Analysis of zz-www.sudokuoftheday.co.uk-20060705-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: ...21...617..5..3..9..7..4...3......78.......4.5...6..2...6.4.....53.27....72.1.. initial

Autosolve

position: ...21.7.617.45..32.9287.541..3......78....3..4.53..6..2.796.4.....53.27....72.16. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C8: 4,8 => CTR => C8: 1,6,9
* DIS # C9: 4,8 => CTR => C9: 9
* PRF # C9: 9 => SOL
* DIS # C8: 6,8 => CTR => C8: 1,4,9
* DIS # H4: 8,9 => CTR => H4: 1,2,5
* PRF # H6: 8,9 => SOL
* DIS # H6: 1,2 => CTR => H6: 8,9
* DIS # C5: 1 => CTR => C5: 6,9
* DIS # A8: 6,9 => CTR => A8: 8
* DIS # B4: 6 => CTR => B4: 1,2
* DIS # H6: 1,2 => CTR => H6: 8,9
* PRF # H6: 8,9 => SOL
* DIS # B4: 1,6 => CTR => B4: 2
* PRF # C5: 1,6 => SOL
* DIS # C5: 9 => CTR => C5: 1,6
* PRF # E4: 4,9 => SOL
* DIS # E4: 8 => CTR => E4: 4,9
* DIS # F4: 2,5 => CTR => F4: 7
* PRF # F4: 7 => SOL
* PRF # H5: 2,5 => SOL
* DIS # H5: 1,9 => CTR => H5: 2,5
* DIS # E4: 8,9 => CTR => E4: 4
* PRF # E4: 4 => SOL
* PRF # H6: 8,9 => SOL
* DIS # H6: 1,2 => CTR => H6: 8,9
* PRF # F4: 2,7 => SOL
* DIS # F4: 5 => CTR => F4: 2,7
* DIS # H4: 8,9 => CTR => H4: 1,2,5
* PRF # H6: 8,9 => SOL
* DIS # H6: 1,2 => CTR => H6: 8,9
* DIS # E4: 8,9 => CTR => E4: 4
* PRF # E4: 4 => SOL
* PRF # I4: 4,5 => SOL
* DIS # I4: 7,8 => CTR => I4: 4,5
* DIS # I4: 7,8 => CTR => I4: 4,5
* PRF # I4: 4,5 => SOL
* DIS # F8: 1 => CTR => F8: 4,8
* DIS # C9: 4,8 => CTR => C9: 9
* PRF # C9: 9 => SOL
* DIS # H4: 5,8 => CTR => H4: 1,2,9
* PRF # H4: 1,2,9 => SOL
* DIS # I9: 8,9 => CTR => I9: 3,5
* DIS # C8: 8,9 => CTR => C8: 1,4,6
* CNT  43 HDP CHAINS /  59 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 # C8: 4,8 => CTR => C8: 1,6,9
* DIS C8: 1,6,9 # C9: 4,8 => CTR => C9: 9
* PRF C8: 1,6,9 + C9: 9 => SOL
* STA C8: 1,6,9 + C9: 9
* CNT   3 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

...21...617..5..3..9..7..4...3......78.......4.5...6..2...6.4.....53.27....72.1.. initial
...21.7.617.45..32.9287.541..3......78....3..4.53..6..2.796.4.....53.27....72.16. autosolve
354219786178456932692873541923647815786195324415382697237961458861534279549728163 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (23)
C1: 4,8
C2: 6,8
A3: 3,6
F1: 3,9
F2: 6,9
F3: 3,6
H1: 8,9
G2: 8,9
A4: 6,9
B6: 1,2
D4: 1,6
D5: 1,6
E5: 4,9
F5: 2,5
E6: 8,9
F6: 2,7
G4: 8,9
I5: 4,5
I6: 7,8
F7: 1,8
F9: 4,8
H7: 5,8
I8: 8,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D4,D5: 1.. / D4 = 1  => 23 pairs (_) / D5 = 1  =>  0 pairs (*)
F7,F8: 1.. / F7 = 1  => 25 pairs (_) / F8 = 1  =>  0 pairs (X)
B6,H6: 1.. / B6 = 1  => 25 pairs (_) / H6 = 1  =>  0 pairs (X)
B7,F7: 1.. / B7 = 1  =>  0 pairs (X) / F7 = 1  => 25 pairs (_)
C5,C8: 1.. / C5 = 1  =>  0 pairs (X) / C8 = 1  => 26 pairs (_)
