Analysis of zz-www.sudokuoftheday.co.uk-20060529-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: .8.1......2..8.46..6....7.....9.....1..42..35....3.84..145.....6.....9..97...2... initial

Autosolve

position: .8.1......2..8.46..6.2..7...4.9.....19.42.635.5..31849.145.....63....9..97...2... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # F1: 3,7 => CTR => F1: 4,5,6,9
* DIS # F2: 3,7 => CTR => F2: 5,9
* DIS # G1: 2,3 => CTR => G1: 5
* DIS # I7: 2,3 => CTR => I7: 6,7,8
* PRF # I3: 1,3 => SOL
* DIS # C2: 1,3 => CTR => C2: 7,9
* DIS # I9: 1,3 => CTR => I9: 4,6,8
* DIS # C4: 3,8 => CTR => C4: 6
* DIS # C6: 6 => CTR => C6: 2,7
* DIS # F4: 5,6 => CTR => F4: 8
* DIS # E1: 5,6 => CTR => E1: 4,7,9
* DIS # C6: 2 => CTR => C6: 6,7
* DIS # I4: 1,2 => CTR => I4: 7
* DIS # C8: 5 => CTR => C8: 2,8
* DIS # H7: 2,8 => CTR => H7: 7
* DIS # I7: 2,8 => CTR => I7: 3,6,7
* DIS # C8: 5,8 => CTR => C8: 2
* DIS # H8: 7,8 => CTR => H8: 1,2,5
* DIS # E8: 4,7 => CTR => E8: 1
* DIS # F1: 4,7 => CTR => F1: 3,5,6,9
* DIS # I7: 2,3 => CTR => I7: 6,7,8
* DIS # G1: 2,3 => CTR => G1: 5
* CNT  22 HDP CHAINS /  52 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 # F1: 3,7 => CTR => F1: 4,5,6,9
* DIS F1: 4,5,6,9 # F2: 3,7 => CTR => F2: 5,9
* DIS F1: 4,5,6,9 + F2: 5,9 # G1: 2,3 => CTR => G1: 5
* PRF F1: 4,5,6,9 + F2: 5,9 + G1: 5 # I3: 1,3 => SOL
* STA F1: 4,5,6,9 + F2: 5,9 + G1: 5 + I3: 1,3
* CNT   4 HDP CHAINS /   6 HYP OPENED

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

Details

Positions

.8.1......2..8.46..6....7.....9.....1..42..35....3.84..145.....6.....9..97...2... initial
.8.1......2..8.46..6.2..7...4.9.....19.42.635.5..31849.145.....63....9..97...2... autosolve
483176592729385461561249783346958127198427635257631849814593276632714958975862314 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
D2: 3,7
I1: 2,3
I2: 1,3
A4: 3,8
C5: 7,8
A6: 2,7
E4: 5,6
F5: 7,8
D6: 6,7
G4: 1,2
A7: 2,8
C9: 5,8
D8: 7,8
F8: 4,7
G7: 2,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C2,C3: 1.. / C2 = 1  =>  0 pairs (X) / C3 = 1  => 16 pairs (_)
E8,E9: 1.. / E8 = 1  => 16 pairs (_) / E9 = 1  =>  0 pairs (X)
C2,I2: 1.. / C2 = 1  =>  0 pairs (X) / I2 = 1  => 16 pairs (_)
G4,G9: 1.. / G4 = 1  => 17 pairs (_) / G9 = 1  =>  0 pairs (X)
A6,C6: 2.. / A6 = 2  => 21 pairs (_) / C6 = 2  =>  0 pairs (X)
A7,C8: 2.. / A7 = 2  =>  0 pairs (X) / C8 = 2  => 21 pairs (_)
A6,A7: 2.. / A6 = 2  => 21 pairs (_) / A7 = 2  =>  0 pairs (X)
C6,C8: 2.. / C6 = 2  =>  0 pairs (X) / C8 = 2  => 21 pairs (_)
A4,C4: 3.. / A4 = 3  => 21 pairs (_) / C4 = 3  =>  0 pairs (X)
F7,D9: 3.. / F7 = 3  =>  0 pairs (*) / D9 = 3  =>  0 pairs (X)
D2,D9: 3.. / D2 = 3  =>  0 pairs (*) / D9 = 3  =>  0 pairs (X)
