5 ROW 2
A2: 2,5,4                                # reduction candidate for 2,5
A2: 2,5                                  # 23 pairs
D2: 2,5,3,8                              # reduction candidate for 2,5
D2: 2,5 => CTR
* .387..641461538..22791465...548273.93..9...57.973...287.36....49452718.68164.3275
D2: 3,8                                  # 16 pairs
E2: 2,5,3,8,9                            # reduction candidate for 2,5
E2: 2,5 => CTR
* .387..6414613.8....79146....548273.93..9....7.97.3..2.7.36....49452718...1.4.3...
E2: 3,8,9                                # 15 pairs
F2: 2,5,8,9                              # reduction candidate for 2,5
F2: 2,5 => CTR
* .387..641461.......79146....548273.93..9....7.97534.2.7.36....49452718...1.4.3...
F2: 8,9                                  # 16 pairs
* PAIR G3: 2,5 COL G
G7: 2,5,1,9                              # reduction candidate for 2,5
G7: 2,5 => CTR
* 538792641.61.......79146....54827369382964157697.154287236..514945271836816453..2
G7: 1,9                                  # 18 pairs
G9: 2,5,7,9                              # reduction candidate for 2,5
G9: 2,5 => CTR
* .387..6.1.61...7...79146....54827369382964157697.1542872365.9149452718..816493.7.
G9: 7,9                                  # 16 pairs
* PAIR D4: 2,8 BLK 5
E4: 2,8,1,6                              # reduction candidate for 2,8
E4: 2,8                                  # 24 pairs
E5: 2,8,1,5,6                            # reduction candidate for 2,8
E5: 2,8                                  # 22 pairs
F5: 2,8,4,5                              # reduction candidate for 2,8
F5: 2,8                                  # 19 pairs
* PAIR D4: 2,8 COL D
D2: 2,8,3,5                              # reduction candidate for 2,8
D2: 2,8 => CTR
* 4387..6912618394755791462...5...734934.9....7.973.4.2.7836....49254718..614583..2
D2: 3,5                                  # 16 pairs
D9: 2,8,4,5                              # reduction candidate for 2,8
D9: 2,8 => CTR
* 4387..691261389475579146238.5...734934.9....7.975341267836..914925471863614893752
D9: 4,5                                  # 16 pairs
* PAIR I6: 6,8 BLK 6
H4: 6,8,1,4                              # reduction candidate for 6,8
H4: 6,8 => CTR
* .387.26.1.61538..227914658315482736938296..57697315.2872368...49452718368164.3...
H4: 1,4                                  # 19 pairs
H5: 6,8,1,4,5                            # reduction candidate for 6,8
H5: 6,8                                  # 19 pairs
* PAIR I6: 6,8 ROW 6
A6: 6,8,1                                # reduction candidate for 6,8
A6: 6,8                                  # 18 pairs
E6: 6,8,1,3,5                            # reduction candidate for 6,8
E6: 6,8                                  # 19 pairs
* PAIR B7: 2,8 ROW 7
E7: 2,8,5,9                              # reduction candidate for 2,8
E7: 2,8                                  # 19 pairs
F7: 2,8,5,9                              # reduction candidate for 2,8
F7: 2,8                                  # 20 pairs
* PAIR B7: 2,8 COL B
B5: 2,8,4                                # reduction candidate for 2,8
B5: 4 => CTR
* 4387..691.61..94755791462...5...734934.9.8.67.975.4.2.7836..9149254718..614.93752
B5: 2,8                                  # 18 pairs
* PAIR B8: 2,4 BLK 7
C9: 2,4,6                                # reduction candidate for 2,4
C9: 2,4                                  # 17 pairs
C9: 6                                    # 13 pairs
* PAIR B8: 2,4 COL B
B5: 2,4,8                                # reduction candidate for 2,4
B5: 2,4                                  # 17 pairs
B5: 8                                    # 13 pairs
* PAIR A9: 6,8 COL A
A4: 6,8,1                                # reduction candidate for 6,8
A4: 6,8                                  # 17 pairs
A6: 6,8,1                                # reduction candidate for 6,8
A6: 6,8                                  # 18 pairs
* PAIR D8: 2,4 BLK 8
D9: 2,4,5,8                              # reduction candidate for 2,4
D9: 5,8 => CTR
* 4387..691261389475579146238.5...734934.9....7.975341267836..914925471863614893752
D9: 2,4                                  # 19 pairs
* PAIR I9: 2,5 BLK 9