B4,B6: 2.. / B4 = 2  => 25 pairs (_) / B6 = 2  =>  0 pairs (X)
F5,H5: 2.. / F5 = 2  =>  0 pairs (X) / H5 = 2  =>  0 pairs (_)
F1,F3: 3.. / F1 = 3  =>  0 pairs (X) / F3 = 3  =>  0 pairs (_)
I7,I9: 3.. / I7 = 3  => 24 pairs (_) / I9 = 3  => 27 pairs (_)
A3,F3: 3.. / A3 = 3  =>  0 pairs (X) / F3 = 3  =>  0 pairs (_)
B7,I7: 3.. / B7 = 3  => 27 pairs (_) / I7 = 3  => 24 pairs (_)
B1,C1: 4.. / B1 = 4  =>  0 pairs (X) / C1 = 4  => 24 pairs (_)
E4,E5: 4.. / E4 = 4  =>  0 pairs (*) / E5 = 4  =>  0 pairs (X)
I4,I5: 4.. / I4 = 4  =>  0 pairs (X) / I5 = 4  =>  0 pairs (_)
F8,F9: 4.. / F8 = 4  => 25 pairs (_) / F9 = 4  => 25 pairs (_)
E4,I4: 4.. / E4 = 4  =>  0 pairs (*) / I4 = 4  =>  0 pairs (X)
E5,I5: 4.. / E5 = 4  =>  0 pairs (X) / I5 = 4  =>  0 pairs (_)
A1,B1: 5.. / A1 = 5  => 25 pairs (_) / B1 = 5  => 26 pairs (_)
F4,F5: 5.. / F4 = 5  =>  0 pairs (X) / F5 = 5  =>  0 pairs (_)
A1,A9: 5.. / A1 = 5  => 25 pairs (_) / A9 = 5  => 26 pairs (_)
C2,A3: 6.. / C2 = 6  =>  0 pairs (X) / A3 = 6  =>  0 pairs (_)
F2,F3: 6.. / F2 = 6  =>  0 pairs (*) / F3 = 6  =>  0 pairs (X)
D4,D5: 6.. / D4 = 6  =>  0 pairs (*) / D5 = 6  =>  0 pairs (X)
C2,F2: 6.. / C2 = 6  =>  0 pairs (X) / F2 = 6  =>  0 pairs (_)
A3,F3: 6.. / A3 = 6  =>  0 pairs (*) / F3 = 6  =>  0 pairs (X)
C5,D5: 6.. / C5 = 6  =>  0 pairs (*) / D5 = 6  =>  0 pairs (X)
B4,B8: 6.. / B4 = 6  =>  0 pairs (X) / B8 = 6  => 26 pairs (_)
F4,F6: 7.. / F4 = 7  =>  0 pairs (*) / F6 = 7  =>  0 pairs (X)
I4,I6: 7.. / I4 = 7  =>  0 pairs (X) / I6 = 7  =>  0 pairs (_)
F4,I4: 7.. / F4 = 7  =>  0 pairs (*) / I4 = 7  =>  0 pairs (X)
F6,I6: 7.. / F6 = 7  =>  0 pairs (X) / I6 = 7  =>  0 pairs (_)
H1,G2: 8.. / H1 = 8  =>  0 pairs (*) / G2 = 8  =>  0 pairs (X)
E4,E6: 8.. / E4 = 8  =>  0 pairs (X) / E6 = 8  =>  0 pairs (_)
C2,G2: 8.. / C2 = 8  =>  0 pairs (*) / G2 = 8  =>  0 pairs (X)
G2,G4: 8.. / G2 = 8  =>  0 pairs (X) / G4 = 8  =>  0 pairs (_)
F1,F2: 9.. / F1 = 9  =>  0 pairs (*) / F2 = 9  =>  0 pairs (X)
H1,G2: 9.. / H1 = 9  =>  0 pairs (X) / G2 = 9  =>  0 pairs (_)
A4,C5: 9.. / A4 = 9  =>  0 pairs (*) / C5 = 9  =>  0 pairs (X)
I8,I9: 9.. / I8 = 9  => 23 pairs (_) / I9 = 9  =>  0 pairs (X)
F1,H1: 9.. / F1 = 9  =>  0 pairs (*) / H1 = 9  =>  0 pairs (X)
F2,G2: 9.. / F2 = 9  =>  0 pairs (X) / G2 = 9  =>  0 pairs (_)
E6,H6: 9.. / E6 = 9  =>  0 pairs (X) / H6 = 9  =>  0 pairs (_)
G2,G4: 9.. / G2 = 9  =>  0 pairs (*) / G4 = 9  =>  0 pairs (X)
* DURATION: 0:00:58.414208  START: 00:20:46.531146  END: 00:21:44.945354 2019-05-01
* CP COUNT: (43)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B6,C1,C2,D4,D5,E5,E6,F1,F2,F3,F5,F6,F7,F9,G2,G4,H1,H7,I5,I6,I8)
* ...21.7.617.45..32.9287.541..3......78....3..4.53..6..2.796.4.....53.27....72.16.