A1,A3: 4.. / A1 = 4  => 16 pairs (_) / A3 = 4  => 23 pairs (_)
I8,I9: 4.. / I8 = 4  =>  0 pairs (X) / I9 = 4  => 18 pairs (_)
E9,I9: 4.. / E9 = 4  =>  0 pairs (X) / I9 = 4  => 18 pairs (_)
E4,F4: 5.. / E4 = 5  => 16 pairs (_) / F4 = 5  =>  0 pairs (X)
C8,C9: 5.. / C8 = 5  =>  0 pairs (X) / C9 = 5  => 18 pairs (_)
A2,F2: 5.. / A2 = 5  => 16 pairs (_) / F2 = 5  => 21 pairs (_)
C8,H8: 5.. / C8 = 5  =>  0 pairs (X) / H8 = 5  => 18 pairs (_)
G1,G9: 5.. / G1 = 5  => 17 pairs (_) / G9 = 5  =>  0 pairs (X)
E1,F1: 6.. / E1 = 6  =>  0 pairs (X) / F1 = 6  => 16 pairs (_)
C4,C6: 6.. / C4 = 6  => 20 pairs (_) / C6 = 6  =>  0 pairs (X)
I7,I9: 6.. / I7 = 6  => 16 pairs (_) / I9 = 6  =>  0 pairs (X)
C6,D6: 6.. / C6 = 6  =>  0 pairs (X) / D6 = 6  => 20 pairs (_)
D6,D9: 6.. / D6 = 6  => 20 pairs (_) / D9 = 6  =>  0 pairs (X)
F5,D6: 7.. / F5 = 7  => 20 pairs (_) / D6 = 7  =>  0 pairs (X)
H4,I4: 7.. / H4 = 7  =>  0 pairs (X) / I4 = 7  => 16 pairs (_)
C5,F5: 7.. / C5 = 7  =>  0 pairs (X) / F5 = 7  => 20 pairs (_)
H3,I3: 8.. / H3 = 8  =>  0 pairs (*) / I3 = 8  =>  0 pairs (X)
F4,F5: 8.. / F4 = 8  => 20 pairs (_) / F5 = 8  =>  0 pairs (X)
D8,D9: 8.. / D8 = 8  => 16 pairs (_) / D9 = 8  =>  0 pairs (*)
C5,F5: 8.. / C5 = 8  => 20 pairs (_) / F5 = 8  =>  0 pairs (X)
A4,A7: 8.. / A4 = 8  =>  0 pairs (X) / A7 = 8  => 21 pairs (_)
H1,H3: 9.. / H1 = 9  => 18 pairs (_) / H3 = 9  => 19 pairs (_)
E7,F7: 9.. / E7 = 9  => 16 pairs (_) / F7 = 9  =>  0 pairs (X)
C2,F2: 9.. / C2 = 9  => 17 pairs (_) / F2 = 9  => 19 pairs (_)
* DURATION: 0:00:38.189470  START: 23:28:51.089583  END: 23:29:29.279053 2019-04-30
* CP COUNT: (35)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,A7,C5,C9,D2,D6,D8,E4,F5,F8,G4,G7,I1,I2)
* .8.1......2..8.46..6.2..7...4.9.....19.42.635.5..31849.145.....63....9..97...2...
* PAIR D2: 3,7 BLK 2
F1: 3,7,4,5,6,9                          # reduction candidate for 3,7
F1: 3,7 => CTR
* 48.16.5...2.38.461.6124.7.8.4.9561.719.428635.56731849.145932.663.8749..97.6123.4
F1: 4,5,6,9                              # 15 pairs
F2: 3,7,5,9                              # reduction candidate for 3,7
F2: 3,7 => CTR
* .8.1....3529.8.46136124.7.88439.....19742.635.5..31849.145....663.8.49..97...2..4
F2: 5,9                                  # 16 pairs
* PAIR D2: 3,7 ROW 2
A2: 3,7,5                                # reduction candidate for 3,7
A2: 3,7                                  # 21 pairs
C2: 3,7,1,9                              # reduction candidate for 3,7
C2: 3,7                                  # 20 pairs
* PAIR I1: 2,3 BLK 3
G1: 2,3,5                                # reduction candidate for 2,3
G1: 2,3 => CTR
* .8.1......2..8.46..6.2..7..8439..1..19742.635.5..31849.145.....635...9..978..251.