G7: 2,5,1,9                              # reduction candidate for 2,5
G7: 2,5 => CTR
* 538792641.61.......79146....54827369382964157697.154287236..514945271836816453..2
G7: 1,9                                  # 18 pairs
G9: 2,5,7,9                              # reduction candidate for 2,5
G9: 2,5 => CTR
* .387..6.1.61...7...79146....54827369382964157697.1542872365.9149452718..816493.7.
G9: 7,9                                  # 16 pairs
* PAIR I9: 2,5 ROW 9
D9: 2,5,4,8                              # reduction candidate for 2,5
D9: 2,5 => CTR
* 4387..691.61...47..79146....5...734934.9....7.97..4.2.7836....49254718..614.83...
D9: 4,8                                  # 18 pairs
E9: 2,5,8,9                              # reduction candidate for 2,5
E9: 2,5 => CTR
* .387..6.1.61.....55791462...548273.93829....7.97534.2.7236....49452718..816453..2
E9: 8,9                                  # 16 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190412-absurd-base-pr-000.dot
* REASONING
* DIS # A1: 2,5 => CTR => A1: 4
* DIS # H2: 4,9 => CTR => H2: 7
* DIS # D2: 2,5 => CTR => D2: 3,8
* DIS # E2: 2,5 => CTR => E2: 3,8,9
* DIS # F2: 2,5 => CTR => F2: 8,9
* DIS # G7: 2,5 => CTR => G7: 1,9
* DIS # G9: 2,5 => CTR => G9: 7,9
* DIS # D2: 2,8 => CTR => D2: 3,5
* DIS # D9: 2,8 => CTR => D9: 4,5
* DIS # H4: 6,8 => CTR => H4: 1,4
* DIS # B5: 4 => CTR => B5: 2,8
* DIS # D9: 5,8 => CTR => D9: 2,4
* DIS # G7: 2,5 => CTR => G7: 1,9
* DIS # G9: 2,5 => CTR => G9: 7,9
* DIS # D9: 2,5 => CTR => D9: 4,8
* DIS # E9: 2,5 => CTR => E9: 8,9
* CNT  16 HDP CHAINS /  49 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A9,B7,B8,D4,D8,G3,H1,H3,H8,I2,I3,I6,I8,I9)
* .387..6.1.61.......79146....5...73.93..9....7.97....2.7.36....49.5.718...1...3...
* PAIR A3: 2,5 BLK 1
A1: 2,5,4                                # reduction candidate for 2,5
A1: 2,5 => CTR
* .387..641461538..22791465...548273.93..9...57.973.54287.3659.149452718.681.4.3...
* RESTART
* PAIR G3: 2,5 COL G
G7: 2,5,1,9                              # reduction candidate for 2,5
G7: 2,5 => CTR
* 4387..691.61...74..79146....548273693829641576975...2.7.36...149452718...1.4.397.
G9: 2,5,7,9                              # reduction candidate for 2,5
G9: 2,5 => CTR
* 4387.2691.61..974..79146....5482736938296.1576975...2.7236..9149452718..816493.7.
* PAIR RESTART
* PAIR D4: 2,8 BLK 5
E4: 2,8,1,6                              # reduction candidate for 2,8
E4: 2,8 => CTR
* 438752691261.39..55791462...5...73.93.29....7.973...2.7.36.8.549.5.718..816..3..2
E5: 2,8,1,5,6                            # reduction candidate for 2,8
E5: 2,8 => CTR
* 438752691261.39..55791462...5...73.93..9....7.973...2.7.36.8.549.5.718..816..3..2
F5: 2,8,4,5                              # reduction candidate for 2,8
F5: 2,8                                  # 26 pairs
* RESTART
* PAIR D4: 2,8 BLK 5
F5: 2,8,4,5                              # reduction candidate for 2,8
F5: 4,5 => CTR
* 4387..691261.....55791462...562173493429.5187197..45267836..9149254718636145.3..2
* PAIR I6: 6,8 BLK 6
H4: 6,8,1,4                              # reduction candidate for 6,8
H4: 6,8 => CTR
* 4387..691261.....55791462...542.73.938.9....7.97..4.2.7.36....49.5.718...1...3..2
H4: 1,4 => SOLVED
* 438725691261389475579146283152867349384912567697534128723658914945271836816493752
* DURATION: 0:00:09.247265  START: 05:15:44.940227  END: 05:15:54.187492 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190412-absurd-base-pr-001.dot
* REASONING
* DIS # A1: 2,5 => CTR => A1: 4
* DIS A1: 4 # G7: 2,5 => CTR => G7: 1,9
* DIS A1: 4 + G7: 1,9 # G9: 2,5 => CTR => G9: 7,9
* DIS A1: 4 + G7: 1,9 + G9: 7,9 # E4: 2,8 => CTR => E4: 1,6
* DIS A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 # E5: 2,8 => CTR => E5: 1,5,6
* DIS A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 # F5: 4,5 => CTR => F5: 2,8
* DIS A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 + F5: 2,8 # H4: 6,8 => CTR => H4: 1,4
* PRF A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 + F5: 2,8 + H4: 1,4 => SOL
* STA A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 + F5: 2,8 + H4: 1,4
* CNT   8 HDP CHAINS /   9 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190412, absurd