* PAIR C1: 4,8 COL C
C8: 4,8,1,6,9                            # reduction candidate for 4,8
C8: 4,8 => CTR
* ...21.7961764598323928765419.3......7816..3..4253.76182.796.48....53.279..972.16.
C8: 1,6,9                                # 23 pairs
C9: 4,8,9                                # reduction candidate for 4,8
C9: 4,8 => CTR
* 54821379617645983239287654162318.9..78964.31541539.6..2.7961458..153.27995.72.163
C9: 9 => SOLVED
* 354219786178456932692873541923647815786195324415382697237961458861534279549728163
* PAIR C2: 6,8 COL C
C8: 6,8,1,4,9                            # reduction candidate for 6,8
C8: 6,8 => CTR
* ..421.79617.459832.928765419.3......7816..3..4253.76182.796.48....53.279..972.16.
C8: 1,4,9                                # 23 pairs
* PAIR H1: 8,9 COL H
H4: 8,9,1,2,5                            # reduction candidate for 8,9
H4: 8,9 => CTR
* ...21.7.617.45..32.9287.541..3......78....3..4.53..6..2.796.4.....53.27....72.16.
H4: 1,2,5                                # 23 pairs
H6: 8,9,1,2                              # reduction candidate for 8,9
H6: 8,9 => SOLVED
* 354219786178456932692873541923647815786195324415382697237961458861534279549728163
H6: 1,2 => CTR
* ...21.79617.459832.92876541..3.8.9..78....3..4.539.6.82.796.48....53.279...72.16.
* PAIR A4: 6,9 BLK 4
C5: 6,9,1                                # reduction candidate for 6,9
C5: 1 => CTR
* ...21.7.617.45..32.9287.5419631..8..7816..3..4253876..2.796.4.....53.27....72.16.
C5: 6,9                                  # 26 pairs
* PAIR A4: 6,9 COL A
A8: 6,9,8                                # reduction candidate for 6,9
A8: 6,9 => CTR
* ...21.7.6176459832392876541..3...9..78964.31541539.6..2.79614589..53.27....72.16.
A8: 8                                    # 25 pairs
* PAIR B6: 1,2 BLK 4
B4: 1,2,6                                # reduction candidate for 1,2
B4: 6 => CTR
* ...21.7.617.45..32.9287.541.631.....78.6..3..4253.76182.796.48....53.279...72.16.
B4: 1,2                                  # 26 pairs
* PAIR B6: 1,2 ROW 6
H6: 1,2,8,9                              # reduction candidate for 1,2
H6: 1,2 => CTR
* ...21.79617.459832.92876541..3.8.9..78....3..4.539.6.82.796.48....53.279...72.16.
H6: 8,9 => SOLVED
* 354219786178456932692873541923647815786195324415382697237961458861534279549728163
* PAIR D4: 1,6 ROW 4
B4: 1,6,2                                # reduction candidate for 1,6
B4: 1,6 => CTR
* ...21.79617.459832.92876541..3.8.9..78....3..4253.76182.796.48....53.279...72.16.
B4: 2                                    # 25 pairs
* PAIR D5: 1,6 ROW 5
C5: 1,6,9                                # reduction candidate for 1,6
C5: 1,6 => SOLVED
* 354219786178456932692873541923647815786195324415382697237961458861534279549728163
C5: 9 => CTR
* 5..21.7.61764598323928765416231.59..78964.3154153..6..2.7961458..153.27995.72.163
* PAIR E5: 4,9 BLK 5
E4: 4,9,8                                # reduction candidate for 4,9
E4: 4,9 => SOLVED
* 354219786178456932692873541923647815786195324415382697237961458861534279549728163
E4: 8 => CTR
* ...21.7.617.45..32.9287.541..3.8.9.478964.31541539.6..2.796.4.....53.27....72.16.
