Analysis of zz-www.sudokuoftheday.co.uk-20190312-absurd-base.sdk

Contents

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

level: medium

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

position: .4.2.......8...3....918...2..3..1......745.3..5.9....7.92...7..6....9.1448......3 initial

Autosolve

position: .4.2.......8...3....918...2..3..1......745.3..549....7.92...7..6....9.1448......3 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C1: 1,6 => CTR => C1: 5,7
* DIS # F6: 6,8 => CTR => F6: 2,3
* PRF # F6: 2,3 => SOL
* DIS # G4: 6,8 => CTR => G4: 2,4,5,9
* DIS # H4: 6,8 => CTR => H4: 2,4,5,9
* DIS # I4: 6,8 => CTR => I4: 5,9
* DIS # E6: 2,6 => CTR => E6: 3
* PRF # F6: 2,6 => SOL
* DIS # F6: 3,8 => CTR => F6: 2,6
* PRF # B4: 2,6 => SOL
* DIS # B4: 7 => CTR => B4: 2,6
* DIS # G4: 2,6 => CTR => G4: 4,5,8,9
* DIS # H4: 2,6 => CTR => H4: 4,5,8,9
* DIS # E9: 2,6 => CTR => E9: 1,5,7
* PRF # B3: 3,7 => SOL
* DIS # B3: 6 => CTR => B3: 3,7
* DIS # C9: 5,7 => CTR => C9: 1
* DIS # E8: 5,7 => CTR => E8: 2
* PRF # E8: 2 => SOL
* DIS # C1: 1,6 => CTR => C1: 5,7
* PRF # D7: 4,8 => SOL
* DIS # D7: 3 => CTR => D7: 4,8
* DIS # D7: 3,8 => CTR => D7: 4
* PRF # D7: 4 => SOL
* DIS # E7: 5,6 => CTR => E7: 1
* PRF # E9: 5,6 => SOL
* DIS # G9: 5,6 => CTR => G9: 2,9
* DIS # H9: 5,6 => CTR => H9: 2,9
* PRF # D2: 5,6 => SOL
* DIS # D2: 4 => CTR => D2: 5,6
* CNT  30 HDP CHAINS /  48 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 # C1: 1,6 => CTR => C1: 5,7
* DIS C1: 5,7 # F6: 6,8 => CTR => F6: 2,3
* PRF C1: 5,7 + F6: 2,3 => SOL
* STA C1: 5,7 + F6: 2,3
* CNT   3 HDP CHAINS /   6 HYP OPENED