Solution

position: 438725691261389475579146283152867349384912567697534128723658914945271836816493752 solved
Solution

See section Pair Reduction for the HDP chains leading to this result.

Appendix: Full HDP Chains

A1. Pair Reduction Analysis

Full list of HDP chains traversed:

* DIS # A1: 2,5 => CTR => A1: 4
* INC # A1: 4 => UNS
* INC # A2: 2,5 => UNS
* INC # G2: 4,9 => UNS
* DIS # H2: 4,9 => CTR => H2: 7
* INC # H2: 7 => UNS
* INC # A2: 2,5 => UNS
* DIS # D2: 2,5 => CTR => D2: 3,8
* INC # D2: 3,8 => UNS
* DIS # E2: 2,5 => CTR => E2: 3,8,9
* INC # E2: 3,8,9 => UNS
* DIS # F2: 2,5 => CTR => F2: 8,9
* INC # F2: 8,9 => UNS
* DIS # G7: 2,5 => CTR => G7: 1,9
* INC # G7: 1,9 => UNS
* DIS # G9: 2,5 => CTR => G9: 7,9
* INC # G9: 7,9 => UNS
* INC # E4: 2,8 => UNS
* INC # E5: 2,8 => UNS
* INC # F5: 2,8 => UNS
* DIS # D2: 2,8 => CTR => D2: 3,5
* INC # D2: 3,5 => UNS
* DIS # D9: 2,8 => CTR => D9: 4,5
* INC # D9: 4,5 => UNS
* DIS # H4: 6,8 => CTR => H4: 1,4
* INC # H4: 1,4 => UNS
* INC # H5: 6,8 => UNS
* INC # A6: 6,8 => UNS
* INC # E6: 6,8 => UNS
* INC # E7: 2,8 => UNS
* INC # F7: 2,8 => UNS
* INC # B5: 2,8 => UNS
* DIS # B5: 4 => CTR => B5: 2,8
* INC # C9: 2,4 => UNS
* INC # C9: 6 => UNS
* INC # B5: 2,4 => UNS
* INC # B5: 8 => UNS
* INC # A4: 6,8 => UNS
* INC # A6: 6,8 => UNS
* INC # D9: 2,4 => UNS
* DIS # D9: 5,8 => CTR => D9: 2,4
* DIS # G7: 2,5 => CTR => G7: 1,9
* INC # G7: 1,9 => UNS
* DIS # G9: 2,5 => CTR => G9: 7,9
* INC # G9: 7,9 => UNS
* DIS # D9: 2,5 => CTR => D9: 4,8
* INC # D9: 4,8 => UNS
* DIS # E9: 2,5 => CTR => E9: 8,9
* INC # E9: 8,9 => UNS
* CNT  49 HDP CHAINS /  49 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A1: 2,5 => CTR => A1: 4
* DIS A1: 4 # G7: 2,5 => CTR => G7: 1,9
* DIS A1: 4 + G7: 1,9 # G9: 2,5 => CTR => G9: 7,9
* DIS A1: 4 + G7: 1,9 + G9: 7,9 # E4: 2,8 => CTR => E4: 1,6
* DIS A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 # E5: 2,8 => CTR => E5: 1,5,6
* INC A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 # F5: 2,8 => UNS
* INC A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 # F5: 2,8 => UNS
* DIS A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 # F5: 4,5 => CTR => F5: 2,8
* DIS A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 + F5: 2,8 # H4: 6,8 => CTR => H4: 1,4
* PRF A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 + F5: 2,8 + H4: 1,4 => SOL
* STA A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 + F5: 2,8 + H4: 1,4
* CNT  10 HDP CHAINS /   9 HYP OPENED