Analysis of zz-www.sudokuoftheday.co.uk-20060725-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006

position: ..9.438......17....3.8.....3....4.1.6......48...19.3.25.....2.....538.7..86.....4 initial

Autosolve

position: ..9.438......17..3.3.8.....3...84.1.6..3...48...19.3.25.34..28....538.7..86...534 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D2: 2,6 => CTR => D2: 9
* DIS # E3: 2,6 => CTR => E3: 5
* PRF # B1: 2,6 => SOL
* DIS # D4: 7 => CTR => D4: 2,6
* PRF # G3: 4,6 => SOL
* PRF # B2: 2,5 => SOL
* DIS # B4: 2,5 => CTR => B4: 9
* PRF # C5: 2,5 => SOL
* DIS # C2: 2,5 => CTR => C2: 4,8
* PRF # C2: 4,8 => SOL
* DIS # A6: 4,7 => CTR => A6: 8
* PRF # A6: 8 => SOL
* PRF # C6: 4,7 => SOL
* DIS # C6: 8 => CTR => C6: 4,7
* DIS # E5: 2,5 => CTR => E5: 7
* PRF # C5: 2,5 => SOL
* DIS # F3: 2,5 => CTR => F3: 6,9
* DIS # F3: 2,9 => CTR => F3: 5,6
* DIS # I4: 7,9 => CTR => I4: 5,6
* DIS # I4: 7,9 => CTR => I4: 5,6
* DIS # H2: 5,6 => CTR => H2: 2,9
* DIS # B1: 1,7 => CTR => B1: 2,5,6
* PRF # B1: 2,5,6 => SOL
* DIS # D9: 9 => CTR => D9: 2,7
* DIS # E5: 5 => CTR => E5: 2,7
* DIS # F7: 6 => CTR => F7: 1,9
* CNT  26 HDP CHAINS /  54 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 # D2: 2,6 => CTR => D2: 9
* DIS D2: 9 # F3: 5 => CTR => F3: 2,6
* PRF D2: 9 + F3: 2,6 # B1: 2,6 => SOL
* STA D2: 9 + F3: 2,6 + B1: 2,6
* CNT   3 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

..9.438......17....3.8.....3....4.1.6......48...19.3.25.....2.....538.7..86.....4 initial
..9.438......17..3.3.8.....3...84.1.6..3...48...19.3.25.34..28....538.7..86...534 autosolve
769243851458917623231856497392684715615372948847195362573461289924538176186729534 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (12)
D1: 2,6
G2: 4,6
C4: 2,5
B6: 4,7
F5: 2,5
F6: 5,6
G5: 7,9
H6: 5,6
B7: 1,7
E7: 6,7
E9: 2,7
I7: 1,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B5,C5: 1.. / B5 = 1  =>  0 pairs (*) / C5 = 1  =>  0 pairs (X)
F7,F9: 1.. / F7 = 1  => 19 pairs (_) / F9 = 1  => 14 pairs (_)
A9,F9: 1.. / A9 = 1  => 19 pairs (_) / F9 = 1  => 14 pairs (_)
G3,G8: 1.. / G3 = 1  => 14 pairs (_) / G8 = 1  => 17 pairs (_)
G2,G3: 4.. / G2 = 4  => 12 pairs (_) / G3 = 4  =>  0 pairs (*)
E3,F3: 5.. / E3 = 5  => 15 pairs (_) / F3 = 5  =>  0 pairs (X)
I4,H6: 5.. / I4 = 5  => 17 pairs (_) / H6 = 5  =>  0 pairs (X)
F6,H6: 5.. / F6 = 5  => 17 pairs (_) / H6 = 5  =>  0 pairs (X)
E3,E5: 5.. / E3 = 5  => 15 pairs (_) / E5 = 5  =>  0 pairs (X)
I1,I4: 5.. / I1 = 5  =>  0 pairs (X) / I4 = 5  => 17 pairs (_)
B1,B2: 6.. / B1 = 6  =>  0 pairs (*) / B2 = 6  =>  0 pairs (X)
D4,F6: 6.. / D4 = 6  => 17 pairs (_) / F6 = 6  =>  0 pairs (X)
E7,F7: 6.. / E7 = 6  => 15 pairs (_) / F7 = 6  =>  0 pairs (X)
G8,I8: 6.. / G8 = 6  => 16 pairs (_) / I8 = 6  => 14 pairs (_)
F6,H6: 6.. / F6 = 6  =>  0 pairs (X) / H6 = 6  => 17 pairs (_)
E3,E7: 6.. / E3 = 6  =>  0 pairs (X) / E7 = 6  => 15 pairs (_)
D4,E5: 7.. / D4 = 7  =>  0 pairs (X) / E5 = 7  => 17 pairs (_)
B7,A9: 7.. / B7 = 7  => 15 pairs (_) / A9 = 7  =>  0 pairs (X)
