Analysis of zz-www.sudokuoftheday.co.uk-20060507-absurd-base.sdk

Contents

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

level: medium

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

position: ..6....9..1...4..5...6..4..5.9741.2....3.6....3.92...77.1.......8..6..5.....1.8.. initial

Autosolve

position: ..61...9..1...4..5...6..4..569741328...3.6....3.92...77.1.....6.8..6..5.6...1.8.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D7: 2,8 => CTR => D7: 4,5
* DIS # G2: 2,7 => CTR => G2: 6
* DIS # B1: 2,7 => CTR => B1: 4,5
* DIS # G8: 2,7 => CTR => G8: 1,9
* DIS # I3: 2,3 => CTR => I3: 1
* DIS # A1: 2,3 => CTR => A1: 4,8
* DIS # A6: 4,8 => CTR => A6: 1
* DIS # E3: 5,8 => CTR => E3: 3,7,9
* DIS # F3: 5,8 => CTR => F3: 2,3,9
* DIS # H6: 1,4 => CTR => H6: 6
* DIS # A5: 1,4 => CTR => A5: 2,8
* PRF # D9: 2,4 => SOL
* DIS # G8: 2,9 => CTR => G8: 1,7
* PRF # B7: 2,9 => SOL
* DIS # H9: 3,4 => CTR => H9: 7
* CNT  15 HDP CHAINS /  51 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 # D7: 2,8 => CTR => D7: 4,5
* DIS D7: 4,5 # G2: 2,7 => CTR => G2: 6
* PRF D7: 4,5 + G2: 6 => SOL
* STA D7: 4,5 + G2: 6
* CNT   3 HDP CHAINS /   6 HYP OPENED

