Analysis of zz-sudoku-de-792840-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .4......6..21.....9.5.62..8.....1.53..6.3.4..58.2.....2..34.7.5.....91..3......9. initial

Autosolve

position: .4...3..66321...4.9.54623.84..6.1.53..6.354..5832.4..12..34.7.5.6.529134354.1..92 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B5: 1,7 => CTR => B5: 2,9
* DIS # E1: 7,9 => CTR => E1: 5
* DIS # E2: 7,9 => CTR => E2: 5,8
* DIS # D5: 7,9 => CTR => D5: 8
* PRF # D5: 8 => SOL
* PRF # E2: 7,8 => SOL
* DIS # E2: 5,9 => CTR => E2: 7,8
* PRF # F9: 7,8 => SOL
* DIS # F9: 6 => CTR => F9: 7,8
* DIS # G1: 5,9 => CTR => G1: 2
* PRF # G1: 2 => SOL
* DIS # E2: 5,9 => CTR => E2: 7,8
* PRF # E2: 7,8 => SOL
* DIS # E2: 7,9 => CTR => E2: 5,8
* PRF # H1: 1,7 => SOL
* DIS # H1: 2 => CTR => H1: 1,7
* DIS # B4: 7,9 => CTR => B4: 2
* PRF # B4: 2 => SOL
* PRF # B5: 7,9 => SOL
* PRF # E4: 7,9 => SOL
* DIS # E4: 8 => CTR => E4: 7,9
* DIS # B5: 1,7 => CTR => B5: 2,9
* PRF # E4: 7,9 => SOL
* DIS # E4: 8 => CTR => E4: 7,9
* DIS # D5: 7,9 => CTR => D5: 8
* PRF # D5: 8 => SOL
* DIS # E1: 7,9 => CTR => E1: 5
* DIS # E2: 7,9 => CTR => E2: 5,8
* PRF # B5: 7,9 => SOL
* DIS # D5: 7,9 => CTR => D5: 8
* PRF # D5: 8 => SOL
* PRF # B5: 1,9 => SOL
* DIS # A1: 1 => CTR => A1: 7,8
* PRF # F9: 6,8 => SOL
* DIS # F9: 7 => CTR => F9: 6,8
* PRF # F9: 7,8 => SOL
* DIS # F9: 6 => CTR => F9: 7,8
* DIS # D5: 9 => CTR => D5: 7,8
* PRF # F9: 6,8 => SOL
* DIS # F9: 7 => CTR => F9: 6,8
* CNT  40 HDP CHAINS /  58 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 # B5: 1,7 => CTR => B5: 2,9
* DIS B5: 2,9 # C1: 8 => CTR => C1: 1,7
* DIS B5: 2,9 + C1: 1,7 # E1: 7,9 => CTR => E1: 5
* DIS B5: 2,9 + C1: 1,7 + E1: 5 # E2: 7,9 => CTR => E2: 8
* PRF B5: 2,9 + C1: 1,7 + E1: 5 + E2: 8 => SOL
* STA B5: 2,9 + C1: 1,7 + E1: 5 + E2: 8
* CNT   5 HDP CHAINS /   7 HYP OPENED

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

Details

Positions

.4......6..21.....9.5.62..8.....1.53..6.3.4..58.2.....2..34.7.5.....91..3......9. initial
.4...3..66321...4.9.54623.84..6.1.53..6.354..5832.4..12..34.7.5.6.529134354.1..92 autosolve
841953276632187549975462318427691853196835427583274961219346785768529134354718692 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (22)
B3: 1,7
D1: 7,9
F2: 7,8
G2: 5,9
I2: 7,9
H3: 1,7
C4: 7,9
A5: 1,7
E6: 7,9
G4: 2,8
H5: 2,8
I5: 7,9
G6: 6,9
H6: 6,7
B7: 1,9
C7: 1,9
A8: 7,8
C8: 7,8
F7: 6,8
D9: 7,8
H7: 6,8
G9: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H1,H3: 1.. / H1 = 1  =>  0 pairs (X) / H3 = 1  => 24 pairs (_)
A5,B5: 1.. / A5 = 1  => 22 pairs (_) / B5 = 1  =>  0 pairs (X)
B7,C7: 1.. / B7 = 1  => 18 pairs (_) / C7 = 1  => 22 pairs (_)
B3,H3: 1.. / B3 = 1  =>  0 pairs (X) / H3 = 1  => 24 pairs (_)
A1,A5: 1.. / A1 = 1  =>  0 pairs (X) / A5 = 1  => 22 pairs (_)
C1,C7: 1.. / C1 = 1  => 18 pairs (_) / C7 = 1  => 22 pairs (_)
G1,H1: 2.. / G1 = 2  =>  0 pairs (*) / H1 = 2  =>  0 pairs (X)
B4,B5: 2.. / B4 = 2  =>  0 pairs (*) / B5 = 2  =>  0 pairs (X)