* PAIR F5: 2,5 BLK 5
F4: 2,5,7                                # reduction candidate for 2,5
F4: 2,5 => CTR
* ...21.7.617.45..32.9287.541..3.....778....3.44.53.76.82.796.48....53.279...72.16.
F4: 7 => SOLVED
* 354219786178456932692873541923647815786195324415382697237961458861534279549728163
* PAIR F5: 2,5 ROW 5
H5: 2,5,1,9                              # reduction candidate for 2,5
H5: 2,5 => SOLVED
* 354219786178456932692873541923647815786195324415382697237961458861534279549728163
H5: 1,9 => CTR
* ...21.7.617.45..32.9287.541..3......78...23.54.53.76.82.796.4.....53.27....72.16.
* PAIR E6: 8,9 BLK 5
E4: 8,9,4                                # reduction candidate for 8,9
E4: 8,9 => CTR
* ...21.7.617.45..32.9287.541..3.....478..4.3.54.53..6.72.796.45....53.27....72.16.
E4: 4 => SOLVED
* 354219786178456932692873541923647815786195324415382697237961458861534279549728163
* PAIR E6: 8,9 ROW 6
H6: 8,9,1,2                              # reduction candidate for 8,9
H6: 8,9 => SOLVED
* 354219786178456932692873541923647815786195324415382697237961458861534279549728163
H6: 1,2 => CTR
* ...21.79617.459832.92876541..3.8.9..78....3..4.539.6.82.796.48....53.279...72.16.
* PAIR F6: 2,7 BLK 5
F4: 2,7,5                                # reduction candidate for 2,7
F4: 2,7 => SOLVED
* 354219786178456932692873541923647815786195324415382697237961458861534279549728163
F4: 5 => CTR
* ...21.7.617.45..32.9287.541..3..5..778...23.44.53.76.82.796.48....53.279...72.16.
* PAIR G4: 8,9 BLK 6
H4: 8,9,1,2,5                            # reduction candidate for 8,9
H4: 8,9 => CTR
* ...21.7.617.45..32.9287.541..3......78....3..4.53..6..2.796.4.....53.27....72.16.
H4: 1,2,5                                # 23 pairs
H6: 8,9,1,2                              # reduction candidate for 8,9
H6: 8,9 => SOLVED
* 354219786178456932692873541923647815786195324415382697237961458861534279549728163
H6: 1,2 => CTR
* ...21.79617.459832.92876541..3.8.9..78....3..4.539.6.82.796.48....53.279...72.16.
* PAIR G4: 8,9 ROW 4
E4: 8,9,4                                # reduction candidate for 8,9
E4: 8,9 => CTR
* ...21.7.617.45..32.9287.541..3.....478..4.3.54.53..6.72.796.45....53.27....72.16.
E4: 4 => SOLVED
* 354219786178456932692873541923647815786195324415382697237961458861534279549728163
* PAIR I5: 4,5 BLK 6
I4: 4,5,7,8                              # reduction candidate for 4,5
I4: 4,5 => SOLVED
* 354219786178456932692873541923647815786195324415382697237961458861534279549728163
I4: 7,8 => CTR
* ...21.7.617.45..32.9287.541..3.4....78..9.3.44.538.6972.796.4.....53.27....72.16.
* PAIR I6: 7,8 BLK 6
I4: 7,8,4,5                              # reduction candidate for 7,8
I4: 7,8 => CTR
* ...21.7.617.45..32.9287.541..3.4....78..9.3.44.538.6972.796.4.....53.27....72.16.
I4: 4,5 => SOLVED
* 354219786178456932692873541923647815786195324415382697237961458861534279549728163
* PAIR F7: 1,8 BLK 8
F8: 1,8,4                                # reduction candidate for 1,8
F8: 4                                    # 25 pairs
F8: 1,8                                  # 25 pairs
* PAIR F9: 4,8 BLK 8
F8: 4,8,1                                # reduction candidate for 4,8
F8: 1 => CTR
* ...21.7.617.45..32.9287.541..3......7816..3..4253.7618217968453...531279...72416.