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

Details

Positions

.4.2.......8...3....918...2..3..1......745.3..5.9....7.92...7..6....9.1448......3 initial
.4.2.......8...3....918...2..3..1......745.3..549....7.92...7..6....9.1448......3 autosolve
147293685268574391539186472723861549916745238854932167392418756675329814481657923 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
C5: 1,6
D4: 6,8
E4: 2,6
B8: 3,7
C8: 5,7
F7: 4,8
D8: 3,8
D9: 5,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A7,C9: 1.. / A7 = 1  =>  0 pairs (X) / C9 = 1  => 12 pairs (_)
E7,E9: 1.. / E7 = 1  => 12 pairs (_) / E9 = 1  =>  0 pairs (X)
A6,G6: 1.. / A6 = 1  =>  0 pairs (X) / G6 = 1  =>  9 pairs (_)
A7,E7: 1.. / A7 = 1  =>  0 pairs (X) / E7 = 1  => 12 pairs (_)
C9,E9: 1.. / C9 = 1  => 12 pairs (_) / E9 = 1  =>  0 pairs (X)
B2,B5: 1.. / B2 = 1  => 10 pairs (_) / B5 = 1  => 10 pairs (_)
A2,B2: 2.. / A2 = 2  =>  9 pairs (_) / B2 = 2  =>  0 pairs (X)
E8,G8: 2.. / E8 = 2  =>  0 pairs (*) / G8 = 2  =>  0 pairs (X)
F6,F9: 2.. / F6 = 2  =>  0 pairs (*) / F9 = 2  =>  0 pairs (X)
E6,F6: 3.. / E6 = 3  =>  8 pairs (_) / F6 = 3  =>  0 pairs (X)
A7,B8: 3.. / A7 = 3  =>  0 pairs (*) / B8 = 3  =>  0 pairs (X)
D7,D8: 3.. / D7 = 3  =>  0 pairs (X) / D8 = 3  =>  0 pairs (_)
A7,D7: 3.. / A7 = 3  =>  0 pairs (*) / D7 = 3  =>  0 pairs (X)
B8,D8: 3.. / B8 = 3  =>  0 pairs (X) / D8 = 3  =>  0 pairs (_)
B3,B8: 3.. / B3 = 3  =>  0 pairs (*) / B8 = 3  =>  0 pairs (X)
E1,E6: 3.. / E1 = 3  =>  0 pairs (X) / E6 = 3  =>  8 pairs (_)
G4,H4: 4.. / G4 = 4  =>  9 pairs (_) / H4 = 4  =>  8 pairs (_)
D7,F7: 4.. / D7 = 4  =>  0 pairs (*) / F7 = 4  =>  0 pairs (X)
D2,D7: 4.. / D2 = 4  =>  0 pairs (X) / D7 = 4  =>  0 pairs (_)
G3,G4: 4.. / G3 = 4  =>  8 pairs (_) / G4 = 4  =>  9 pairs (_)
D2,D9: 5.. / D2 = 5  =>  0 pairs (*) / D9 = 5  =>  0 pairs (X)
C1,C5: 6.. / C1 = 6  =>  0 pairs (X) / C5 = 6  =>  9 pairs (_)
A4,B4: 7.. / A4 = 7  =>  0 pairs (*) / B4 = 7  =>  0 pairs (X)
D4,F6: 8.. / D4 = 8  =>  0 pairs (*) / F6 = 8  =>  0 pairs (X)
D8,G8: 8.. / D8 = 8  =>  0 pairs (X) / G8 = 8  =>  0 pairs (_)
F6,F7: 8.. / F6 = 8  =>  0 pairs (X) / F7 = 8  =>  0 pairs (_)
E1,E2: 9.. / E1 = 9  =>  8 pairs (_) / E2 = 9  =>  8 pairs (_)
A4,A5: 9.. / A4 = 9  =>  0 pairs (X) / A5 = 9  => 10 pairs (_)
G9,H9: 9.. / G9 = 9  =>  8 pairs (_) / H9 = 9  => 12 pairs (_)
* DURATION: 0:00:34.187588  START: 04:27:22.270340  END: 04:27:56.457928 2019-05-01
* CP COUNT: (29)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,C5,C8,D4,D8,D9,E4,F7)
* .4.2.......8...3....918...2..3..1......745.3..549....7.92...7..6....9.1448......3
* PAIR C5: 1,6 BLK 4
B5: 1,6,2                                # reduction candidate for 1,6
B5: 1,6                                  # 12 pairs
B5: 2                                    # 10 pairs
* PAIR C5: 1,6 ROW 5
G5: 1,6,2,8,9                            # reduction candidate for 1,6
G5: 1,6                                  # 13 pairs
I5: 1,6,8,9                              # reduction candidate for 1,6
I5: 1,6                                  # 13 pairs
* PAIR C5: 1,6 COL C
C1: 1,6,5,7                              # reduction candidate for 1,6
C1: 1,6 => CTR
* .4.2.......84..3....918...2.73621......745.3.2549381671923647..635879214487512693
C1: 5,7                                  # 12 pairs
* PAIR D4: 6,8 BLK 5
F6: 6,8,2,3                              # reduction candidate for 6,8
F6: 6,8 => CTR
* .4.2.......84..3....918...2.73621......745.3.1549386275923.47..63.8.921448.5.2963
F6: 2,3 => SOLVED
* 147293685268574391539186472723861549916745238854932167392418756675329814481657923
* PAIR D4: 6,8 ROW 4
G4: 6,8,2,4,5,9                          # reduction candidate for 6,8
G4: 6,8 => CTR
