Analysis of zz-www.sudokuwiki.org-interesting-5x5-blank-center-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ...7.......24397...4.....6..9.....45.3.....1.76.....3..7.....2...58643.......2... initial

Autosolve

position: ...7.6...6.24397...47..1.6.2983176455346.8.17761.45.3..7...3.2..2586437.....72... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 3,9 => CTR => A1: 1,8
* DIS # I1: 3,9 => CTR => I1: 1,2,4,8
* DIS # C9: 6 => CTR => C9: 3,9
* DIS # E3: 2,5 => CTR => E3: 8
* DIS # G3: 8,9 => CTR => G3: 2,5
* DIS # G1: 5,8 => CTR => G1: 1,2,4,9
* DIS # H1: 5,8 => CTR => H1: 9
* PRF # G3: 5,8 => SOL
* DIS # B2: 1 => CTR => B2: 5,8
* DIS # H9: 9 => CTR => H9: 5,8
* DIS # G1: 1,8 => CTR => G1: 2,4,5,9
* DIS # I1: 1,8 => CTR => I1: 2,3,4,9
* PRF # I7: 1,8 => SOL
* DIS # I9: 1,8 => CTR => I9: 4,6,9
* DIS # G6: 2,9 => CTR => G6: 8
* DIS # G6: 2,9 => CTR => G6: 8
* PRF # G1: 2,9 => SOL
* DIS # C9: 3 => CTR => C9: 6,9
* DIS # I7: 6,9 => CTR => I7: 1,4,8
* DIS # A7: 1,9 => CTR => A7: 4,8
* DIS # A9: 1,9 => CTR => A9: 3,4,8
* DIS # A1: 1,9 => CTR => A1: 3,8
* DIS # A7: 1,8 => CTR => A7: 4,9
* DIS # A9: 1,8 => CTR => A9: 3,4,9
* DIS # G9: 1,8 => CTR => G9: 4,5,9
* DIS # I9: 1,8 => CTR => I9: 4,6,9
* PRF # D7: 5,9 => SOL
* PRF # G7: 1,9 => SOL
* DIS # I7: 1,9 => CTR => I7: 4,6,8
* DIS # G9: 1,9 => CTR => G9: 4,5,8
* DIS # I9: 1,9 => CTR => I9: 4,6,8
* DIS # I1: 1,9 => CTR => I1: 2,3,4,8
* CNT  32 HDP CHAINS /  76 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 # A1: 3,9 => CTR => A1: 1,8
* DIS A1: 1,8 # I1: 3,9 => CTR => I1: 1,2,4,8
* DIS A1: 1,8 + I1: 1,2,4,8 # G6: 2,9 => CTR => G6: 8
* PRF A1: 1,8 + I1: 1,2,4,8 + G6: 8 => SOL
* STA A1: 1,8 + I1: 1,2,4,8 + G6: 8
* CNT   4 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

...7.......24397...4.....6..9.....45.3.....1.76.....3..7.....2...58643.......2... initial
...7.6...6.24397...47..1.6.2983176455346.8.17761.45.3..7...3.2..2586437.....72... autosolve
813756294652439781947281563298317645534628917761945832476593128125864379389172456 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (12)
C1: 3,9
D3: 2,5
H2: 5,8
I2: 1,8
E5: 2,9
D6: 2,9
G5: 2,9
C7: 6,9
A8: 1,9
B9: 1,8
E7: 5,9
I8: 1,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D7,D9: 1.. / D7 = 1  => 13 pairs (_) / D9 = 1  =>  0 pairs (*)
B2,I2: 1.. / B2 = 1  =>  0 pairs (X) / I2 = 1  => 16 pairs (_)
A8,I8: 1.. / A8 = 1  => 16 pairs (_) / I8 = 1  =>  0 pairs (X)
E5,D6: 2.. / E5 = 2  =>  0 pairs (*) / D6 = 2  =>  0 pairs (X)
E5,G5: 2.. / E5 = 2  =>  0 pairs (*) / G5 = 2  =>  0 pairs (X)
D3,D6: 2.. / D3 = 2  =>  0 pairs (*) / D6 = 2  =>  0 pairs (X)
I1,I3: 3.. / I1 = 3  =>  0 pairs (X) / I3 = 3  => 13 pairs (_)
A9,C9: 3.. / A9 = 3  => 16 pairs (_) / C9 = 3  =>  0 pairs (X)
A3,I3: 3.. / A3 = 3  =>  0 pairs (X) / I3 = 3  => 13 pairs (_)
C1,C9: 3.. / C1 = 3  => 16 pairs (_) / C9 = 3  =>  0 pairs (X)
G1,I1: 4.. / G1 = 4  =>  0 pairs (X) / I1 = 4  =>  0 pairs (_)
A7,A9: 4.. / A7 = 4  => 16 pairs (_) / A9 = 4  =>  0 pairs (X)
