Analysis of zz-sudoku-de-754055-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 45..9.7.2..7.....41....4.6...39.8...8...6...1...3.72...9.1....85.....1..2.1.3..45 initial

Autosolve

position: 45..9.7.2..7.....41....4.6...39.845.8...6...1..53.728..9.1....85.....1..2.1.3..45 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B2: 2,3 => CTR => B2: 6,8
* DIS # C8: 4 => CTR => C8: 6,8
* DIS # H2: 1 => CTR => H2: 3,9
* DIS # D2: 6,8 => CTR => D2: 2,5
* DIS # H2: 1,3 => CTR => H2: 9
* PRF # H2: 9 => SOL
* DIS # H2: 1,3 => CTR => H2: 9
* PRF # H2: 9 => SOL
* DIS # D2: 5,8 => CTR => D2: 2,6
* DIS # E3: 5,8 => CTR => E3: 2,7
* DIS # H2: 1 => CTR => H2: 3,9
* PRF # I8: 3,9 => SOL
* DIS # I8: 7 => CTR => I8: 3,9
* DIS # D5: 2,5 => CTR => D5: 4
* PRF # F7: 6 => SOL
* PRF # H5: 3,9 => SOL
* DIS # H5: 7 => CTR => H5: 3,9
* DIS # B8: 6,8 => CTR => B8: 3,7
* DIS # C8: 8 => CTR => C8: 4,6
* DIS # B8: 7,8 => CTR => B8: 3,6
* PRF # F8: 2 => SOL
* CNT  21 HDP CHAINS /  42 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 # B2: 2,3 => CTR => B2: 6,8
* DIS B2: 6,8 # C8: 4 => CTR => C8: 6,8
* DIS B2: 6,8 + C8: 6,8 # H2: 1 => CTR => H2: 3,9
* DIS B2: 6,8 + C8: 6,8 + H2: 3,9 # D2: 6,8 => CTR => D2: 2,5
* DIS B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 # E2: 2 => CTR => E2: 5,8
* DIS B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 + E2: 5,8 # E3: 5,8 => CTR => E3: 7
* PRF B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 + E2: 5,8 + E3: 7 # I8: 3,9 => SOL
* STA B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 + E2: 5,8 + E3: 7 + I8: 3,9
* CNT   7 HDP CHAINS /  12 HYP OPENED