E5,G5: 7.. / E5 = 7  => 17 pairs (_) / G5 = 7  =>  0 pairs (X)
B7,E7: 7.. / B7 = 7  => 15 pairs (_) / E7 = 7  =>  0 pairs (X)
C3,C6: 7.. / C3 = 7  =>  0 pairs (X) / C6 = 7  =>  0 pairs (_)
D4,D9: 7.. / D4 = 7  =>  0 pairs (X) / D9 = 7  => 17 pairs (_)
A2,C2: 8.. / A2 = 8  =>  0 pairs (X) / C2 = 8  =>  0 pairs (_)
A6,C6: 8.. / A6 = 8  =>  0 pairs (*) / C6 = 8  =>  0 pairs (X)
A2,A6: 8.. / A2 = 8  =>  0 pairs (X) / A6 = 8  =>  0 pairs (_)
C2,C6: 8.. / C2 = 8  =>  0 pairs (*) / C6 = 8  =>  0 pairs (X)
D2,F3: 9.. / D2 = 9  => 17 pairs (_) / F3 = 9  =>  0 pairs (X)
H2,H3: 9.. / H2 = 9  =>  0 pairs (X) / H3 = 9  => 17 pairs (_)
B4,B5: 9.. / B4 = 9  => 17 pairs (_) / B5 = 9  =>  0 pairs (X)
A8,A9: 9.. / A8 = 9  => 17 pairs (_) / A9 = 9  => 16 pairs (_)
D2,H2: 9.. / D2 = 9  => 17 pairs (_) / H2 = 9  =>  0 pairs (X)
F3,H3: 9.. / F3 = 9  =>  0 pairs (X) / H3 = 9  => 17 pairs (_)
B5,G5: 9.. / B5 = 9  =>  0 pairs (X) / G5 = 9  => 17 pairs (_)
F7,I7: 9.. / F7 = 9  => 16 pairs (_) / I7 = 9  => 17 pairs (_)
D2,D9: 9.. / D2 = 9  => 17 pairs (_) / D9 = 9  =>  0 pairs (X)
* DURATION: 0:00:45.265179  START: 01:16:35.198589  END: 01:17:20.463768 2019-05-01
* CP COUNT: (35)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,B7,C4,D1,E7,E9,F5,F6,G2,G5,H6,I7)
* ..9.438......17..3.3.8.....3...84.1.6..3...48...19.3.25.34..28....538.7..86...534
* PAIR D1: 2,6 BLK 2
D2: 2,6,9                                # reduction candidate for 2,6
D2: 2,6 => CTR
* 719.438.5.6..17.93.3.859..73..784916691325748..71963525734612899..538671186972534
D2: 9                                    # 17 pairs
E3: 2,6,5                                # reduction candidate for 2,6
E3: 2,6 => CTR
* ..9.438.5...917..3.3.825.973..784.1.691352748..719635257346.28....538.7..8627.534
E3: 5                                    # 15 pairs
F3: 2,6,5,9                              # reduction candidate for 2,6
F3: 2,6                                  # 18 pairs
* PAIR D1: 2,6 ROW 1
B1: 2,6,1,5,7                            # reduction candidate for 2,6
B1: 2,6 => SOLVED
* 769243851458917623231856497392684715615372948847195362573461289924538176186729534
B1: 1,5,7                                # 13 pairs
H1: 2,6,5                                # reduction candidate for 2,6
H1: 2,6                                  # 15 pairs
* PAIR D1: 2,6 COL D
D4: 2,6,7                                # reduction candidate for 2,6
D4: 7 => CTR
* 719.438.5.6..17..3.3.8....73..784.1.6913..748..719635257346.28....538.7..86.7.534
D4: 2,6                                  # 17 pairs
* PAIR G2: 4,6 BLK 3
G3: 4,6,1,7                              # reduction candidate for 4,6
G3: 4,6 => SOLVED
* 769243851458917623231856497392684715615372948847195362573461289924538176186729534
G3: 1,7                                  # 13 pairs
* PAIR G2: 4,6 ROW 2
B2: 4,6,2,5                              # reduction candidate for 4,6
B2: 2,5 => SOLVED
* 769243851458917623231856497392684715615372948847195362573461289924538176186729534
B2: 4,6                                  # 15 pairs