G4,H5: 2.. / G4 = 2  =>  0 pairs (X) / H5 = 2  =>  0 pairs (_)
B4,G4: 2.. / B4 = 2  =>  0 pairs (*) / G4 = 2  =>  0 pairs (X)
B5,H5: 2.. / B5 = 2  =>  0 pairs (X) / H5 = 2  =>  0 pairs (_)
G1,G4: 2.. / G1 = 2  =>  0 pairs (*) / G4 = 2  =>  0 pairs (X)
H1,H5: 2.. / H1 = 2  =>  0 pairs (X) / H5 = 2  =>  0 pairs (_)
E1,E2: 5.. / E1 = 5  => 22 pairs (_) / E2 = 5  =>  0 pairs (X)
G1,G2: 5.. / G1 = 5  =>  0 pairs (X) / G2 = 5  => 22 pairs (_)
E1,G1: 5.. / E1 = 5  => 22 pairs (_) / G1 = 5  =>  0 pairs (X)
E2,G2: 5.. / E2 = 5  =>  0 pairs (X) / G2 = 5  => 22 pairs (_)
G6,H6: 6.. / G6 = 6  =>  0 pairs (X) / H6 = 6  =>  0 pairs (_)
F7,F9: 6.. / F7 = 6  =>  0 pairs (*) / F9 = 6  =>  0 pairs (X)
H7,G9: 6.. / H7 = 6  =>  0 pairs (X) / G9 = 6  =>  0 pairs (_)
F7,H7: 6.. / F7 = 6  =>  0 pairs (*) / H7 = 6  =>  0 pairs (X)
F9,G9: 6.. / F9 = 6  =>  0 pairs (X) / G9 = 6  =>  0 pairs (_)
G6,G9: 6.. / G6 = 6  =>  0 pairs (X) / G9 = 6  =>  0 pairs (_)
H6,H7: 6.. / H6 = 6  =>  0 pairs (*) / H7 = 6  =>  0 pairs (X)
I5,H6: 7.. / I5 = 7  =>  0 pairs (*) / H6 = 7  =>  0 pairs (X)
A8,C8: 7.. / A8 = 7  => 20 pairs (_) / C8 = 7  => 20 pairs (_)
D9,F9: 7.. / D9 = 7  =>  0 pairs (*) / F9 = 7  =>  0 pairs (X)
B3,H3: 7.. / B3 = 7  => 24 pairs (_) / H3 = 7  =>  0 pairs (X)
E6,H6: 7.. / E6 = 7  =>  0 pairs (*) / H6 = 7  =>  0 pairs (X)
F2,F9: 7.. / F2 = 7  =>  0 pairs (*) / F9 = 7  =>  0 pairs (X)
I2,I5: 7.. / I2 = 7  =>  0 pairs (X) / I5 = 7  =>  0 pairs (_)
A1,C1: 8.. / A1 = 8  => 20 pairs (_) / C1 = 8  => 20 pairs (_)
E2,F2: 8.. / E2 = 8  =>  0 pairs (*) / F2 = 8  =>  0 pairs (X)
E4,D5: 8.. / E4 = 8  =>  0 pairs (X) / D5 = 8  =>  0 pairs (_)
G4,H5: 8.. / G4 = 8  =>  0 pairs (*) / H5 = 8  =>  0 pairs (X)
A8,C8: 8.. / A8 = 8  => 20 pairs (_) / C8 = 8  => 20 pairs (_)
H7,G9: 8.. / H7 = 8  =>  0 pairs (*) / G9 = 8  =>  0 pairs (X)
E4,G4: 8.. / E4 = 8  =>  0 pairs (X) / G4 = 8  =>  0 pairs (_)
D5,H5: 8.. / D5 = 8  =>  0 pairs (*) / H5 = 8  =>  0 pairs (X)
F7,H7: 8.. / F7 = 8  =>  0 pairs (X) / H7 = 8  =>  0 pairs (_)
A1,A8: 8.. / A1 = 8  => 20 pairs (_) / A8 = 8  => 20 pairs (_)
C1,C8: 8.. / C1 = 8  => 20 pairs (_) / C8 = 8  => 20 pairs (_)
D5,D9: 8.. / D5 = 8  =>  0 pairs (*) / D9 = 8  =>  0 pairs (X)
E2,E4: 8.. / E2 = 8  =>  0 pairs (*) / E4 = 8  =>  0 pairs (X)
G4,G9: 8.. / G4 = 8  =>  0 pairs (*) / G9 = 8  =>  0 pairs (X)
H5,H7: 8.. / H5 = 8  =>  0 pairs (X) / H7 = 8  =>  0 pairs (_)
I5,G6: 9.. / I5 = 9  =>  0 pairs (X) / G6 = 9  =>  0 pairs (_)
B7,C7: 9.. / B7 = 9  => 22 pairs (_) / C7 = 9  => 18 pairs (_)
E6,G6: 9.. / E6 = 9  =>  0 pairs (X) / G6 = 9  =>  0 pairs (_)
C4,C7: 9.. / C4 = 9  => 22 pairs (_) / C7 = 9  => 18 pairs (_)
D1,D5: 9.. / D1 = 9  => 24 pairs (_) / D5 = 9  =>  0 pairs (X)
I2,I5: 9.. / I2 = 9  =>  0 pairs (*) / I5 = 9  =>  0 pairs (X)
* DURATION: 0:01:26.018815  START: 08:52:11.896862  END: 08:53:37.915677 2017-05-01