G1: 5                                    # 17 pairs
* PAIR I1: 2,3 COL I
I7: 2,3,6,7,8                            # reduction candidate for 2,3
I7: 2,3 => CTR
* .8.1......2..8.46..6.2..7.8.46958..7198427635.5.631849.145.....63....9.497..42..6
I7: 6,7,8                                # 15 pairs
* PAIR I2: 1,3 BLK 3
I3: 1,3,8                                # reduction candidate for 1,3
I3: 1,3 => SOLVED
* 483176592729385461561249783346958127198427635257631849814593276632714958975862314
I3: 8                                    # 15 pairs
* PAIR I2: 1,3 ROW 2
C2: 1,3,7,9                              # reduction candidate for 1,3
C2: 1,3 => CTR
* .8.1.....52.78946..6.2..7...4.9.....19.427635.5.631849.1459....63.8749..97.3125..
C2: 7,9                                  # 17 pairs
* PAIR I2: 1,3 COL I
I9: 1,3,4,6,8                            # reduction candidate for 1,3
I9: 1,3 => CTR
* .8.176..2.2.38.461.612.47.8.4.965..719742863525..31849.145....663..179.497.642...
I9: 4,6,8                                # 15 pairs
* PAIR A4: 3,8 BLK 4
C4: 3,8,6                                # reduction candidate for 3,8
C4: 3,8 => CTR
* .8.1765..729385461.612..7...4.9.....1974286352567318498145.3276632817954975642318
C4: 6                                    # 20 pairs
* PAIR A6: 2,7 BLK 4
C6: 2,7,6                                # reduction candidate for 2,7
C6: 6 => CTR
* .83176592729385461.612..7..3489.....1974286352567318498145.3276632817954975642318
C6: 2,7                                  # 20 pairs
* PAIR E4: 5,6 BLK 5
F4: 5,6,8                                # reduction candidate for 5,6
F4: 5,6 => CTR
* .8.1..5...2938.461.612..7..3489..127197428635256731849814593276632817954975642318
F4: 8                                    # 20 pairs
* PAIR E4: 5,6 COL E
E1: 5,6,4,7,9                            # reduction candidate for 5,6
E1: 5,6 => CTR
* 48.1..5.2.2138.46..6.24.7.8.4.9..1.719.42.635.5..31849.14593276632874951975612384
E1: 4,7,9                                # 16 pairs
* PAIR D6: 6,7 ROW 6
C6: 6,7,2                                # reduction candidate for 6,7
C6: 2 => CTR
* .8.1......2..8.46..6.2..7...46958...198427635752631849.145.....63....9..97...2...
C6: 6,7                                  # 21 pairs
* PAIR G4: 1,2 BLK 6
H4: 1,2,7                                # reduction candidate for 1,2
H4: 1,2                                  # 16 pairs
I4: 1,2,7                                # reduction candidate for 1,2
I4: 1,2 => CTR
* .8.1.6....2978.461.612..7.8.46958172198427635.5.63184981457932663.8149.797.362..4
I4: 7                                    # 16 pairs
* PAIR A7: 2,8 BLK 7
C8: 2,8,5                                # reduction candidate for 2,8
C8: 5 => CTR
* .8.1......2..8.46..6.2..7...4.9.....19.42.635.526318492145..3..635...9..9783.2...
C8: 2,8                                  # 18 pairs
* PAIR A7: 2,8 ROW 7
H7: 2,8,7                                # reduction candidate for 2,8
H7: 2,8 => CTR
* .8.1.6592.2.78.463.6.2.3718346958271198427635257631849814579326632814957975362184
H7: 7                                    # 17 pairs
I7: 2,8,3,6,7                            # reduction candidate for 2,8
I7: 2,8 => CTR
* .8.1......2..8.46..6.2..7...46958..7198427635.5.631849.145.....63....9.497..42..6
I7: 3,6,7                                # 15 pairs
* PAIR C9: 5,8 BLK 7
C8: 5,8,2                                # reduction candidate for 5,8
C8: 5,8 => CTR
* .8.1......2.78.46..6.2..7..84.9.....19.42.635.526318492145..3..63....9..97.3.2...