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

Details

Positions

45..9.7.2..7.....41....4.6...39.8...8...6...1...3.72...9.1....85.....1..2.1.3..45 initial
45..9.7.2..7.....41....4.6...39.845.8...6...1..53.728..9.1....85.....1..2.1.3..45 autosolve
458693712367281594129574863613928457872465931945317286794156328536842179281739645 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (28)
C1: 6,8
A2: 3,9
C3: 2,9
D1: 6,8
F1: 1,3
F2: 1,3
H1: 1,3
G2: 5,8
G3: 5,8
I3: 3,9
A4: 6,7
B4: 1,2
C5: 2,9
A6: 6,9
B6: 1,4
E4: 1,2
F5: 2,5
E6: 1,4
I4: 6,7
G5: 3,9
I6: 6,9
A7: 3,7
C7: 4,6
B9: 7,8
D9: 7,8
F9: 6,9
G7: 3,6
G9: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F1,F2: 1.. / F1 = 1  =>  0 pairs (X) / F2 = 1  => 26 pairs (_)
H1,H2: 1.. / H1 = 1  => 26 pairs (_) / H2 = 1  =>  0 pairs (X)
B4,B6: 1.. / B4 = 1  => 23 pairs (_) / B6 = 1  =>  0 pairs (X)
E4,E6: 1.. / E4 = 1  =>  0 pairs (X) / E6 = 1  => 23 pairs (_)
F1,H1: 1.. / F1 = 1  =>  0 pairs (X) / H1 = 1  => 26 pairs (_)
F2,H2: 1.. / F2 = 1  => 26 pairs (_) / H2 = 1  =>  0 pairs (X)
B4,E4: 1.. / B4 = 1  => 23 pairs (_) / E4 = 1  =>  0 pairs (X)
B6,E6: 1.. / B6 = 1  =>  0 pairs (X) / E6 = 1  => 23 pairs (_)
H7,H8: 2.. / H7 = 2  => 29 pairs (_) / H8 = 2  => 29 pairs (_)
B4,E4: 2.. / B4 = 2  =>  0 pairs (X) / E4 = 2  => 23 pairs (_)
C3,C5: 2.. / C3 = 2  =>  0 pairs (X) / C5 = 2  =>  0 pairs (_)
F1,F2: 3.. / F1 = 3  => 26 pairs (_) / F2 = 3  =>  0 pairs (X)
G5,H5: 3.. / G5 = 3  => 27 pairs (_) / H5 = 3  =>  0 pairs (*)
A7,B8: 3.. / A7 = 3  =>  0 pairs (X) / B8 = 3  =>  0 pairs (_)
F1,H1: 3.. / F1 = 3  => 26 pairs (_) / H1 = 3  =>  0 pairs (X)
B3,I3: 3.. / B3 = 3  =>  0 pairs (X) / I3 = 3  =>  0 pairs (_)
A2,A7: 3.. / A2 = 3  =>  0 pairs (*) / A7 = 3  =>  0 pairs (X)
G5,G7: 3.. / G5 = 3  => 27 pairs (_) / G7 = 3  =>  0 pairs (*)
I3,I8: 3.. / I3 = 3  =>  0 pairs (*) / I8 = 3  =>  0 pairs (X)
B5,B6: 4.. / B5 = 4  =>  0 pairs (X) / B6 = 4  => 23 pairs (_)
D5,E6: 4.. / D5 = 4  => 23 pairs (_) / E6 = 4  =>  0 pairs (X)
C7,C8: 4.. / C7 = 4  => 29 pairs (_) / C8 = 4  =>  0 pairs (X)
B5,D5: 4.. / B5 = 4  =>  0 pairs (X) / D5 = 4  => 23 pairs (_)
B6,E6: 4.. / B6 = 4  => 23 pairs (_) / E6 = 4  =>  0 pairs (X)
C7,E7: 4.. / C7 = 4  => 29 pairs (_) / E7 = 4  =>  0 pairs (X)
D5,D8: 4.. / D5 = 4  => 23 pairs (_) / D8 = 4  =>  0 pairs (X)
G2,G3: 5.. / G2 = 5  => 31 pairs (_) / G3 = 5  => 28 pairs (_)
D5,F5: 5.. / D5 = 5  =>  0 pairs (X) / F5 = 5  => 31 pairs (_)
E7,F7: 5.. / E7 = 5  => 31 pairs (_) / F7 = 5  =>  0 pairs (X)
F5,F7: 5.. / F5 = 5  => 31 pairs (_) / F7 = 5  =>  0 pairs (X)
C1,B2: 6.. / C1 = 6  =>  0 pairs (X) / B2 = 6  => 28 pairs (_)
D1,D2: 6.. / D1 = 6  => 28 pairs (_) / D2 = 6  =>  0 pairs (X)
A4,A6: 6.. / A4 = 6  =>  0 pairs (*) / A6 = 6  =>  0 pairs (X)
I4,I6: 6.. / I4 = 6  =>  0 pairs (X) / I6 = 6  =>  0 pairs (_)
G7,G9: 6.. / G7 = 6  => 27 pairs (_) / G9 = 6  =>  0 pairs (*)
C1,D1: 6.. / C1 = 6  =>  0 pairs (X) / D1 = 6  => 28 pairs (_)
B2,D2: 6.. / B2 = 6  => 28 pairs (_) / D2 = 6  =>  0 pairs (X)
A4,I4: 6.. / A4 = 6  =>  0 pairs (*) / I4 = 6  =>  0 pairs (X)
A6,I6: 6.. / A6 = 6  =>  0 pairs (X) / I6 = 6  =>  0 pairs (_)
F9,G9: 6.. / F9 = 6  => 27 pairs (_) / G9 = 6  =>  0 pairs (*)
B2,B8: 6.. / B2 = 6  => 28 pairs (_) / B8 = 6  =>  0 pairs (X)
D3,E3: 7.. / D3 = 7  =>  0 pairs (X) / E3 = 7  => 28 pairs (_)
A4,B5: 7.. / A4 = 7  =>  0 pairs (X) / B5 = 7  =>  0 pairs (_)