* CP COUNT: (52)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,B3,B7,C4,C7,C8,D1,D9,E6,F2,F7,G2,G4,G6,G9,H3,H5,H6,H7,I2,I5)
* .4...3..66321...4.9.54623.84..6.1.53..6.354..5832.4..12..34.7.5.6.529134354.1..92
* PAIR B3: 1,7 BLK 1
A1: 1,7,8                                # reduction candidate for 1,7
A1: 1,7                                  # 20 pairs
C1: 1,7,8                                # reduction candidate for 1,7
C1: 1,7                                  # 20 pairs
* PAIR B3: 1,7 COL B
B5: 1,7,2,9                              # reduction candidate for 1,7
B5: 1,7 => CTR
* .4...3..66321...4.9.54623.8429671853..68354295832946.12..34.7.5.6.529134354.1..92
B5: 2,9                                  # 24 pairs
* PAIR D1: 7,9 BLK 2
E1: 7,9,5                                # reduction candidate for 7,9
E1: 7,9 => CTR
* .4...35266321589479754623184..681253.26.354895832946712193467.5.6.529134354.1..92
E1: 5                                    # 22 pairs
E2: 7,9,5,8                              # reduction candidate for 7,9
E2: 7,9 => CTR
* .4..53..66321.854.9.54623.84..681253.26.3548.5832.4..12..3467.5.6.529134354.1..92
E2: 5,8                                  # 24 pairs
* PAIR D1: 7,9 COL D
D5: 7,9,8                                # reduction candidate for 7,9
D5: 7,9 => CTR
* .4...3..66321...4.9.54623.84..681253.26.3548.5832.4..12..348765.6.529134354716892
D5: 8 => SOLVED
* 841953276632187549975462318427691853196835427583274961219346785768529134354718692
* PAIR F2: 7,8 BLK 2
E2: 7,8,5,9                              # reduction candidate for 7,8
E2: 7,8 => SOLVED
* 841953276632187549975462318427691853196835427583274961219346785768529134354718692
E2: 5,9 => CTR
* .4...3..66321.8.479754623184..681253.26.354895832946712193467.5.6.529134354.1..92
* PAIR F2: 7,8 COL F
F9: 7,8,6                                # reduction candidate for 7,8
F9: 7,8 => SOLVED
* 841953276632187549975462318427691853196835427583274961219346785768529134354718692
F9: 6 => CTR
* .4...3..66321.7.499.54623.84..6.1.53..6.354.75832749612..34.7.5.6.529134354.1..92
* PAIR G2: 5,9 BLK 3
G1: 5,9,2                                # reduction candidate for 5,9
G1: 5,9 => CTR
* .4...3.266321...4.9.54623184..6.1253.26.3548.5832.4.71219348765.6.529134354716892
G1: 2 => SOLVED
* 841953276632187549975462318427691853196835427583274961219346785768529134354718692
* PAIR G2: 5,9 ROW 2
E2: 5,9,7,8                              # reduction candidate for 5,9
E2: 5,9 => CTR
* .4...3..66321.8.479754623184..681253.26.354895832946712193467.5.6.529134354.1..92
E2: 7,8 => SOLVED
* 841953276632187549975462318427691853196835427583274961219346785768529134354718692
* PAIR I2: 7,9 ROW 2
E2: 7,9,5,8                              # reduction candidate for 7,9
E2: 7,9 => CTR
* .4..53..66321.854.9.54623.84..681253.26.3548.5832.4..12..3467.5.6.529134354.1..92
E2: 5,8                                  # 24 pairs
* PAIR H3: 1,7 BLK 3
H1: 1,7,2                                # reduction candidate for 1,7
H1: 1,7 => SOLVED