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

Details

Positions

..6....9..1...4..5...6..4..5.9741.2....3.6....3.92...77.1.......8..6..5.....1.8.. initial
..61...9..1...4..5...6..4..569741328...3.6....3.92...77.1.....6.8..6..5.6...1.8.. autosolve
846135792912874635357692481569741328278356914134928567791583246483267159625419873 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
D2: 2,8
G1: 2,7
I1: 2,3
C6: 4,8
E5: 5,8
F6: 5,8
H5: 1,4
D8: 2,4
G7: 2,9
H7: 3,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H3,I3: 1.. / H3 = 1  =>  0 pairs (X) / I3 = 1  => 14 pairs (_)
A5,A6: 1.. / A5 = 1  =>  0 pairs (X) / A6 = 1  => 12 pairs (_)
G8,I8: 1.. / G8 = 1  => 12 pairs (_) / I8 = 1  =>  0 pairs (X)
A1,B1: 4.. / A1 = 4  =>  0 pairs (X) / B1 = 4  => 11 pairs (_)
E5,F6: 5.. / E5 = 5  => 11 pairs (_) / F6 = 5  =>  0 pairs (X)
G5,G6: 5.. / G5 = 5  =>  0 pairs (X) / G6 = 5  => 11 pairs (_)
D7,D9: 5.. / D7 = 5  =>  0 pairs (*) / D9 = 5  =>  0 pairs (X)
E5,G5: 5.. / E5 = 5  => 11 pairs (_) / G5 = 5  =>  0 pairs (X)
F6,G6: 5.. / F6 = 5  =>  0 pairs (X) / G6 = 5  => 11 pairs (_)
B7,D7: 5.. / B7 = 5  => 10 pairs (_) / D7 = 5  =>  0 pairs (*)
C3,C9: 5.. / C3 = 5  => 10 pairs (_) / C9 = 5  =>  0 pairs (*)
G2,H2: 6.. / G2 = 6  => 12 pairs (_) / H2 = 6  =>  0 pairs (X)
G6,H6: 6.. / G6 = 6  =>  0 pairs (X) / H6 = 6  => 12 pairs (_)
G2,G6: 6.. / G2 = 6  => 12 pairs (_) / G6 = 6  =>  0 pairs (X)
H2,H6: 6.. / H2 = 6  =>  0 pairs (X) / H6 = 6  => 12 pairs (_)
B5,C5: 7.. / B5 = 7  => 10 pairs (_) / C5 = 7  => 11 pairs (_)
F8,F9: 7.. / F8 = 7  => 10 pairs (_) / F9 = 7  =>  0 pairs (X)
G8,H9: 7.. / G8 = 7  =>  0 pairs (X) / H9 = 7  => 10 pairs (_)
F8,G8: 7.. / F8 = 7  => 10 pairs (_) / G8 = 7  =>  0 pairs (X)
F9,H9: 7.. / F9 = 7  =>  0 pairs (X) / H9 = 7  => 10 pairs (_)
H2,H3: 8.. / H2 = 8  =>  0 pairs (X) / H3 = 8  => 14 pairs (_)
E5,F6: 8.. / E5 = 8  =>  0 pairs (X) / F6 = 8  => 11 pairs (_)
D2,D7: 8.. / D2 = 8  => 16 pairs (_) / D7 = 8  =>  0 pairs (X)
G5,I5: 9.. / G5 = 9  => 12 pairs (_) / I5 = 9  =>  0 pairs (X)
A2,E2: 9.. / A2 = 9  => 12 pairs (_) / E2 = 9  => 11 pairs (_)
* DURATION: 0:00:24.090385  START: 22:58:42.391895  END: 22:59:06.482280 2019-04-30
* CP COUNT: (25)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C6,D2,D8,E5,F6,G1,G7,H5,H7,I1)
* ..61...9..1...4..5...6..4..569741328...3.6....3.92...77.1.....6.8..6..5.6...1.8..
* PAIR D2: 2,8 BLK 2
F1: 2,8,3,5                              # reduction candidate for 2,8
F1: 2,8                                  # 11 pairs
F3: 2,8,3,5,9                            # reduction candidate for 2,8
F3: 2,8                                  # 17 pairs
* PAIR D2: 2,8 ROW 2
A2: 2,8,3,9                              # reduction candidate for 2,8
A2: 2,8                                  # 19 pairs
C2: 2,8,3,7                              # reduction candidate for 2,8
C2: 2,8                                  # 17 pairs
* PAIR D2: 2,8 COL D
D7: 2,8,4,5                              # reduction candidate for 2,8
D7: 2,8 => CTR
* 4.6185.93.1.2.4685..56..4..569741328...3.6.14134928567751....46.8.46.15.64.51.87.
D7: 4,5                                  # 17 pairs
* PAIR G1: 2,7 BLK 3
G2: 2,7,6                                # reduction candidate for 2,7
G2: 2,7 => CTR
* ..61...93.1...4.65...6..481569741328...3.65.9.3.9256.77.1...936.8..6715.6...1.87.
G2: 6                                    # 12 pairs
* PAIR G1: 2,7 ROW 1
B1: 2,7,4,5                              # reduction candidate for 2,7
B1: 2,7 => CTR
* 4.6185.93.1.2.4685..56..4..569741328...3.6.141349285677518...46.8.46.15.64.51.87.
B1: 4,5                                  # 11 pairs
* PAIR G1: 2,7 COL G
G8: 2,7,1,9                              # reduction candidate for 2,7
G8: 2,7 => CTR
* ..61...9..1...4685...6..41.569741328...3.6.49.3.92..677.18..936.8..6..516...1.874
G8: 1,9                                  # 11 pairs
* PAIR I1: 2,3 BLK 3
I3: 2,3,1                                # reduction candidate for 2,3
I3: 2,3 => CTR
* ..61...9..1...4685...6..41.569741328...3.6.4..3.92..677.189..36.8..6..5.6...1.87.
I3: 1                                    # 14 pairs
* PAIR I1: 2,3 ROW 1
A1: 2,3,4,8                              # reduction candidate for 2,3
A1: 2,3 => CTR
* .461...9..1.2.4..5..56..4..569741328...3.6.14.3.92...77.18...46.8.46..5.6.451.8..
A1: 4,8                                  # 11 pairs
F1: 2,3,5,8                              # reduction candidate for 2,3
F1: 2,3                                  # 15 pairs
* PAIR I1: 2,3 COL I
I8: 2,3,1,4,9                            # reduction candidate for 2,3
I8: 2,3                                  # 17 pairs
I9: 2,3,4,9                              # reduction candidate for 2,3
I9: 2,3                                  # 16 pairs
* PAIR C6: 4,8 BLK 4
A5: 4,8,1,2                              # reduction candidate for 4,8
A5: 4,8                                  # 15 pairs
C5: 4,8,2,7                              # reduction candidate for 4,8
C5: 4,8                                  # 14 pairs
A6: 4,8,1                                # reduction candidate for 4,8
A6: 4,8 => CTR
* ..61..79.91...4685...6.941.5697413281..386549.3.9251677.189.236.8..6795169..13874
A6: 1                                    # 12 pairs
* PAIR E5: 5,8 COL E
E1: 5,8,3,7                              # reduction candidate for 5,8
E1: 5,8                                  # 12 pairs
E3: 5,8,3,7,9                            # reduction candidate for 5,8