I4,H5: 7.. / I4 = 7  =>  0 pairs (*) / H5 = 7  =>  0 pairs (X)
A4,I4: 7.. / A4 = 7  =>  0 pairs (X) / I4 = 7  =>  0 pairs (_)
B5,H5: 7.. / B5 = 7  =>  0 pairs (*) / H5 = 7  =>  0 pairs (X)
B9,D9: 7.. / B9 = 7  =>  0 pairs (X) / D9 = 7  => 28 pairs (_)
A4,A7: 7.. / A4 = 7  =>  0 pairs (X) / A7 = 7  =>  0 pairs (_)
I4,I8: 7.. / I4 = 7  =>  0 pairs (*) / I8 = 7  =>  0 pairs (X)
G2,G3: 8.. / G2 = 8  => 28 pairs (_) / G3 = 8  => 31 pairs (_)
C1,D1: 8.. / C1 = 8  => 28 pairs (_) / D1 = 8  =>  0 pairs (X)
B9,D9: 8.. / B9 = 8  => 28 pairs (_) / D9 = 8  =>  0 pairs (X)
C1,C8: 8.. / C1 = 8  => 28 pairs (_) / C8 = 8  =>  0 pairs (X)
A2,C3: 9.. / A2 = 9  =>  0 pairs (X) / C3 = 9  =>  0 pairs (_)
H2,I3: 9.. / H2 = 9  =>  0 pairs (*) / I3 = 9  =>  0 pairs (X)
C5,A6: 9.. / C5 = 9  =>  0 pairs (X) / A6 = 9  =>  0 pairs (_)
F8,F9: 9.. / F8 = 9  => 27 pairs (_) / F9 = 9  =>  0 pairs (*)
A2,H2: 9.. / A2 = 9  =>  0 pairs (X) / H2 = 9  =>  0 pairs (_)
C3,I3: 9.. / C3 = 9  =>  0 pairs (*) / I3 = 9  =>  0 pairs (X)
A6,I6: 9.. / A6 = 9  =>  0 pairs (*) / I6 = 9  =>  0 pairs (X)
F9,G9: 9.. / F9 = 9  =>  0 pairs (*) / G9 = 9  =>  0 pairs (X)
A2,A6: 9.. / A2 = 9  =>  0 pairs (X) / A6 = 9  =>  0 pairs (_)
C3,C5: 9.. / C3 = 9  =>  0 pairs (*) / C5 = 9  =>  0 pairs (X)
G5,G9: 9.. / G5 = 9  =>  0 pairs (*) / G9 = 9  =>  0 pairs (X)
* DURATION: 0:02:06.206642  START: 08:30:06.741033  END: 08:32:12.947675 2017-05-01
* CP COUNT: (64)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,A6,A7,B4,B6,B9,C1,C3,C5,C7,D1,D9,E4,E6,F1,F2,F5,F9,G2,G3,G5,G7,G9,H1,I3,I4,I6)
* 45..9.7.2..7.....41....4.6...39.845.8...6...1..53.728..9.1....85.....1..2.1.3..45
* PAIR C1: 6,8 BLK 1
B2: 6,8,2,3                              # reduction candidate for 6,8
B2: 2,3 => CTR
* 45689.7.2..76..8.418...4563..39.845.8..562..1..534728..941....85.....1..2.1.3..45
B2: 6,8                                  # 30 pairs
* PAIR C1: 6,8 COL C
C8: 6,8,4                                # reduction candidate for 6,8
C8: 4 => CTR
* 45869.7.2.67.....41....4.6...39.845.8...6...1..53.728..96145328534..61..28173..45
C8: 6,8                                  # 29 pairs
* PAIR A2: 3,9 ROW 2
H2: 3,9,1                                # reduction candidate for 3,9
H2: 1 => CTR
* 45..9.7.29.7....141.2..4.69..39.845.8.9.6.3716.53.728..9.1....85.....1..2.1.3..45
H2: 3,9                                  # 26 pairs
* PAIR D1: 6,8 BLK 2
D2: 6,8,2,5                              # reduction candidate for 6,8
D2: 6,8 => CTR
* 45869.7.2.6782.5.41..57486..2391845.8.9.6537161534728979.1....85...8.1..28173..45
D2: 2,5                                  # 29 pairs
* PAIR F2: 1,3 ROW 2
H2: 1,3,9                                # reduction candidate for 1,3
H2: 1,3 => CTR
* 45..9.7.29.7.....41.2..4.69..39.845.8.9.6.3716.53.728..9.1....85.....1..2.1.3..45
H2: 9 => SOLVED
* 458693712367281594129574863613928457872465931945317286794156328536842179281739645
* PAIR H1: 1,3 BLK 3
H2: 1,3,9                                # reduction candidate for 1,3
H2: 1,3 => CTR
* 45..9.7.29.7.....41.2..4.69..39.845.8.9.6.3716.53.728..9.1....85.....1..2.1.3..45
H2: 9 => SOLVED
* 458693712367281594129574863613928457872465931945317286794156328536842179281739645
* PAIR G2: 5,8 ROW 2
D2: 5,8,2,6                              # reduction candidate for 5,8
D2: 5,8 => CTR
* 45.69.7.2.67.2...41....4.6..2391845.8.9.6.371615347289.941..6.85.64..1.727183..45