* 841953276632187549975462318427691853196835427583274961219346785768529134354718692
H1: 2 => CTR
* .4...3.266321...4.9.54623184..6.1253.26.3548.5832.4.71219348765.6.529134354716892
* PAIR C4: 7,9 BLK 4
B4: 7,9,2                                # reduction candidate for 7,9
B4: 7,9 => CTR
* .4...3..66321...4.9.54623.84..6.1253.26.3548.5832.4..12..348765.6.529134354716892
B4: 2 => SOLVED
* 841953276632187549975462318427691853196835427583274961219346785768529134354718692
B5: 7,9,1,2                              # reduction candidate for 7,9
B5: 7,9 => SOLVED
* 841953276632187549975462318427691853196835427583274961219346785768529134354718692
B5: 1,2                                  # 24 pairs
* PAIR C4: 7,9 ROW 4
E4: 7,9,8                                # reduction candidate for 7,9
E4: 7,9 => SOLVED
* 841953276632187549975462318427691853196835427583274961219346785768529134354718692
E4: 8 => CTR
* .4...3..66321...4.9.54623.84..681253.26.3548.5832.4..12..348765.6.529134354716892
* PAIR A5: 1,7 BLK 4
B5: 1,7,2,9                              # reduction candidate for 1,7
B5: 1,7 => CTR
* .4...3..66321...4.9.54623.8429671853..68354295832946.12..34.7.5.6.529134354.1..92
B5: 2,9                                  # 24 pairs
* PAIR A5: 1,7 COL A
A1: 1,7,8                                # reduction candidate for 1,7
A1: 8                                    # 20 pairs
A1: 1,7                                  # 20 pairs
* PAIR E6: 7,9 BLK 5
E4: 7,9,8                                # reduction candidate for 7,9
E4: 7,9 => SOLVED
* 841953276632187549975462318427691853196835427583274961219346785768529134354718692
E4: 8 => CTR
* .4...3..66321...4.9.54623.84..681253.26.3548.5832.4..12..348765.6.529134354716892
D5: 7,9,8                                # reduction candidate for 7,9
D5: 7,9 => CTR
* .4...3..66321...4.9.54623.84..681253.26.3548.5832.4..12..348765.6.529134354716892
D5: 8 => SOLVED
* 841953276632187549975462318427691853196835427583274961219346785768529134354718692
* PAIR E6: 7,9 COL E
E1: 7,9,5                                # reduction candidate for 7,9
E1: 7,9 => CTR
* .4...35266321589479754623184..681253.26.354895832946712193467.5.6.529134354.1..92
E1: 5                                    # 22 pairs
E2: 7,9,5,8                              # reduction candidate for 7,9
E2: 7,9 => CTR
* .4..53..66321.854.9.54623.84..681253.26.3548.5832.4..12..3467.5.6.529134354.1..92
E2: 5,8                                  # 24 pairs
* PAIR I5: 7,9 ROW 5
B5: 7,9,1,2                              # reduction candidate for 7,9
B5: 7,9 => SOLVED
* 841953276632187549975462318427691853196835427583274961219346785768529134354718692
B5: 1,2                                  # 24 pairs
D5: 7,9,8                                # reduction candidate for 7,9
D5: 7,9 => CTR
* .4...3..66321...4.9.54623.84..681253.26.3548.5832.4..12..348765.6.529134354716892
D5: 8 => SOLVED
* 841953276632187549975462318427691853196835427583274961219346785768529134354718692