B1,B2: 5.. / B1 = 5  => 16 pairs (_) / B2 = 5  => 16 pairs (_)
B2,H2: 5.. / B2 = 5  => 16 pairs (_) / H2 = 5  => 16 pairs (_)
C7,C9: 6.. / C7 = 6  => 12 pairs (_) / C9 = 6  =>  0 pairs (X)
I7,I9: 6.. / I7 = 6  =>  0 pairs (X) / I9 = 6  => 12 pairs (_)
C7,I7: 6.. / C7 = 6  => 12 pairs (_) / I7 = 6  =>  0 pairs (X)
C9,I9: 6.. / C9 = 6  =>  0 pairs (X) / I9 = 6  => 12 pairs (_)
E1,E3: 8.. / E1 = 8  =>  0 pairs (X) / E3 = 8  => 15 pairs (_)
G6,I6: 8.. / G6 = 8  => 13 pairs (_) / I6 = 8  =>  0 pairs (X)
E5,D6: 9.. / E5 = 9  =>  0 pairs (X) / D6 = 9  =>  0 pairs (_)
E5,G5: 9.. / E5 = 9  =>  0 pairs (X) / G5 = 9  =>  0 pairs (_)
A8,I8: 9.. / A8 = 9  =>  0 pairs (X) / I8 = 9  => 16 pairs (_)
E5,E7: 9.. / E5 = 9  =>  0 pairs (X) / E7 = 9  =>  0 pairs (_)
H1,H9: 9.. / H1 = 9  => 16 pairs (_) / H9 = 9  =>  0 pairs (X)
* DURATION: 0:00:28.720072  START: 23:23:18.956326  END: 23:23:47.676398 2019-04-28
* CP COUNT: (25)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B9,C1,C7,D3,D6,E5,E7,G5,H2,I2,I8)
* ...7.6...6.24397...47..1.6.2983176455346.8.17761.45.3..7...3.2..2586437.....72...
* PAIR C1: 3,9 BLK 1
A1: 3,9,1,8                              # reduction candidate for 3,9
A1: 3,9 => CTR
* ...786...6.2439781847..1963298317645534698217761245839.7...3.2..2586437..8..72...
A1: 1,8                                  # 14 pairs
A3: 3,9,8                                # reduction candidate for 3,9
A3: 3,9                                  # 14 pairs
* PAIR C1: 3,9 ROW 1
I1: 3,9,1,2,4,8                          # reduction candidate for 3,9
I1: 3,9 => CTR
* .1.7.64..6.24397.1.47..1.6.2983176455346.8.17761.45.3..7...3.2.125864379.8..72.5.
I1: 1,2,4,8                              # 13 pairs
* PAIR C1: 3,9 COL C
C9: 3,9,6                                # reduction candidate for 3,9
C9: 6 => CTR
* ..37.6.9.6524397819475812632983176455346.8.17761.45.3..79.53.26125864379386972.5.
C9: 3,9                                  # 12 pairs
* PAIR D3: 2,5 BLK 2
E1: 2,5,8                                # reduction candidate for 2,5
E1: 2,5                                  # 15 pairs
E3: 2,5,8                                # reduction candidate for 2,5
E3: 2,5 => CTR
* ...7864.26.24397.1.47..1.632983176455346.8.17761.45.3..7...3.2.125864379.8..72.5.
E3: 8                                    # 15 pairs
* PAIR D3: 2,5 ROW 3
G3: 2,5,8,9                              # reduction candidate for 2,5
G3: 8,9 => CTR
* ...7.64..6.24397.1.47..1.6.2983176455346.8.17761.45.3..7...3.2.125864379.8..72.5.
G3: 2,5                                  # 17 pairs
* PAIR H2: 5,8 BLK 3
G1: 5,8,1,2,4,9                          # reduction candidate for 5,8
G1: 5,8 => CTR
* .1.726594652439781947581263298317645534698.17761.45.32.7...3.2.125864379.8..72.56
G1: 1,2,4,9                              # 12 pairs
H1: 5,8,9                                # reduction candidate for 5,8
H1: 5,8 => CTR
* ..97.61.4612439758.47..1.6.2983176455346.8.17761.45.3..7...3.2.925864371....72.9.