D2: 2,6                                  # 29 pairs
E2: 5,8,2                                # reduction candidate for 5,8
E2: 5,8                                  # 31 pairs
* PAIR G3: 5,8 ROW 3
D3: 5,8,2,7                              # reduction candidate for 5,8
D3: 5,8                                  # 31 pairs
E3: 5,8,2,7                              # reduction candidate for 5,8
E3: 5,8 => CTR
* 45869.7.2967.....413.7.4.6.7.39.84568...6..716.53.728939.175628586...1.7271836945
E3: 2,7                                  # 29 pairs
* PAIR I3: 3,9 BLK 3
H2: 3,9,1                                # reduction candidate for 3,9
H2: 1 => CTR
* 45..9.7.29.7....141.2..4.69..39.845.8.9.6.3716.53.728..9.1....85.....1..2.1.3..45
H2: 3,9                                  # 26 pairs
* PAIR I3: 3,9 COL I
I8: 3,9,7                                # reduction candidate for 3,9
I8: 3,9 => SOLVED
* 458693712367281594129574863613928457872465931945317286794156328536842179281739645
I8: 7 => CTR
* 45..937129.7.....41....4.63..39.845.8...6...1..53.7289.9.1....85.....1.72.1.3.945
* PAIR F5: 2,5 BLK 5
D5: 2,5,4                                # reduction candidate for 2,5
D5: 2,5 => CTR
* 45869.7.2.67.....41..7.4.637239.845.84..6..71.1534728..941....85..4..1.727183..45
D5: 4                                    # 23 pairs
* PAIR F5: 2,5 COL F
F7: 2,5,6                                # reduction candidate for 2,5
F7: 6 => SOLVED
* 458693712367281594129574863613928457872465931945317286794156328536842179281739645
F7: 2,5                                  # 30 pairs
* PAIR G5: 3,9 BLK 6
H5: 3,9,7                                # reduction candidate for 3,9
H5: 3,9 => SOLVED
* 458693712367281594129574863613928457872465931945317286794156328536842179281739645
H5: 7 => CTR
* 45869.7.2967.....413...4.6...39.845.8...6.371..53.7289.9.1..6.85.....1.7271836945
* PAIR A7: 3,7 BLK 7
B8: 3,7,6,8                              # reduction candidate for 3,7
B8: 6,8 => CTR
* 45869.7.2967.....4132..4.697.39.84568...6...1..53.728.39.1..6.85.....1..271836945
B8: 3,7                                  # 28 pairs
* PAIR A7: 3,7 ROW 7
H7: 3,7,2                                # reduction candidate for 3,7
H7: 3,7                                  # 29 pairs
H7: 2                                    # 29 pairs
* PAIR C7: 4,6 BLK 7
C8: 4,6,8                                # reduction candidate for 4,6
C8: 8 => CTR
* 45..9.7.2..7.....41....4.6...39.845.8...6...1..53.728..941....8568...1..27183..45
C8: 4,6                                  # 28 pairs
* PAIR B9: 7,8 BLK 7
B8: 7,8,3,6                              # reduction candidate for 7,8
B8: 7,8 => CTR
* 45..9.7.2.67.....4132..4.69..39.845.8.9.6.3716.53.728..9.1....85.....1..2.1.3..45
B8: 3,6                                  # 29 pairs
* PAIR D9: 7,8 BLK 8
D8: 7,8,2,4                              # reduction candidate for 7,8
D8: 7,8                                  # 23 pairs
E8: 7,8,2,4                              # reduction candidate for 7,8
E8: 7,8                                  # 30 pairs
* PAIR D9: 7,8 COL D
D3: 7,8,2,5                              # reduction candidate for 7,8
D3: 7,8                                  # 31 pairs
D3: 2,5                                  # 29 pairs
* PAIR F9: 6,9 BLK 8
F8: 6,9,2                                # reduction candidate for 6,9
F8: 2 => SOLVED