* PAIR B7: 1,9 COL B
B5: 1,9,2,7                              # reduction candidate for 1,9
B5: 1,9 => SOLVED
* 841953276632187549975462318427691853196835427583274961219346785768529134354718692
B5: 2,7                                  # 24 pairs
* PAIR A8: 7,8 COL A
A1: 7,8,1                                # reduction candidate for 7,8
A1: 1 => CTR
* 148..3..66321...4.9754623184..6.1.53716.354295832946712..34.7.5.6.529134354.1..92
A1: 7,8                                  # 22 pairs
* PAIR C8: 7,8 COL C
C1: 7,8,1                                # reduction candidate for 7,8
C1: 7,8                                  # 22 pairs
C1: 1                                    # 18 pairs
* PAIR F7: 6,8 BLK 8
F9: 6,8,7                                # reduction candidate for 6,8
F9: 6,8 => SOLVED
* 841953276632187549975462318427691853196835427583274961219346785768529134354718692
F9: 7 => CTR
* .4...3..66321...4.9.54623.84..6.1.53..6.354..5832.4..12..346785.6.529134354817692
* PAIR D9: 7,8 BLK 8
F9: 7,8,6                                # reduction candidate for 7,8
F9: 7,8 => SOLVED
* 841953276632187549975462318427691853196835427583274961219346785768529134354718692
F9: 6 => CTR
* .4...3..66321.7.499.54623.84..6.1.53..6.354.75832749612..34.7.5.6.529134354.1..92
* PAIR D9: 7,8 COL D
D5: 7,8,9                                # reduction candidate for 7,8
D5: 9 => CTR
* .4...3..66321...4.9.54623.84..681253.269354875832749612..34.7.5.6.529134354.1..92
D5: 7,8                                  # 24 pairs
* PAIR G9: 6,8 ROW 9
F9: 6,8,7                                # reduction candidate for 6,8
F9: 6,8 => SOLVED
* 841953276632187549975462318427691853196835427583274961219346785768529134354718692
F9: 7 => CTR
* .4...3..66321...4.9.54623.84..6.1.53..6.354..5832.4..12..346785.6.529134354817692
* INCONCLUSIVE
* SAVE PR GRAPH zz-sudoku-de-792840-base-pr-000.dot
* REASONING
* DIS # B5: 1,7 => CTR => B5: 2,9
* DIS # E1: 7,9 => CTR => E1: 5
* DIS # E2: 7,9 => CTR => E2: 5,8
* DIS # D5: 7,9 => CTR => D5: 8
* PRF # D5: 8 => SOL
* PRF # E2: 7,8 => SOL
* DIS # E2: 5,9 => CTR => E2: 7,8
* PRF # F9: 7,8 => SOL
* DIS # F9: 6 => CTR => F9: 7,8
* DIS # G1: 5,9 => CTR => G1: 2
* PRF # G1: 2 => SOL
* DIS # E2: 5,9 => CTR => E2: 7,8
* PRF # E2: 7,8 => SOL
* DIS # E2: 7,9 => CTR => E2: 5,8
* PRF # H1: 1,7 => SOL
* DIS # H1: 2 => CTR => H1: 1,7
* DIS # B4: 7,9 => CTR => B4: 2
* PRF # B4: 2 => SOL
* PRF # B5: 7,9 => SOL
* PRF # E4: 7,9 => SOL
* DIS # E4: 8 => CTR => E4: 7,9
* DIS # B5: 1,7 => CTR => B5: 2,9
* PRF # E4: 7,9 => SOL
* DIS # E4: 8 => CTR => E4: 7,9
* DIS # D5: 7,9 => CTR => D5: 8
* PRF # D5: 8 => SOL
* DIS # E1: 7,9 => CTR => E1: 5
* DIS # E2: 7,9 => CTR => E2: 5,8
* PRF # B5: 7,9 => SOL
* DIS # D5: 7,9 => CTR => D5: 8
* PRF # D5: 8 => SOL
* PRF # B5: 1,9 => SOL
* DIS # A1: 1 => CTR => A1: 7,8
* PRF # F9: 6,8 => SOL
* DIS # F9: 7 => CTR => F9: 6,8
* PRF # F9: 7,8 => SOL
* DIS # F9: 6 => CTR => F9: 7,8