H1: 9                                    # 16 pairs
G3: 5,8,2,9                              # reduction candidate for 5,8
G3: 5,8 => SOLVED
* 813756294652439781947281563298317645534628917761945832476593128125864379389172456
G3: 2,9                                  # 15 pairs
* PAIR H2: 5,8 ROW 2
B2: 5,8,1                                # reduction candidate for 5,8
B2: 1 => CTR
* .5.7.6...612439758.47..1.6.2983176455346.8.17761.4583.87...3.2..2586437.....72...
B2: 5,8                                  # 16 pairs
* PAIR H2: 5,8 COL H
H9: 5,8,9                                # reduction candidate for 5,8
H9: 9 => CTR
* ..97.61.4612439758.47..1.6.2983176455346.8.17761.45.3..7...3.2.925864371....72.9.
H9: 5,8                                  # 16 pairs
* PAIR I2: 1,8 BLK 3
G1: 1,8,2,4,5,9                          # reduction candidate for 1,8
G1: 1,8 => CTR
* ...726..46.24397...47581263298317645534698.17761.45.32.7...3.2..2586437.....72...
G1: 2,4,5,9                              # 16 pairs
I1: 1,8,2,3,4,9                          # reduction candidate for 1,8
I1: 1,8 => CTR
* ...7264..6.24397...47581263298317645534698.17761.45.32.7...3.2..2586437.....72...
I1: 2,3,4,9                              # 12 pairs
* PAIR I2: 1,8 ROW 2
B2: 1,8,5                                # reduction candidate for 1,8
B2: 5                                    # 16 pairs
B2: 1,8                                  # 16 pairs
* PAIR I2: 1,8 COL I
I7: 1,8,4,6,9                            # reduction candidate for 1,8
I7: 1,8 => SOLVED
* 813756294652439781947281563298317645534628917761945832476593128125864379389172456
I7: 4,6,9                                # 12 pairs
I9: 1,8,4,6,9                            # reduction candidate for 1,8
I9: 1,8 => CTR
* ..37.6..46.24397...47..1.632983176455346.8.17761.45.32.79.53.26.2586437...6.72...
I9: 4,6,9                                # 12 pairs
* PAIR D6: 2,9 ROW 6
G6: 2,9,8                                # reduction candidate for 2,9
G6: 2,9 => CTR
* 8137.6492652439781947281.632983176455346.8.17761.45.3847...3826125864379386972154
G6: 8                                    # 13 pairs
I6: 2,9,8                                # reduction candidate for 2,9
I6: 2,9                                  # 13 pairs
* PAIR G5: 2,9 BLK 6
G6: 2,9,8                                # reduction candidate for 2,9
G6: 2,9 => CTR
* 8137.6492652439781947281.632983176455346.8.17761.45.3847...3826125864379386972154
G6: 8                                    # 13 pairs
I6: 2,9,8                                # reduction candidate for 2,9
I6: 2,9                                  # 13 pairs
* PAIR G5: 2,9 COL G
G1: 2,9,1,4,5,8                          # reduction candidate for 2,9
G1: 2,9 => SOLVED
* 813756294652439781947281563298317645534628917761945832476593128125864379389172456
G1: 1,4,5,8                              # 12 pairs
G3: 2,9,5,8                              # reduction candidate for 2,9
G3: 2,9                                  # 15 pairs
* PAIR C7: 6,9 BLK 7
C9: 6,9,3                                # reduction candidate for 6,9
C9: 3 => CTR
* ..97.61.4612439758.47..1.6.2983176455346.8.17761.45.3..76..3.2.925864371..3.72.96
C9: 6,9                                  # 16 pairs
* PAIR C7: 6,9 ROW 7
I7: 6,9,1,4,8                            # reduction candidate for 6,9
I7: 6,9 => CTR
* ...7.6.9.6.24397..9475.1863298317645534698217761245938879153426.2586437....972...
I7: 1,4,8                                # 12 pairs
* PAIR A8: 1,9 BLK 7
A7: 1,9,4,8                              # reduction candidate for 1,9
A7: 1,9 => CTR
* ..97.61.4612439758.47..1.6.2983176455346.8.17761.45.3..76..3.2.925864371483172596
A7: 4,8                                  # 13 pairs
A9: 1,9,3,4,8                            # reduction candidate for 1,9
A9: 1,9 => CTR
* ..97.6..46.24397...47..1.632983176455346.8.17761.45.32476..3.2..2586437..83.72496
A9: 3,4,8                                # 12 pairs
* PAIR A8: 1,9 COL A
A1: 1,9,3,8                              # reduction candidate for 1,9
A1: 1,9 => CTR
* ...7.6...6.24397...47..1.6.2983176455346.8.17761.45.3..7...3.2.925864371.1..72.9.