* PAIR C4: 2,5 BLK 4
B4: 2,5,9                                # reduction candidate for 2,5
B4: 2,5 => CTR
* 719.438.5.6..17..3.3.8....73..784.1.6913..748..719635257346.28....538.7..86.7.534
B4: 9                                    # 17 pairs
B5: 2,5,1,9                              # reduction candidate for 2,5
B5: 2,5                                  # 19 pairs
C5: 2,5,1                                # reduction candidate for 2,5
C5: 2,5 => SOLVED
* 769243851458917623231856497392684715615372948847195362573461289924538176186729534
C5: 1                                    # 13 pairs
* PAIR C4: 2,5 COL C
C2: 2,5,4,8                              # reduction candidate for 2,5
C2: 2,5 => CTR
* .692438578.5917623237856491392684715651372948..819536257346.28...4538.7..8672.534
C2: 4,8 => SOLVED
* 769243851458917623231856497392684715615372948847195362573461289924538176186729534
* PAIR B6: 4,7 BLK 4
A6: 4,7,8                                # reduction candidate for 4,7
A6: 4,7 => CTR
* .692438578..9176232378564913926847156..372948748195362573461289...538.7..8672.534
A6: 8 => SOLVED
* 769243851458917623231856497392684715615372948847195362573461289924538176186729534
C6: 4,7,8                                # reduction candidate for 4,7
C6: 4,7 => SOLVED
* 769243851458917623231856497392684715615372948847195362573461289924538176186729534
C6: 8 => CTR
* .692438578..9176232378564913926847156..372948748195362573461289...538.7..8672.534
* PAIR F5: 2,5 BLK 5
E5: 2,5,7                                # reduction candidate for 2,5
E5: 2,5 => CTR
* 719.438.5.6..17..3.3.8....73..784.1.6913..748..719635257346.28....538.7..86.7.534
E5: 7                                    # 17 pairs
* PAIR F5: 2,5 ROW 5
B5: 2,5,1,9                              # reduction candidate for 2,5
B5: 2,5                                  # 19 pairs
C5: 2,5,1                                # reduction candidate for 2,5
C5: 2,5 => SOLVED
* 769243851458917623231856497392684715615372948847195362573461289924538176186729534
C5: 1                                    # 13 pairs
* PAIR F5: 2,5 COL F
F3: 2,5,6,9                              # reduction candidate for 2,5
F3: 2,5 => CTR
* ..9643825.6.917..3.3.8...9.3...84.1.6..3...48...19635257346.28....538.7..86...534
F3: 6,9                                  # 19 pairs
* PAIR F6: 5,6 COL F
F3: 5,6,2,9                              # reduction candidate for 5,6
F3: 2,9 => CTR
* 719.438.5.65.174.3.3.85....35..84.1.6..3.5.48.4.19635257346.28....538.7..86...534
F3: 5,6                                  # 20 pairs
* PAIR G5: 7,9 BLK 6
G4: 7,9,6                                # reduction candidate for 7,9
G4: 7,9                                  # 15 pairs
I4: 7,9,5,6                              # reduction candidate for 7,9
I4: 7,9 => CTR
* 719643825.65.17493.3.8.9.6.35..8461.6..3...48...19635257346.28....538.76.86...534
I4: 5,6                                  # 15 pairs
* PAIR H6: 5,6 BLK 6
I4: 5,6,7,9                              # reduction candidate for 5,6