F8: 4,8                                  # 25 pairs
* PAIR F9: 4,8 ROW 9
C9: 4,8,9                                # reduction candidate for 4,8
C9: 4,8 => CTR
* 54821379617645983239287654162318.9..78964.31541539.6..2.7961458..153.27995.72.163
C9: 9 => SOLVED
* 354219786178456932692873541923647815786195324415382697237961458861534279549728163
* PAIR H7: 5,8 BLK 9
I7: 5,8,3                                # reduction candidate for 5,8
I7: 5,8                                  # 27 pairs
I9: 5,8,3,9                              # reduction candidate for 5,8
I9: 5,8                                  # 25 pairs
* PAIR H7: 5,8 COL H
H4: 5,8,1,2,9                            # reduction candidate for 5,8
H4: 5,8 => CTR
* ...21.79617.459832.92876541..3...9.778964.3154153976282.796.4.....53.27....72.16.
H4: 1,2,9 => SOLVED
* 354219786178456932692873541923647815786195324415382697237961458861534279549728163
* PAIR I8: 8,9 BLK 9
I9: 8,9,3,5                              # reduction candidate for 8,9
I9: 8,9 => CTR
* ...21.7.617.45..32.9287.541..3......7816..3..4253.7618217968453...531279...72416.
I9: 3,5                                  # 25 pairs
* PAIR I8: 8,9 ROW 8
A8: 8,9,6                                # reduction candidate for 8,9
A8: 8,9                                  # 25 pairs
C8: 8,9,1,4,6                            # reduction candidate for 8,9
C8: 8,9 => CTR
* ..421.7961764598323928765419.3......7816..3..4253.76182.796.48....53.279..972.16.
C8: 1,4,6                                # 23 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060705-absurd-base-pr-000.dot
* REASONING
* DIS # C8: 4,8 => CTR => C8: 1,6,9
* DIS # C9: 4,8 => CTR => C9: 9
* PRF # C9: 9 => SOL
* DIS # C8: 6,8 => CTR => C8: 1,4,9
* DIS # H4: 8,9 => CTR => H4: 1,2,5
* PRF # H6: 8,9 => SOL
* DIS # H6: 1,2 => CTR => H6: 8,9
* DIS # C5: 1 => CTR => C5: 6,9
* DIS # A8: 6,9 => CTR => A8: 8
* DIS # B4: 6 => CTR => B4: 1,2
* DIS # H6: 1,2 => CTR => H6: 8,9
* PRF # H6: 8,9 => SOL
* DIS # B4: 1,6 => CTR => B4: 2
* PRF # C5: 1,6 => SOL
* DIS # C5: 9 => CTR => C5: 1,6
* PRF # E4: 4,9 => SOL
* DIS # E4: 8 => CTR => E4: 4,9
* DIS # F4: 2,5 => CTR => F4: 7
* PRF # F4: 7 => SOL
* PRF # H5: 2,5 => SOL
* DIS # H5: 1,9 => CTR => H5: 2,5
* DIS # E4: 8,9 => CTR => E4: 4
* PRF # E4: 4 => SOL
* PRF # H6: 8,9 => SOL
* DIS # H6: 1,2 => CTR => H6: 8,9
* PRF # F4: 2,7 => SOL
* DIS # F4: 5 => CTR => F4: 2,7
* DIS # H4: 8,9 => CTR => H4: 1,2,5
* PRF # H6: 8,9 => SOL
* DIS # H6: 1,2 => CTR => H6: 8,9
* DIS # E4: 8,9 => CTR => E4: 4
* PRF # E4: 4 => SOL
* PRF # I4: 4,5 => SOL
* DIS # I4: 7,8 => CTR => I4: 4,5
* DIS # I4: 7,8 => CTR => I4: 4,5
* PRF # I4: 4,5 => SOL
* DIS # F8: 1 => CTR => F8: 4,8
* DIS # C9: 4,8 => CTR => C9: 9
* PRF # C9: 9 => SOL
* DIS # H4: 5,8 => CTR => H4: 1,2,9
* PRF # H4: 1,2,9 => SOL
* DIS # I9: 8,9 => CTR => I9: 3,5
* DIS # C8: 8,9 => CTR => C8: 1,4,6
* CNT  43 HDP CHAINS /  59 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B6,C1,C2,D4,D5,E5,E6,F1,F2,F3,F5,F6,F7,F9,G2,G4,H1,H7,I5,I6,I8)
* ...21.7.617.45..32.9287.541..3......78....3..4.53..6..2.796.4.....53.27....72.16.
* PAIR C1: 4,8 COL C
C8: 4,8,1,6,9                            # reduction candidate for 4,8
C8: 4,8 => CTR
* ...21.7961764598323928765419.3......7816..3..4253.76182.796.48....53.279..972.16.