A1: 3,8                                  # 16 pairs
* PAIR B9: 1,8 BLK 7
A7: 1,8,4,9                              # reduction candidate for 1,8
A7: 1,8 => CTR
* ..97.61.4612439758.47..1.6.2983176455346.8.17761.45.3..76..3.2.9258643714.3.72.96
A7: 4,9                                  # 16 pairs
A9: 1,8,3,4,9                            # reduction candidate for 1,8
A9: 1,8 => CTR
* ..97.6..46.24397...47..1.632983176455346.8.17761.45.32476..3.2.925864371..3.72496
A9: 3,4,9                                # 12 pairs
* PAIR B9: 1,8 ROW 9
G9: 1,8,4,5,9                            # reduction candidate for 1,8
G9: 1,8 => CTR
* .1.7.6.9.6524397819475812632983176455346.8.17761.45.3..7.1.3.2.125864379.8.97215.
G9: 4,5,9                                # 12 pairs
I9: 1,8,4,6,9                            # reduction candidate for 1,8
I9: 1,8 => CTR
* ..37.6..46.24397...47..1.632983176455346.8.17761.45.32.79.53.26.2586437...6.72...
I9: 4,6,9                                # 12 pairs
* PAIR B9: 1,8 COL B
B1: 1,8,5                                # reduction candidate for 1,8
B1: 1,8                                  # 16 pairs
B2: 1,8,5                                # reduction candidate for 1,8
B2: 1,8                                  # 16 pairs
* PAIR E7: 5,9 BLK 8
D7: 5,9,1                                # reduction candidate for 5,9
D7: 5,9 => SOLVED
* 813756294652439781947281563298317645534628917761945832476593128125864379389172456
D7: 1                                    # 13 pairs
D9: 5,9,1                                # reduction candidate for 5,9
D9: 5,9                                  # 13 pairs
* PAIR E7: 5,9 ROW 7
G7: 5,9,1,4,8                            # reduction candidate for 5,9
G7: 5,9                                  # 18 pairs
G7: 1,4,8                                # 13 pairs
* PAIR I8: 1,9 BLK 9
G7: 1,9,4,5,8                            # reduction candidate for 1,9
G7: 1,9 => SOLVED
* 813756294652439781947281563298317645534628917761945832476593128125864379389172456
G7: 4,5,8                                # 12 pairs
I7: 1,9,4,6,8                            # reduction candidate for 1,9
I7: 1,9 => CTR
* ...7.6..46.24397.8.472.1.63298317645534628917761.45.32.76..3.2..2586437.....72..6
I7: 4,6,8                                # 12 pairs
G9: 1,9,4,5,8                            # reduction candidate for 1,9
G9: 1,9 => CTR
* 8.37264916.24397..947..1.632983176455346.8.17761.45.3..79.53.26125864379.86972154
G9: 4,5,8                                # 12 pairs
I9: 1,9,4,6,8                            # reduction candidate for 1,9
I9: 1,9 => CTR
* ..37.6..46.24397...47..1.632983176455346.8.17761.45.32.79.53.26.2586437...6.72...
I9: 4,6,8                                # 12 pairs
* PAIR I8: 1,9 COL I
I1: 1,9,2,3,4,8                          # reduction candidate for 1,9
I1: 1,9 => CTR
* ...7264..6.24397...47581263298317645534698.17761.45.32.7...3.2..2586437.....72...