E3: 5,8 => CTR
* 8461.5.9..1.2.4685..568.4..569741328..8356.14.3.9285677518...46.8.46..5.6..51.8..
E3: 3,7,9                                # 10 pairs
* PAIR F6: 5,8 COL F
F1: 5,8,2,3                              # reduction candidate for 5,8
F1: 5,8                                  # 11 pairs
F3: 5,8,2,3,9                            # reduction candidate for 5,8
F3: 5,8 => CTR
* ..61.3792.1.2.46.5..56.84..569741328...38651..3.92..677.183..46.8.467.5.6..51.87.
F3: 2,3,9                                # 10 pairs
* PAIR H5: 1,4 BLK 6
I5: 1,4,9                                # reduction candidate for 1,4
I5: 1,4                                  # 12 pairs
H6: 1,4,6                                # reduction candidate for 1,4
H6: 1,4 => CTR
* ..61...93.1...4.65...6..481569741328...3.65.9.3.9256.77.1...936.8..6715.6...1.87.
H6: 6                                    # 12 pairs
* PAIR H5: 1,4 ROW 5
A5: 1,4,2,8                              # reduction candidate for 1,4
A5: 1,4 => CTR
* ..61..79.91...4685...6.941.5697413281..386549.3.9251677.189.236.8..6795169..13874
A5: 2,8                                  # 13 pairs
* PAIR D8: 2,4 BLK 8
D7: 2,4,5,8                              # reduction candidate for 2,4
D7: 2,4                                  # 18 pairs
D9: 2,4,5                                # reduction candidate for 2,4
D9: 2,4 => SOLVED
* 846135792912874635357692481569741328278356914134928567791583246483267159625419873
D9: 5                                    # 10 pairs
* PAIR D8: 2,4 ROW 8
A8: 2,4,3,9                              # reduction candidate for 2,4
A8: 2,4                                  # 13 pairs
C8: 2,4,3                                # reduction candidate for 2,4
C8: 2,4                                  # 12 pairs
I8: 2,4,1,3,9                            # reduction candidate for 2,4
I8: 2,4                                  # 16 pairs
* PAIR G7: 2,9 BLK 9
G8: 2,9,1,7                              # reduction candidate for 2,9
G8: 2,9 => CTR
* ..61...9..1...4685...6..41.569741328...3.6.49.3.92..677.189..36.8..67.516...13874
G8: 1,7                                  # 11 pairs
I8: 2,9,1,3,4                            # reduction candidate for 2,9
I8: 2,9                                  # 14 pairs
I9: 2,9,3,4                              # reduction candidate for 2,9
I9: 2,9                                  # 12 pairs
* PAIR G7: 2,9 ROW 7
B7: 2,9,4,5                              # reduction candidate for 2,9
B7: 2,9 => SOLVED
* 846135792912874635357692481569741328278356914134928567791583246483267159625419873
B7: 4,5                                  # 11 pairs
F7: 2,9,3,8                              # reduction candidate for 2,9
F7: 2,9                                  # 13 pairs
* PAIR H7: 3,4 BLK 9
I8: 3,4,1,2,9                            # reduction candidate for 3,4
I8: 3,4                                  # 15 pairs
H9: 3,4,7                                # reduction candidate for 3,4
H9: 3,4 => CTR
* ..61..293.1...4..5...6..4..569741328...3.6....3.92...77.1.....6.8..6.7516...178..
H9: 7                                    # 10 pairs
I9: 3,4,2,9                              # reduction candidate for 3,4
I9: 3,4                                  # 11 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060507-absurd-base-pr-000.dot
* REASONING
* DIS # D7: 2,8 => CTR => D7: 4,5
* DIS # G2: 2,7 => CTR => G2: 6
* DIS # B1: 2,7 => CTR => B1: 4,5
* DIS # G8: 2,7 => CTR => G8: 1,9
* DIS # I3: 2,3 => CTR => I3: 1
* DIS # A1: 2,3 => CTR => A1: 4,8
* DIS # A6: 4,8 => CTR => A6: 1
* DIS # E3: 5,8 => CTR => E3: 3,7,9
* DIS # F3: 5,8 => CTR => F3: 2,3,9
* DIS # H6: 1,4 => CTR => H6: 6
* DIS # A5: 1,4 => CTR => A5: 2,8
* PRF # D9: 2,4 => SOL
* DIS # G8: 2,9 => CTR => G8: 1,7
* PRF # B7: 2,9 => SOL
* DIS # H9: 3,4 => CTR => H9: 7
* CNT  15 HDP CHAINS /  51 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C6,D2,D8,E5,F6,G1,G7,H5,H7,I1)
* ..61...9..1...4..5...6..4..569741328...3.6....3.92...77.1.....6.8..6..5.6...1.8..
* PAIR D2: 2,8 BLK 2
F1: 2,8,3,5                              # reduction candidate for 2,8
F1: 2,8                                  # 11 pairs
F3: 2,8,3,5,9                            # reduction candidate for 2,8
F3: 2,8                                  # 17 pairs
* PAIR D2: 2,8 ROW 2
A2: 2,8,3,9                              # reduction candidate for 2,8
A2: 2,8                                  # 19 pairs
C2: 2,8,3,7                              # reduction candidate for 2,8
C2: 2,8                                  # 17 pairs
* PAIR D2: 2,8 COL D
D7: 2,8,4,5                              # reduction candidate for 2,8
D7: 2,8 => CTR
* 4.6185.93.1.2.4685..56..4..569741328...3.6.14134928567751....46.8.46.15.64.51.87.
* PAIR RESTART
* PAIR G1: 2,7 BLK 3
G2: 2,7,6                                # reduction candidate for 2,7
G2: 2,7 => CTR
* 8461...93.1.8.4.65...6..481569741328...3.65.9.3.9256.77.14.8936.8..6715.6...1387.
G2: 6 => SOLVED
* 846135792912874635357692481569741328278356914134928567791583246483267159625419873
* DURATION: 0:00:05.499700  START: 22:59:33.013290  END: 22:59:38.512990 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060507-absurd-base-pr-001.dot
* REASONING
* DIS # D7: 2,8 => CTR => D7: 4,5
* DIS D7: 4,5 # G2: 2,7 => CTR => G2: 6
* PRF D7: 4,5 + G2: 6 => SOL
* STA D7: 4,5 + G2: 6
* CNT   3 HDP CHAINS /   6 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060507, absurd