C9: 4,8,9                                # reduction candidate for 4,8
C9: 4,8 => CTR
* 54821379617645983239287654162318.9..78964.31541539.6..2.7961458..153.27995.72.163
C9: 9 => SOLVED
* 354219786178456932692873541923647815786195324415382697237961458861534279549728163
* DURATION: 0:00:02.467107  START: 00:22:31.330988  END: 00:22:33.798095 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060705-absurd-base-pr-001.dot
* REASONING
* DIS # C8: 4,8 => CTR => C8: 1,6,9
* DIS C8: 1,6,9 # C9: 4,8 => CTR => C9: 9
* PRF C8: 1,6,9 + C9: 9 => SOL
* STA C8: 1,6,9 + C9: 9
* CNT   3 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060705, absurd

Solution

position: 354219786178456932692873541923647815786195324415382697237961458861534279549728163 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 # C8: 4,8 => CTR => C8: 1,6,9
* INC # C8: 1,6,9 => UNS
* DIS # C9: 4,8 => CTR => C9: 9
* PRF # C9: 9 => SOL
* DIS # C8: 6,8 => CTR => C8: 1,4,9
* INC # C8: 1,4,9 => UNS
* DIS # H4: 8,9 => CTR => H4: 1,2,5
* INC # H4: 1,2,5 => UNS
* PRF # H6: 8,9 => SOL
* DIS # H6: 1,2 => CTR => H6: 8,9
* INC # C5: 6,9 => UNS
* DIS # C5: 1 => CTR => C5: 6,9
* DIS # A8: 6,9 => CTR => A8: 8
* INC # A8: 8 => UNS
* INC # B4: 1,2 => UNS
* DIS # B4: 6 => CTR => B4: 1,2
* DIS # H6: 1,2 => CTR => H6: 8,9
* PRF # H6: 8,9 => SOL
* DIS # B4: 1,6 => CTR => B4: 2
* INC # B4: 2 => UNS
* PRF # C5: 1,6 => SOL
* DIS # C5: 9 => CTR => C5: 1,6
* PRF # E4: 4,9 => SOL
* DIS # E4: 8 => CTR => E4: 4,9
* DIS # F4: 2,5 => CTR => F4: 7
* PRF # F4: 7 => SOL
* PRF # H5: 2,5 => SOL
* DIS # H5: 1,9 => CTR => H5: 2,5
* DIS # E4: 8,9 => CTR => E4: 4
* PRF # E4: 4 => SOL
* PRF # H6: 8,9 => SOL
* DIS # H6: 1,2 => CTR => H6: 8,9
* PRF # F4: 2,7 => SOL
* DIS # F4: 5 => CTR => F4: 2,7
* DIS # H4: 8,9 => CTR => H4: 1,2,5
* INC # H4: 1,2,5 => UNS
* PRF # H6: 8,9 => SOL
* DIS # H6: 1,2 => CTR => H6: 8,9
* DIS # E4: 8,9 => CTR => E4: 4
* PRF # E4: 4 => SOL
* PRF # I4: 4,5 => SOL
* DIS # I4: 7,8 => CTR => I4: 4,5
* DIS # I4: 7,8 => CTR => I4: 4,5
* PRF # I4: 4,5 => SOL
* INC # F8: 1,8 => UNS
* INC # F8: 4 => UNS
* INC # F8: 4,8 => UNS
* DIS # F8: 1 => CTR => F8: 4,8
* DIS # C9: 4,8 => CTR => C9: 9
* PRF # C9: 9 => SOL
* INC # I7: 5,8 => UNS
* INC # I9: 5,8 => UNS
* DIS # H4: 5,8 => CTR => H4: 1,2,9
* PRF # H4: 1,2,9 => SOL
* DIS # I9: 8,9 => CTR => I9: 3,5
* INC # I9: 3,5 => UNS
* INC # A8: 8,9 => UNS
* DIS # C8: 8,9 => CTR => C8: 1,4,6
* INC # C8: 1,4,6 => UNS
* CNT  59 HDP CHAINS /  59 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # C8: 4,8 => CTR => C8: 1,6,9
* DIS C8: 1,6,9 # C9: 4,8 => CTR => C9: 9
* PRF C8: 1,6,9 + C9: 9 => SOL
* STA C8: 1,6,9 + C9: 9
* CNT   3 HDP CHAINS /   2 HYP OPENED