* DIS # D5: 9 => CTR => D5: 7,8
* PRF # F9: 6,8 => SOL
* DIS # F9: 7 => CTR => F9: 6,8
* CNT  40 HDP CHAINS /  58 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,B3,B7,C4,C7,C8,D1,D9,E6,F2,F7,G2,G4,G6,G9,H3,H5,H6,H7,I2,I5)
* .4...3..66321...4.9.54623.84..6.1.53..6.354..5832.4..12..34.7.5.6.529134354.1..92
* PAIR B3: 1,7 BLK 1
A1: 1,7,8                                # reduction candidate for 1,7
A1: 1,7                                  # 20 pairs
C1: 1,7,8                                # reduction candidate for 1,7
C1: 1,7                                  # 20 pairs
* PAIR B3: 1,7 COL B
B5: 1,7,2,9                              # reduction candidate for 1,7
B5: 1,7 => CTR
* .4...3..66321...4.9.54623.8429671853..68354295832946.12..34.7.5.6.529134354.1..92
* PAIR RESTART
* PAIR B3: 1,7 BLK 1
C1: 1,7,8                                # reduction candidate for 1,7
C1: 8 => CTR
* .48..3.166321...4.9154623784796812531.6.354..5832.4..12..34.7.5.6.529134354.1..92
* PAIR D1: 7,9 BLK 2
E1: 7,9,5                                # reduction candidate for 7,9
E1: 7,9 => CTR
* 84...35266321589479754623184.76812531267354895832946712193467.5768529134354.1..92
E2: 7,9,8                                # reduction candidate for 7,9
E2: 7,9 => CTR
* 84..53..66321.854.9.54623.84..681253126.3548.5832.4..12..3467.5768529134354.1..92
E2: 8 => SOLVED
* 841953276632187549975462318427691853196835427583274961219346785768529134354718692
* DURATION: 0:00:08.425612  START: 08:54:36.780288  END: 08:54:45.205900 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-sudoku-de-792840-base-pr-001.dot
* REASONING
* DIS # B5: 1,7 => CTR => B5: 2,9
* DIS B5: 2,9 # C1: 8 => CTR => C1: 1,7
* DIS B5: 2,9 + C1: 1,7 # E1: 7,9 => CTR => E1: 5
* DIS B5: 2,9 + C1: 1,7 + E1: 5 # E2: 7,9 => CTR => E2: 8
* PRF B5: 2,9 + C1: 1,7 + E1: 5 + E2: 8 => SOL
* STA B5: 2,9 + C1: 1,7 + E1: 5 + E2: 8
* CNT   5 HDP CHAINS /   7 HYP OPENED

Header Info

http://www.sudokus.de/792840.html
sehr schwierig

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level: medium

* PAIR REDUCTION ..
* ROUND 1: .4...3..66321...4.9.54623.84..6.1.53..6.354..5832.4..12..34.7.5.6.529134354.1..92
B3: 1,7
A1: 1,7,8                                # reduction candidate for 1,7
C1: 1,7,8                                # reduction candidate for 1,7
B5: 1,2,7,9                              # reduction candidate for 1,7
B5: 1,7 => CTR
* .4...3..66321...4.9.54623.8429671853..68354295832946.12..34.7.5.6.529134354.1..92
D1: 7,9
E1: 5,7,9                                # reduction candidate for 7,9
E1: 7,9 => CTR
* .4...35266321589479754623184.76812531267354895832946712193467.5.6.529134354.1..92
E2: 7,8,9                                # reduction candidate for 7,9
E2: 7,9 => CTR
* .4..53..66321.854.9.54623.84..681253126.3548.5832.4..12..3467.5.6.529134354.1..92
E2: 8 => SOLVED
* 841953276632187549975462318427691853196835427583274961219346785768529134354718692
* SOLVED!