C8: 2                                    # 21 pairs
* PAIR C9: 5,8 ROW 9
H9: 5,8,1                                # reduction candidate for 5,8
H9: 5,8                                  # 19 pairs
H9: 1                                    # 18 pairs
* PAIR D8: 7,8 ROW 8
H8: 7,8,1,2,5                            # reduction candidate for 7,8
H8: 7,8 => CTR
* .8.1....3.2..8.461.612..7.88439....719742.635.5..31849.145.....635...9.2978..2..4
H8: 1,2,5                                # 15 pairs
I8: 7,8,1,2,4                            # reduction candidate for 7,8
I8: 7,8                                  # 20 pairs
* PAIR F8: 4,7 BLK 8
E8: 4,7,1                                # reduction candidate for 4,7
E8: 4,7 => CTR
* .8.1..5...2.38.461.612..7...4.9..1..19.42.635.56731849.145.32.66328..9..97.6123.4
E8: 1                                    # 16 pairs
* PAIR F8: 4,7 ROW 8
I8: 4,7,1,2,8                            # reduction candidate for 4,7
I8: 4,7                                  # 19 pairs
I8: 1,2,8                                # 19 pairs
* PAIR F8: 4,7 COL F
F1: 4,7,3,5,6,9                          # reduction candidate for 4,7
F1: 4,7 => CTR
* 48.167....2.38.461.6124.7...4.95.1..19742863525673184981459327.63.8.49..97..12..4
F1: 3,5,6,9                              # 15 pairs
* PAIR G7: 2,3 BLK 9
I7: 2,3,6,7,8                            # reduction candidate for 2,3
I7: 2,3 => CTR
* .8.1......2..8.46..6.2..7.8.46958..7198427635.5.631849.145.....63....9.497..42..6
I7: 6,7,8                                # 15 pairs
* PAIR G7: 2,3 COL G
G1: 2,3,5                                # reduction candidate for 2,3
G1: 2,3 => CTR
* .8.1......2..8.46..6.2..7..8439..1..19742.635.5..31849.145.....635...9..978..251.
G1: 5                                    # 17 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060529-absurd-base-pr-000.dot
* REASONING
* DIS # F1: 3,7 => CTR => F1: 4,5,6,9
* DIS # F2: 3,7 => CTR => F2: 5,9
* DIS # G1: 2,3 => CTR => G1: 5
* DIS # I7: 2,3 => CTR => I7: 6,7,8
* PRF # I3: 1,3 => SOL
* DIS # C2: 1,3 => CTR => C2: 7,9
* DIS # I9: 1,3 => CTR => I9: 4,6,8
* DIS # C4: 3,8 => CTR => C4: 6
* DIS # C6: 6 => CTR => C6: 2,7
* DIS # F4: 5,6 => CTR => F4: 8
* DIS # E1: 5,6 => CTR => E1: 4,7,9
* DIS # C6: 2 => CTR => C6: 6,7
* DIS # I4: 1,2 => CTR => I4: 7
* DIS # C8: 5 => CTR => C8: 2,8
* DIS # H7: 2,8 => CTR => H7: 7
* DIS # I7: 2,8 => CTR => I7: 3,6,7
* DIS # C8: 5,8 => CTR => C8: 2
* DIS # H8: 7,8 => CTR => H8: 1,2,5
* DIS # E8: 4,7 => CTR => E8: 1
* DIS # F1: 4,7 => CTR => F1: 3,5,6,9
* DIS # I7: 2,3 => CTR => I7: 6,7,8
* DIS # G1: 2,3 => CTR => G1: 5
* CNT  22 HDP CHAINS /  52 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,A7,C5,C9,D2,D6,D8,E4,F5,F8,G4,G7,I1,I2)
* .8.1......2..8.46..6.2..7...4.9.....19.42.635.5..31849.145.....63....9..97...2...
* PAIR D2: 3,7 BLK 2
F1: 3,7,4,5,6,9                          # reduction candidate for 3,7
F1: 3,7 => CTR
* 48.16.5...2.38.461.6124.7.8.4.9561.719.428635.56731849.145932.663.8749..97.6123.4
F2: 3,7,5,9                              # reduction candidate for 3,7
F2: 3,7 => CTR
* .8.1....3529.8.46136124.7.88439.....19742.635.5..31849.145....663.8.49..97...2..4
* RESTART
* PAIR D2: 3,7 ROW 2
A2: 3,7,5                                # reduction candidate for 3,7
A2: 3,7                                  # 21 pairs
C2: 3,7,1,9                              # reduction candidate for 3,7
C2: 3,7                                  # 21 pairs
* PAIR I1: 2,3 BLK 3
G1: 2,3,5                                # reduction candidate for 2,3
G1: 2,3 => CTR
* .8.1......2..8.46..6.2..7..8439..1..19742.635.5..31849.145.....635...9..978..251.