* 458693712367281594129574863613928457872465931945317286794156328536842179281739645
F8: 6,9                                  # 30 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-sudoku-de-754055-base-pr-000.dot
* REASONING
* DIS # B2: 2,3 => CTR => B2: 6,8
* DIS # C8: 4 => CTR => C8: 6,8
* DIS # H2: 1 => CTR => H2: 3,9
* DIS # D2: 6,8 => CTR => D2: 2,5
* DIS # H2: 1,3 => CTR => H2: 9
* PRF # H2: 9 => SOL
* DIS # H2: 1,3 => CTR => H2: 9
* PRF # H2: 9 => SOL
* DIS # D2: 5,8 => CTR => D2: 2,6
* DIS # E3: 5,8 => CTR => E3: 2,7
* DIS # H2: 1 => CTR => H2: 3,9
* PRF # I8: 3,9 => SOL
* DIS # I8: 7 => CTR => I8: 3,9
* DIS # D5: 2,5 => CTR => D5: 4
* PRF # F7: 6 => SOL
* PRF # H5: 3,9 => SOL
* DIS # H5: 7 => CTR => H5: 3,9
* DIS # B8: 6,8 => CTR => B8: 3,7
* DIS # C8: 8 => CTR => C8: 4,6
* DIS # B8: 7,8 => CTR => B8: 3,6
* PRF # F8: 2 => SOL
* CNT  21 HDP CHAINS /  42 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,A6,A7,B4,B6,B9,C1,C3,C5,C7,D1,D9,E4,E6,F1,F2,F5,F9,G2,G3,G5,G7,G9,H1,I3,I4,I6)
* 45..9.7.2..7.....41....4.6...39.845.8...6...1..53.728..9.1....85.....1..2.1.3..45
* PAIR C1: 6,8 BLK 1
B2: 6,8,2,3                              # reduction candidate for 6,8
B2: 2,3 => CTR
* 45689.7.2..76..8.418...4563..39.845.8..562..1..534728..941....85.....1..2.1.3..45
* PAIR C1: 6,8 COL C
C8: 6,8,4                                # reduction candidate for 6,8
C8: 4 => CTR
* 45869.7.2.67.....41....4.6...39.845.8...6...1..53.728..96145328534..61..28173..45
* PAIR RESTART
* PAIR A2: 3,9 ROW 2
H2: 3,9,1                                # reduction candidate for 3,9
H2: 1 => CTR
* 45..9.7.29.7..3.14132..4.69..39.845.8.9.6.3716.53.728..941....85.....1..2.1.3..45
* PAIR RESTART
* PAIR D1: 6,8 BLK 2
D2: 6,8,2,5                              # reduction candidate for 6,8
D2: 6,8 => CTR
* 45..93712..7.215.41....486..2391845.8.9.6.371615347289.941..6.85..48.1.72.1.3..45
* PAIR G2: 5,8 ROW 2
E2: 5,8,2                                # reduction candidate for 5,8
E2: 2 => CTR
* 458693712.67.218.41....456..2391845.8.9.6.371615347289.9415.6.85.64..1.727183..45
* PAIR RESTART
* PAIR G3: 5,8 ROW 3
D3: 5,8,7                                # reduction candidate for 5,8
D3: 5,8                                  # 30 pairs
E3: 5,8,7                                # reduction candidate for 5,8
E3: 5,8 => CTR
* 458693712.672.1..41.27.4.697239.845.8..562..1..534728..941.56.85.64.91..271836945
* RESTART
* PAIR RESTART
* PAIR I3: 3,9 COL I
I8: 3,9,7                                # reduction candidate for 3,9
I8: 3,9 => SOLVED
* 458693712367281594129574863613928457872465931945317286794156328536842179281739645
* DURATION: 0:00:16.246296  START: 08:32:57.075160  END: 08:33:13.321456 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-sudoku-de-754055-base-pr-001.dot
* REASONING
* DIS # B2: 2,3 => CTR => B2: 6,8
* DIS B2: 6,8 # C8: 4 => CTR => C8: 6,8
* DIS B2: 6,8 + C8: 6,8 # H2: 1 => CTR => H2: 3,9
* DIS B2: 6,8 + C8: 6,8 + H2: 3,9 # D2: 6,8 => CTR => D2: 2,5
* DIS B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 # E2: 2 => CTR => E2: 5,8
* DIS B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 + E2: 5,8 # E3: 5,8 => CTR => E3: 7
* PRF B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 + E2: 5,8 + E3: 7 # I8: 3,9 => SOL
* STA B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 + E2: 5,8 + E3: 7 + I8: 3,9
* CNT   7 HDP CHAINS /  12 HYP OPENED