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|:step:| 00
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* DISABLE VALUE:: H1 != 2

|:step:| 01
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Solution

position: 841953276632187549975462318427691853196835427583274961219346785768529134354718692 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 # A1: 1,7 => UNS
* INC # C1: 1,7 => UNS
* DIS # B5: 1,7 => CTR => B5: 2,9
* INC # B5: 2,9 => UNS
* DIS # E1: 7,9 => CTR => E1: 5
* INC # E1: 5 => UNS
* DIS # E2: 7,9 => CTR => E2: 5,8
* INC # E2: 5,8 => UNS
* DIS # D5: 7,9 => CTR => D5: 8
* PRF # D5: 8 => SOL
* PRF # E2: 7,8 => SOL
* DIS # E2: 5,9 => CTR => E2: 7,8
* PRF # F9: 7,8 => SOL
* DIS # F9: 6 => CTR => F9: 7,8
* DIS # G1: 5,9 => CTR => G1: 2
* PRF # G1: 2 => SOL
* DIS # E2: 5,9 => CTR => E2: 7,8
* PRF # E2: 7,8 => SOL
* DIS # E2: 7,9 => CTR => E2: 5,8
* INC # E2: 5,8 => UNS
* PRF # H1: 1,7 => SOL
* DIS # H1: 2 => CTR => H1: 1,7
* DIS # B4: 7,9 => CTR => B4: 2
* PRF # B4: 2 => SOL
* PRF # B5: 7,9 => SOL
* INC # B5: 1,2 => UNS
* PRF # E4: 7,9 => SOL
* DIS # E4: 8 => CTR => E4: 7,9
* DIS # B5: 1,7 => CTR => B5: 2,9
* INC # B5: 2,9 => UNS
* INC # A1: 1,7 => UNS
* INC # A1: 8 => UNS
* PRF # E4: 7,9 => SOL
* DIS # E4: 8 => CTR => E4: 7,9
* DIS # D5: 7,9 => CTR => D5: 8
* PRF # D5: 8 => SOL
* DIS # E1: 7,9 => CTR => E1: 5
* INC # E1: 5 => UNS
* DIS # E2: 7,9 => CTR => E2: 5,8
* INC # E2: 5,8 => UNS
* PRF # B5: 7,9 => SOL
* INC # B5: 1,2 => UNS
* DIS # D5: 7,9 => CTR => D5: 8
* PRF # D5: 8 => SOL
* PRF # B5: 1,9 => SOL
* INC # B5: 2,7 => UNS
* INC # A1: 7,8 => UNS
* DIS # A1: 1 => CTR => A1: 7,8
* INC # C1: 7,8 => UNS
* INC # C1: 1 => UNS
* PRF # F9: 6,8 => SOL
* DIS # F9: 7 => CTR => F9: 6,8
* PRF # F9: 7,8 => SOL
* DIS # F9: 6 => CTR => F9: 7,8
* INC # D5: 7,8 => UNS
* DIS # D5: 9 => CTR => D5: 7,8
* PRF # F9: 6,8 => SOL
* DIS # F9: 7 => CTR => F9: 6,8
* CNT  58 HDP CHAINS /  58 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A1: 1,7 => UNS
* INC # C1: 1,7 => UNS
* DIS # B5: 1,7 => CTR => B5: 2,9
* INC B5: 2,9 # C1: 1,7 => UNS
* DIS B5: 2,9 # C1: 8 => CTR => C1: 1,7
* DIS B5: 2,9 + C1: 1,7 # E1: 7,9 => CTR => E1: 5
* DIS B5: 2,9 + C1: 1,7 + E1: 5 # E2: 7,9 => CTR => E2: 8
* PRF B5: 2,9 + C1: 1,7 + E1: 5 + E2: 8 => SOL
* STA B5: 2,9 + C1: 1,7 + E1: 5 + E2: 8
* CNT   8 HDP CHAINS /   7 HYP OPENED