Solution

position: 846135792912874635357692481569741328278356914134928567791583246483267159625419873 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 # F1: 2,8 => UNS
* INC # F3: 2,8 => UNS
* INC # A2: 2,8 => UNS
* INC # C2: 2,8 => UNS
* DIS # D7: 2,8 => CTR => D7: 4,5
* INC # D7: 4,5 => UNS
* DIS # G2: 2,7 => CTR => G2: 6
* INC # G2: 6 => UNS
* DIS # B1: 2,7 => CTR => B1: 4,5
* INC # B1: 4,5 => UNS
* DIS # G8: 2,7 => CTR => G8: 1,9
* INC # G8: 1,9 => UNS
* DIS # I3: 2,3 => CTR => I3: 1
* INC # I3: 1 => UNS
* DIS # A1: 2,3 => CTR => A1: 4,8
* INC # A1: 4,8 => UNS
* INC # F1: 2,3 => UNS
* INC # I8: 2,3 => UNS
* INC # I9: 2,3 => UNS
* INC # A5: 4,8 => UNS
* INC # C5: 4,8 => UNS
* DIS # A6: 4,8 => CTR => A6: 1
* INC # A6: 1 => UNS
* INC # E1: 5,8 => UNS
* DIS # E3: 5,8 => CTR => E3: 3,7,9
* INC # E3: 3,7,9 => UNS
* INC # F1: 5,8 => UNS
* DIS # F3: 5,8 => CTR => F3: 2,3,9
* INC # F3: 2,3,9 => UNS
* INC # I5: 1,4 => UNS
* DIS # H6: 1,4 => CTR => H6: 6
* INC # H6: 6 => UNS
* DIS # A5: 1,4 => CTR => A5: 2,8
* INC # A5: 2,8 => UNS
* INC # D7: 2,4 => UNS
* PRF # D9: 2,4 => SOL
* INC # D9: 5 => UNS
* INC # A8: 2,4 => UNS
* INC # C8: 2,4 => UNS
* INC # I8: 2,4 => UNS
* DIS # G8: 2,9 => CTR => G8: 1,7
* INC # G8: 1,7 => UNS
* INC # I8: 2,9 => UNS
* INC # I9: 2,9 => UNS
* PRF # B7: 2,9 => SOL
* INC # B7: 4,5 => UNS
* INC # F7: 2,9 => UNS
* INC # I8: 3,4 => UNS
* DIS # H9: 3,4 => CTR => H9: 7
* INC # H9: 7 => UNS
* INC # I9: 3,4 => UNS
* CNT  51 HDP CHAINS /  51 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F1: 2,8 => UNS
* INC # F3: 2,8 => UNS
* INC # A2: 2,8 => UNS
* INC # C2: 2,8 => UNS
* DIS # D7: 2,8 => CTR => D7: 4,5
* DIS D7: 4,5 # G2: 2,7 => CTR => G2: 6
* PRF D7: 4,5 + G2: 6 => SOL
* STA D7: 4,5 + G2: 6
* CNT   7 HDP CHAINS /   6 HYP OPENED