Header Info

http://www.sudokus.de/754055.html
sehr schwierig

--------------------------------------------------
level: medium

* PAIR REDUCTION ..
* ROUND 1: 45..9.7.2..7.....41....4.6...39.845.8...6...1..53.728..9.1....85.....1..2.1.3..45
C1: 6,8
B2: 2,3,6,8                              # reduction candidate for 6,8
B2: 2,3 => CTR
* 45689.7.2..76..8.418...4563..39.845.8..562..1..534728..941....85.....1..2.1.3..45
C8: 4,6,8                                # reduction candidate for 6,8
C8: 4 => CTR
* 45869.7.2.67.....41....4.6...39.845.8...6...1..53.728..96145328534..61..28173..45
A2: 3,9
H2: 1,3,9                                # reduction candidate for 3,9
H2: 1 => CTR
* 45..9.7.29.7..3.14132..4.69..39.845.8.9.6.3716.53.728..941....85.....1..2.1.3..45
C3: 2,9
D1: 6,8
D2: 2,5,6,8                              # reduction candidate for 6,8
D2: 6,8 => CTR
* 45..93712..7.215.41....486..2391845.8.9.6.371615347289.941..6.85..48.1.72.1.3..45
G2: 5,8
E2: 2,5,8                                # reduction candidate for 5,8
E2: 2 => CTR
* 458693712.67.218.41....456..2391845.8.9.6.371615347289.9415.6.85.64..1.727183..45
G3: 5,8
D3: 5,7,8                                # reduction candidate for 5,8
D3: 7 => CTR
* 458693712.672.1..41.27.4.697239.845.8..562..1..534728..941.56.85.64.91..271836945
I3: 3,9
I8: 3,7,9                                # reduction candidate for 3,9
I8: 3,9 => SOLVED
* 458693712367281594129574863613928457872465931945317286794156328536842179281739645
* SOLVED!
--------------------------------------------------

|:step:| 00
--------------------------------------------------

pair quad
F1: 1,3
H1: 1,3
F2: 1,3
H2: 1,3,9
=> H2 = 9
* SOLVED!