I4: 7,9 => CTR
* 719643825.65.17493.3.8.9.6.35..8461.6..3...48...19635257346.28....538.76.86...534
I4: 5,6                                  # 15 pairs
* PAIR H6: 5,6 COL H
H1: 5,6,2                                # reduction candidate for 5,6
H1: 5,6                                  # 15 pairs
H2: 5,6,2,9                              # reduction candidate for 5,6
H2: 5,6 => CTR
* ..964382..6.917453.3.8...9.3...84.156.53.2.48...19.3.25.34..28....538.7..86...534
H2: 2,9                                  # 13 pairs
* PAIR B7: 1,7 BLK 7
A9: 1,7,9                                # reduction candidate for 1,7
A9: 1,7                                  # 17 pairs
A9: 9                                    # 16 pairs
* PAIR B7: 1,7 COL B
B1: 1,7,2,5,6                            # reduction candidate for 1,7
B1: 1,7 => CTR
* 219643857865.174.34378.....3.2784.1.6.13...4874819.3.257346.28..24538.7..86...534
B1: 2,5,6 => SOLVED
* 769243851458917623231856497392684715615372948847195362573461289924538176186729534
* PAIR E9: 2,7 BLK 8
D9: 2,7,9                                # reduction candidate for 2,7
D9: 9 => CTR
* 719.438.5.6..17.93.3.8.9..73..784.1.691325748..71963525734612899..538.71186972534
D9: 2,7                                  # 17 pairs
* PAIR E9: 2,7 COL E
E5: 2,7,5                                # reduction candidate for 2,7
E5: 5 => CTR
* ..9.438.5....17..3.3.825.973..784.1.691352748..719635257346.28....538.7..8627.534
E5: 2,7                                  # 15 pairs
* PAIR I7: 1,9 BLK 9
G8: 1,9,6                                # reduction candidate for 1,9
G8: 1,9                                  # 14 pairs
I8: 1,9,6                                # reduction candidate for 1,9
I8: 1,9                                  # 16 pairs
* PAIR I7: 1,9 ROW 7
F7: 1,9,6                                # reduction candidate for 1,9
F7: 6 => CTR
* ..9.438......17..3.3.86....3...84.1.6..3...48...19.3.25.34.62899..538.7..86..1534
F7: 1,9                                  # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060725-absurd-base-pr-000.dot
* REASONING
* DIS # D2: 2,6 => CTR => D2: 9
* DIS # E3: 2,6 => CTR => E3: 5
* PRF # B1: 2,6 => SOL
* DIS # D4: 7 => CTR => D4: 2,6
* PRF # G3: 4,6 => SOL
* PRF # B2: 2,5 => SOL
* DIS # B4: 2,5 => CTR => B4: 9
* PRF # C5: 2,5 => SOL
* DIS # C2: 2,5 => CTR => C2: 4,8
* PRF # C2: 4,8 => SOL
* DIS # A6: 4,7 => CTR => A6: 8
* PRF # A6: 8 => SOL
* PRF # C6: 4,7 => SOL
* DIS # C6: 8 => CTR => C6: 4,7
* DIS # E5: 2,5 => CTR => E5: 7
* PRF # C5: 2,5 => SOL
* DIS # F3: 2,5 => CTR => F3: 6,9
* DIS # F3: 2,9 => CTR => F3: 5,6
* DIS # I4: 7,9 => CTR => I4: 5,6
* DIS # I4: 7,9 => CTR => I4: 5,6
* DIS # H2: 5,6 => CTR => H2: 2,9
* DIS # B1: 1,7 => CTR => B1: 2,5,6
* PRF # B1: 2,5,6 => SOL
* DIS # D9: 9 => CTR => D9: 2,7
* DIS # E5: 5 => CTR => E5: 2,7
* DIS # F7: 6 => CTR => F7: 1,9
* CNT  26 HDP CHAINS /  54 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,B7,C4,D1,E7,E9,F5,F6,G2,G5,H6,I7)
* ..9.438......17..3.3.8.....3...84.1.6..3...48...19.3.25.34..28....538.7..86...534