* .4.2.......8...3...6918.4.2973621845826745.3.1549386275923147..63785921448...2..3
G4: 2,4,5,9                              #  8 pairs
H4: 6,8,2,4,5,9                          # reduction candidate for 6,8
H4: 6,8 => CTR
* .4.2.......8...3...6918.5.2973621485826745.3.15493862759231476863785921448...2..3
H4: 2,4,5,9                              #  8 pairs
I4: 6,8,5,9                              # reduction candidate for 6,8
I4: 6,8 => CTR
* .4.2.......8...3...6918...2973621..8826745.3.15493862759231478663785921448...2..3
I4: 5,9                                  #  9 pairs
* PAIR E4: 2,6 BLK 5
E6: 2,6,3                                # reduction candidate for 2,6
E6: 2,6 => CTR
* .4.23......8.9.3....918...2..3..1......745.3..549.3..7.92..87..6..3.981448...2..3
E6: 3                                    #  8 pairs
F6: 2,6,3,8                              # reduction candidate for 2,6
F6: 2,6 => SOLVED
* 147293685268574391539186472723861549916745238854932167392418756675329814481657923
F6: 3,8 => CTR
* .4.2.......84..3....918...2.73621......745.3.1549386275923147..6378.921448.5.2..3
* PAIR E4: 2,6 ROW 4
B4: 2,6,7                                # reduction candidate for 2,6
B4: 2,6 => SOLVED
* 147293685268574391539186472723861549916745238854932167392418756675329814481657923
B4: 7 => CTR
* .4.2.......84..3...6918...2.73621.....6745.3..54938.27.923.47..635879214487512..3
G4: 2,6,4,5,8,9                          # reduction candidate for 2,6
G4: 2,6 => CTR
* .4.2.......8...3....918.4.29738.1.45...745.3..549....7.92..87.663...9.1448......3
G4: 4,5,8,9                              #  8 pairs
H4: 2,6,4,5,8,9                          # reduction candidate for 2,6
H4: 2,6 => CTR
* .4.2.......8...3....918...29738.14.5...745.3..549....7.92..87.663...9.1448......3
H4: 4,5,8,9                              #  8 pairs
* PAIR E4: 2,6 COL E
E9: 2,6,1,5,7                            # reduction candidate for 2,6
E9: 2,6 => CTR
* .4.2.......8...3...3918...2..3861.....6745.3..54932..73924187..675329814481..7..3
E9: 1,5,7                                #  8 pairs
* PAIR B8: 3,7 COL B
B3: 3,7,6                                # reduction candidate for 3,7
B3: 3,7 => SOLVED
* 147293685268574391539186472723861549916745238854932167392418756675329814481657923
B3: 6 => CTR
* .4.2.......84..3...6918...2.73621.....6745.3..54938.27.923.47..635879214487512..3
* PAIR C8: 5,7 BLK 7
C9: 5,7,1                                # reduction candidate for 5,7
C9: 5,7 => CTR
* .4.2.......84..3....918...2..3621......745.3..549381671923.47..63.8.921448.512693
C9: 1                                    # 12 pairs
* PAIR C8: 5,7 ROW 8
E8: 5,7,2                                # reduction candidate for 5,7
E8: 5,7 => CTR
* .4.2.......84..3....918...2.73621......745.3.1549386275923147..6378.921448.5.2..3
E8: 2 => SOLVED
* 147293685268574391539186472723861549916745238854932167392418756675329814481657923
* PAIR C8: 5,7 COL C
C1: 5,7,1,6                              # reduction candidate for 5,7
C1: 1,6 => CTR
* .4.2.......84..3....918...2.73621......745.3.2549381671923647..635879214487512693
C1: 5,7                                  # 12 pairs
* PAIR F7: 4,8 BLK 8
D7: 4,8,3                                # reduction candidate for 4,8
D7: 4,8 => SOLVED
* 147293685268574391539186472723861549916745238854932167392418756675329814481657923
D7: 3 => CTR
* .4.2.......84..3....918...2.73621......745.3..54938.271923.47..63.879214487512..3
* PAIR D8: 3,8 BLK 8
D7: 3,8,4                                # reduction candidate for 3,8
D7: 3,8 => CTR
* .4.2.......84..3....918...2.73621......745.3..54938.27192..47..6...79214487512..3
D7: 4 => SOLVED
* 147293685268574391539186472723861549916745238854932167392418756675329814481657923
* PAIR D9: 5,6 BLK 8