|:step:| 01
--------------------------------------------------

Solution

position: 458693712367281594129574863613928457872465931945317286794156328536842179281739645 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 # B2: 6,8 => UNS
* DIS # B2: 2,3 => CTR => B2: 6,8
* INC # C8: 6,8 => UNS
* DIS # C8: 4 => CTR => C8: 6,8
* INC # H2: 3,9 => UNS
* DIS # H2: 1 => CTR => H2: 3,9
* DIS # D2: 6,8 => CTR => D2: 2,5
* INC # D2: 2,5 => UNS
* DIS # H2: 1,3 => CTR => H2: 9
* PRF # H2: 9 => SOL
* DIS # H2: 1,3 => CTR => H2: 9
* PRF # H2: 9 => SOL
* DIS # D2: 5,8 => CTR => D2: 2,6
* INC # D2: 2,6 => UNS
* INC # E2: 5,8 => UNS
* INC # D3: 5,8 => UNS
* DIS # E3: 5,8 => CTR => E3: 2,7
* INC # E3: 2,7 => UNS
* INC # H2: 3,9 => UNS
* DIS # H2: 1 => CTR => H2: 3,9
* PRF # I8: 3,9 => SOL
* DIS # I8: 7 => CTR => I8: 3,9
* DIS # D5: 2,5 => CTR => D5: 4
* INC # D5: 4 => UNS
* INC # F7: 2,5 => UNS
* PRF # F7: 6 => SOL
* PRF # H5: 3,9 => SOL
* DIS # H5: 7 => CTR => H5: 3,9
* INC # B8: 3,7 => UNS
* DIS # B8: 6,8 => CTR => B8: 3,7
* INC # H7: 3,7 => UNS
* INC # H7: 2 => UNS
* INC # C8: 4,6 => UNS
* DIS # C8: 8 => CTR => C8: 4,6
* DIS # B8: 7,8 => CTR => B8: 3,6
* INC # B8: 3,6 => UNS
* INC # D8: 7,8 => UNS
* INC # E8: 7,8 => UNS
* INC # D3: 7,8 => UNS
* INC # D3: 2,5 => UNS
* INC # F8: 6,9 => UNS
* PRF # F8: 2 => SOL
* CNT  42 HDP CHAINS /  42 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 6,8 => UNS
* DIS # B2: 2,3 => CTR => B2: 6,8
* INC B2: 6,8 # C8: 6,8 => UNS
* DIS B2: 6,8 # C8: 4 => CTR => C8: 6,8
* INC B2: 6,8 + C8: 6,8 # H2: 3,9 => UNS
* DIS B2: 6,8 + C8: 6,8 # H2: 1 => CTR => H2: 3,9
* DIS B2: 6,8 + C8: 6,8 + H2: 3,9 # D2: 6,8 => CTR => D2: 2,5
* INC B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 # E2: 5,8 => UNS
* DIS B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 # E2: 2 => CTR => E2: 5,8
* INC B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 + E2: 5,8 # D3: 5,8 => UNS
* DIS B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 + E2: 5,8 # E3: 5,8 => CTR => E3: 7
* PRF B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 + E2: 5,8 + E3: 7 # I8: 3,9 => SOL
* STA B2: 6,8 + C8: 6,8 + H2: 3,9 + D2: 2,5 + E2: 5,8 + E3: 7 + I8: 3,9
* CNT  12 HDP CHAINS /  12 HYP OPENED