* PAIR D1: 2,6 BLK 2
D2: 2,6,9                                # reduction candidate for 2,6
D2: 2,6 => CTR
* 719.438.5.6..17.93.3.859..73..784916691325748..71963525734612899..538671186972534
F3: 2,6,5                                # reduction candidate for 2,6
F3: 2,6                                  # 18 pairs
* RESTART
* PAIR D1: 2,6 BLK 2
F3: 2,6,5                                # reduction candidate for 2,6
F3: 5 => CTR
* ..96438...6.9174.3.3.825.9.3...84.1.6..352748.4.19.3.257346.28....538.7..86...534
* PAIR D1: 2,6 ROW 1
B1: 2,6,1,5                              # reduction candidate for 2,6
B1: 2,6 => SOLVED
* 769243851458917623231856497392684715615372948847195362573461289924538176186729534
* DURATION: 0:00:04.752042  START: 01:17:59.686298  END: 01:18:04.438340 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060725-absurd-base-pr-001.dot
* REASONING
* DIS # D2: 2,6 => CTR => D2: 9
* DIS D2: 9 # F3: 5 => CTR => F3: 2,6
* PRF D2: 9 + F3: 2,6 # B1: 2,6 => SOL
* STA D2: 9 + F3: 2,6 + B1: 2,6
* CNT   3 HDP CHAINS /   5 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060725, absurd

Solution

position: 769243851458917623231856497392684715615372948847195362573461289924538176186729534 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 # D2: 2,6 => CTR => D2: 9
* INC # D2: 9 => UNS
* DIS # E3: 2,6 => CTR => E3: 5
* INC # E3: 5 => UNS
* INC # F3: 2,6 => UNS
* PRF # B1: 2,6 => SOL
* INC # B1: 1,5,7 => UNS
* INC # H1: 2,6 => UNS
* INC # D4: 2,6 => UNS
* DIS # D4: 7 => CTR => D4: 2,6
* PRF # G3: 4,6 => SOL
* INC # G3: 1,7 => UNS
* INC # B2: 4,6 => UNS
* PRF # B2: 2,5 => SOL
* DIS # B4: 2,5 => CTR => B4: 9
* INC # B4: 9 => UNS
* INC # B5: 2,5 => UNS
* PRF # C5: 2,5 => SOL
* INC # C5: 1 => UNS
* DIS # C2: 2,5 => CTR => C2: 4,8
* PRF # C2: 4,8 => SOL
* DIS # A6: 4,7 => CTR => A6: 8
* PRF # A6: 8 => SOL
* PRF # C6: 4,7 => SOL
* DIS # C6: 8 => CTR => C6: 4,7
* DIS # E5: 2,5 => CTR => E5: 7
* INC # E5: 7 => UNS
* INC # B5: 2,5 => UNS
* PRF # C5: 2,5 => SOL
* INC # C5: 1 => UNS
* DIS # F3: 2,5 => CTR => F3: 6,9
* INC # F3: 6,9 => UNS
* INC # F3: 5,6 => UNS
* DIS # F3: 2,9 => CTR => F3: 5,6
* INC # G4: 7,9 => UNS
* DIS # I4: 7,9 => CTR => I4: 5,6
* INC # I4: 5,6 => UNS
* INC # I4: 5,6 => UNS
* DIS # I4: 7,9 => CTR => I4: 5,6
* INC # H1: 5,6 => UNS
* DIS # H2: 5,6 => CTR => H2: 2,9
* INC # H2: 2,9 => UNS
* INC # A9: 1,7 => UNS
* INC # A9: 9 => UNS
* DIS # B1: 1,7 => CTR => B1: 2,5,6
* PRF # B1: 2,5,6 => SOL
* INC # D9: 2,7 => UNS
* DIS # D9: 9 => CTR => D9: 2,7
* INC # E5: 2,7 => UNS
* DIS # E5: 5 => CTR => E5: 2,7
* INC # G8: 1,9 => UNS
* INC # I8: 1,9 => UNS
* INC # F7: 1,9 => UNS
* DIS # F7: 6 => CTR => F7: 1,9
* CNT  54 HDP CHAINS /  54 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # D2: 2,6 => CTR => D2: 9
* INC D2: 9 # F3: 2,6 => UNS
* INC D2: 9 # F3: 2,6 => UNS
* DIS D2: 9 # F3: 5 => CTR => F3: 2,6
* PRF D2: 9 + F3: 2,6 # B1: 2,6 => SOL
* STA D2: 9 + F3: 2,6 + B1: 2,6
* CNT   5 HDP CHAINS /   5 HYP OPENED