E7: 5,6,1                                # reduction candidate for 5,6
E7: 5,6 => CTR
* .4.2.......84..3....918...2..3621......745.3..549381671923.47..63.8.921448.512693
E7: 1                                    # 12 pairs
E9: 5,6,1,2,7                            # reduction candidate for 5,6
E9: 5,6 => SOLVED
* 147293685268574391539186472723861549916745238854932167392418756675329814481657923
E9: 1,2,7                                #  8 pairs
* PAIR D9: 5,6 ROW 9
G9: 5,6,2,9                              # reduction candidate for 5,6
G9: 5,6 => CTR
* .4.2.......8...3....918...2..3621......745.3..54938.27.923.47..63.8.921448.5.2693
G9: 2,9                                  #  9 pairs
H9: 5,6,2,9                              # reduction candidate for 5,6
H9: 5,6 => CTR
* .4.2.......84..3....918...2.73621......745.3.1549386275923.47..63.8.921448.5.2963
H9: 2,9                                  #  9 pairs
* PAIR D9: 5,6 COL D
D2: 5,6,4                                # reduction candidate for 5,6
D2: 5,6 => SOLVED
* 147293685268574391539186472723861549916745238854932167392418756675329814481657923
D2: 4 => CTR
* .4.2.......84..3....918...2.73621......745.3..54938.27192..47..6...79214487512..3
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190312-absurd-base-pr-000.dot
* REASONING
* DIS # C1: 1,6 => CTR => C1: 5,7
* DIS # F6: 6,8 => CTR => F6: 2,3
* PRF # F6: 2,3 => SOL
* DIS # G4: 6,8 => CTR => G4: 2,4,5,9
* DIS # H4: 6,8 => CTR => H4: 2,4,5,9
* DIS # I4: 6,8 => CTR => I4: 5,9
* DIS # E6: 2,6 => CTR => E6: 3
* PRF # F6: 2,6 => SOL
* DIS # F6: 3,8 => CTR => F6: 2,6
* PRF # B4: 2,6 => SOL
* DIS # B4: 7 => CTR => B4: 2,6
* DIS # G4: 2,6 => CTR => G4: 4,5,8,9
* DIS # H4: 2,6 => CTR => H4: 4,5,8,9
* DIS # E9: 2,6 => CTR => E9: 1,5,7
* PRF # B3: 3,7 => SOL
* DIS # B3: 6 => CTR => B3: 3,7
* DIS # C9: 5,7 => CTR => C9: 1
* DIS # E8: 5,7 => CTR => E8: 2
* PRF # E8: 2 => SOL
* DIS # C1: 1,6 => CTR => C1: 5,7
* PRF # D7: 4,8 => SOL
* DIS # D7: 3 => CTR => D7: 4,8
* DIS # D7: 3,8 => CTR => D7: 4
* PRF # D7: 4 => SOL
* DIS # E7: 5,6 => CTR => E7: 1
* PRF # E9: 5,6 => SOL
* DIS # G9: 5,6 => CTR => G9: 2,9
* DIS # H9: 5,6 => CTR => H9: 2,9
* PRF # D2: 5,6 => SOL
* DIS # D2: 4 => CTR => D2: 5,6
* CNT  30 HDP CHAINS /  48 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,C5,C8,D4,D8,D9,E4,F7)
* .4.2.......8...3....918...2..3..1......745.3..549....7.92...7..6....9.1448......3
* PAIR C5: 1,6 BLK 4
B5: 1,6,2                                # reduction candidate for 1,6
B5: 1,6                                  # 12 pairs
B5: 2                                    # 10 pairs
* PAIR C5: 1,6 ROW 5
G5: 1,6,2,8,9                            # reduction candidate for 1,6
G5: 1,6                                  # 13 pairs
I5: 1,6,8,9                              # reduction candidate for 1,6
I5: 1,6                                  # 13 pairs
* PAIR C5: 1,6 COL C
C1: 1,6,5,7                              # reduction candidate for 1,6
C1: 1,6 => CTR
* .4.2.......84..3....918...2.73621......745.3.2549381671923647..635879214487512693
* PAIR RESTART
* PAIR D4: 6,8 BLK 5
F6: 6,8,2,3                              # reduction candidate for 6,8
F6: 6,8 => CTR
* .452.......85..3....918...2.73821.....6745.3..54936.27592.1.7..6...59214481672..3
F6: 2,3 => SOLVED
* 147293685268574391539186472723861549916745238854932167392418756675329814481657923
* DURATION: 0:00:06.436573  START: 04:28:30.648403  END: 04:28:37.084976 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190312-absurd-base-pr-001.dot
* REASONING
* DIS # C1: 1,6 => CTR => C1: 5,7
* DIS C1: 5,7 # F6: 6,8 => CTR => F6: 2,3
* PRF C1: 5,7 + F6: 2,3 => SOL
* STA C1: 5,7 + F6: 2,3
* CNT   3 HDP CHAINS /   6 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190312, absurd