* PAIR I2: 1,3 BLK 3
I3: 1,3,8                                # reduction candidate for 1,3
I3: 1,3 => SOLVED
* 483176592729385461561249783346958127198427635257631849814593276632714958975862314
* DURATION: 0:00:05.827336  START: 23:29:59.299394  END: 23:30:05.126730 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060529-absurd-base-pr-001.dot
* REASONING
* DIS # F1: 3,7 => CTR => F1: 4,5,6,9
* DIS F1: 4,5,6,9 # F2: 3,7 => CTR => F2: 5,9
* DIS F1: 4,5,6,9 + F2: 5,9 # G1: 2,3 => CTR => G1: 5
* PRF F1: 4,5,6,9 + F2: 5,9 + G1: 5 # I3: 1,3 => SOL
* STA F1: 4,5,6,9 + F2: 5,9 + G1: 5 + I3: 1,3
* CNT   4 HDP CHAINS /   6 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060529, absurd

Solution

position: 483176592729385461561249783346958127198427635257631849814593276632714958975862314 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 # F1: 3,7 => CTR => F1: 4,5,6,9
* INC # F1: 4,5,6,9 => UNS
* DIS # F2: 3,7 => CTR => F2: 5,9
* INC # F2: 5,9 => UNS
* INC # A2: 3,7 => UNS
* INC # C2: 3,7 => UNS
* DIS # G1: 2,3 => CTR => G1: 5
* INC # G1: 5 => UNS
* DIS # I7: 2,3 => CTR => I7: 6,7,8
* INC # I7: 6,7,8 => UNS
* PRF # I3: 1,3 => SOL
* INC # I3: 8 => UNS
* DIS # C2: 1,3 => CTR => C2: 7,9
* INC # C2: 7,9 => UNS
* DIS # I9: 1,3 => CTR => I9: 4,6,8
* INC # I9: 4,6,8 => UNS
* DIS # C4: 3,8 => CTR => C4: 6
* INC # C4: 6 => UNS
* INC # C6: 2,7 => UNS
* DIS # C6: 6 => CTR => C6: 2,7
* DIS # F4: 5,6 => CTR => F4: 8
* INC # F4: 8 => UNS
* DIS # E1: 5,6 => CTR => E1: 4,7,9
* INC # E1: 4,7,9 => UNS
* INC # C6: 6,7 => UNS
* DIS # C6: 2 => CTR => C6: 6,7
* INC # H4: 1,2 => UNS
* DIS # I4: 1,2 => CTR => I4: 7
* INC # I4: 7 => UNS
* INC # C8: 2,8 => UNS
* DIS # C8: 5 => CTR => C8: 2,8
* DIS # H7: 2,8 => CTR => H7: 7
* INC # H7: 7 => UNS
* DIS # I7: 2,8 => CTR => I7: 3,6,7
* INC # I7: 3,6,7 => UNS
* DIS # C8: 5,8 => CTR => C8: 2
* INC # C8: 2 => UNS
* INC # H9: 5,8 => UNS
* INC # H9: 1 => UNS
* DIS # H8: 7,8 => CTR => H8: 1,2,5
* INC # H8: 1,2,5 => UNS
* INC # I8: 7,8 => UNS
* DIS # E8: 4,7 => CTR => E8: 1
* INC # E8: 1 => UNS
* INC # I8: 4,7 => UNS
* INC # I8: 1,2,8 => UNS
* DIS # F1: 4,7 => CTR => F1: 3,5,6,9
* INC # F1: 3,5,6,9 => UNS
* DIS # I7: 2,3 => CTR => I7: 6,7,8
* INC # I7: 6,7,8 => UNS
* DIS # G1: 2,3 => CTR => G1: 5
* INC # G1: 5 => UNS
* CNT  52 HDP CHAINS /  52 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # F1: 3,7 => CTR => F1: 4,5,6,9
* DIS F1: 4,5,6,9 # F2: 3,7 => CTR => F2: 5,9
* INC F1: 4,5,6,9 + F2: 5,9 # A2: 3,7 => UNS
* INC F1: 4,5,6,9 + F2: 5,9 # C2: 3,7 => UNS
* DIS F1: 4,5,6,9 + F2: 5,9 # G1: 2,3 => CTR => G1: 5
* PRF F1: 4,5,6,9 + F2: 5,9 + G1: 5 # I3: 1,3 => SOL
* STA F1: 4,5,6,9 + F2: 5,9 + G1: 5 + I3: 1,3
* CNT   6 HDP CHAINS /   6 HYP OPENED