Solution

position: 147293685268574391539186472723861549916745238854932167392418756675329814481657923 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:

* INC # B5: 1,6 => UNS
* INC # B5: 2 => UNS
* INC # G5: 1,6 => UNS
* INC # I5: 1,6 => UNS
* DIS # C1: 1,6 => CTR => C1: 5,7
* INC # C1: 5,7 => UNS
* DIS # F6: 6,8 => CTR => F6: 2,3
* PRF # F6: 2,3 => SOL
* DIS # G4: 6,8 => CTR => G4: 2,4,5,9
* INC # G4: 2,4,5,9 => UNS
* DIS # H4: 6,8 => CTR => H4: 2,4,5,9
* INC # H4: 2,4,5,9 => UNS
* DIS # I4: 6,8 => CTR => I4: 5,9
* INC # I4: 5,9 => UNS
* DIS # E6: 2,6 => CTR => E6: 3
* INC # E6: 3 => UNS
* PRF # F6: 2,6 => SOL
* DIS # F6: 3,8 => CTR => F6: 2,6
* PRF # B4: 2,6 => SOL
* DIS # B4: 7 => CTR => B4: 2,6
* DIS # G4: 2,6 => CTR => G4: 4,5,8,9
* INC # G4: 4,5,8,9 => UNS
* DIS # H4: 2,6 => CTR => H4: 4,5,8,9
* INC # H4: 4,5,8,9 => UNS
* DIS # E9: 2,6 => CTR => E9: 1,5,7
* INC # E9: 1,5,7 => UNS
* PRF # B3: 3,7 => SOL
* DIS # B3: 6 => CTR => B3: 3,7
* DIS # C9: 5,7 => CTR => C9: 1
* INC # C9: 1 => UNS
* DIS # E8: 5,7 => CTR => E8: 2
* PRF # E8: 2 => SOL
* INC # C1: 5,7 => UNS
* DIS # C1: 1,6 => CTR => C1: 5,7
* PRF # D7: 4,8 => SOL
* DIS # D7: 3 => CTR => D7: 4,8
* DIS # D7: 3,8 => CTR => D7: 4
* PRF # D7: 4 => SOL
* DIS # E7: 5,6 => CTR => E7: 1
* INC # E7: 1 => UNS
* PRF # E9: 5,6 => SOL
* INC # E9: 1,2,7 => UNS
* DIS # G9: 5,6 => CTR => G9: 2,9
* INC # G9: 2,9 => UNS
* DIS # H9: 5,6 => CTR => H9: 2,9
* INC # H9: 2,9 => UNS
* PRF # D2: 5,6 => SOL
* DIS # D2: 4 => CTR => D2: 5,6
* CNT  48 HDP CHAINS /  48 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B5: 1,6 => UNS
* INC # B5: 2 => UNS
* INC # G5: 1,6 => UNS
* INC # I5: 1,6 => UNS
* DIS # C1: 1,6 => CTR => C1: 5,7
* DIS C1: 5,7 # F6: 6,8 => CTR => F6: 2,3
* PRF C1: 5,7 + F6: 2,3 => SOL
* STA C1: 5,7 + F6: 2,3
* CNT   7 HDP CHAINS /   6 HYP OPENED