I1: 2,3,4,8                              # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-interesting-5x5-blank-center-base-pr-000.dot
* REASONING
* DIS # A1: 3,9 => CTR => A1: 1,8
* DIS # I1: 3,9 => CTR => I1: 1,2,4,8
* DIS # C9: 6 => CTR => C9: 3,9
* DIS # E3: 2,5 => CTR => E3: 8
* DIS # G3: 8,9 => CTR => G3: 2,5
* DIS # G1: 5,8 => CTR => G1: 1,2,4,9
* DIS # H1: 5,8 => CTR => H1: 9
* PRF # G3: 5,8 => SOL
* DIS # B2: 1 => CTR => B2: 5,8
* DIS # H9: 9 => CTR => H9: 5,8
* DIS # G1: 1,8 => CTR => G1: 2,4,5,9
* DIS # I1: 1,8 => CTR => I1: 2,3,4,9
* PRF # I7: 1,8 => SOL
* DIS # I9: 1,8 => CTR => I9: 4,6,9
* DIS # G6: 2,9 => CTR => G6: 8
* DIS # G6: 2,9 => CTR => G6: 8
* PRF # G1: 2,9 => SOL
* DIS # C9: 3 => CTR => C9: 6,9
* DIS # I7: 6,9 => CTR => I7: 1,4,8
* DIS # A7: 1,9 => CTR => A7: 4,8
* DIS # A9: 1,9 => CTR => A9: 3,4,8
* DIS # A1: 1,9 => CTR => A1: 3,8
* DIS # A7: 1,8 => CTR => A7: 4,9
* DIS # A9: 1,8 => CTR => A9: 3,4,9
* DIS # G9: 1,8 => CTR => G9: 4,5,9
* DIS # I9: 1,8 => CTR => I9: 4,6,9
* PRF # D7: 5,9 => SOL
* PRF # G7: 1,9 => SOL
* DIS # I7: 1,9 => CTR => I7: 4,6,8
* DIS # G9: 1,9 => CTR => G9: 4,5,8
* DIS # I9: 1,9 => CTR => I9: 4,6,8
* DIS # I1: 1,9 => CTR => I1: 2,3,4,8
* CNT  32 HDP CHAINS /  76 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B9,C1,C7,D3,D6,E5,E7,G5,H2,I2,I8)
* ...7.6...6.24397...47..1.6.2983176455346.8.17761.45.3..7...3.2..2586437.....72...
* PAIR C1: 3,9 BLK 1
A1: 3,9,1,8                              # reduction candidate for 3,9
A1: 3,9 => CTR
* ...786...6.2439781847..1963298317645534698217761245839.7...3.2..2586437..8..72...
* RESTART
* PAIR C1: 3,9 ROW 1
I1: 3,9,1,2,4,8                          # reduction candidate for 3,9
I1: 3,9 => CTR
* 81.7.64..6.24397.1.47..1.6.2983176455346.8.17761.45.3..7...3.2.125864379.8..72.5.
* PAIR RESTART
* PAIR D6: 2,9 ROW 6
G6: 2,9,8                                # reduction candidate for 2,9
G6: 2,9 => CTR
* 8137.6492652439781947281.632983176455346.8.17761.45.3847...3826125864379386972154
G6: 8 => SOLVED
* 813756294652439781947281563298317645534628917761945832476593128125864379389172456
* DURATION: 0:00:04.444545  START: 23:24:32.119425  END: 23:24:36.563970 2019-04-28
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-interesting-5x5-blank-center-base-pr-001.dot
* REASONING
* DIS # A1: 3,9 => CTR => A1: 1,8
* DIS A1: 1,8 # I1: 3,9 => CTR => I1: 1,2,4,8
* DIS A1: 1,8 + I1: 1,2,4,8 # G6: 2,9 => CTR => G6: 8
* PRF A1: 1,8 + I1: 1,2,4,8 + G6: 8 => SOL
* STA A1: 1,8 + I1: 1,2,4,8 + G6: 8
* CNT   4 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.sudokuwiki.org/Interesting_Sudokus

Minimal at 24 Clues with a 5x5 blank space in the center

Discovered by Klaus Brenner

Solution

position: 813756294652439781947281563298317645534628917761945832476593128125864379389172456 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 # A1: 3,9 => CTR => A1: 1,8
* INC # A1: 1,8 => UNS
* INC # A3: 3,9 => UNS
* DIS # I1: 3,9 => CTR => I1: 1,2,4,8
* INC # I1: 1,2,4,8 => UNS
* INC # C9: 3,9 => UNS
* DIS # C9: 6 => CTR => C9: 3,9
* INC # E1: 2,5 => UNS
* DIS # E3: 2,5 => CTR => E3: 8
* INC # E3: 8 => UNS
* INC # G3: 2,5 => UNS
* DIS # G3: 8,9 => CTR => G3: 2,5
* DIS # G1: 5,8 => CTR => G1: 1,2,4,9
* INC # G1: 1,2,4,9 => UNS
* DIS # H1: 5,8 => CTR => H1: 9
* INC # H1: 9 => UNS
* PRF # G3: 5,8 => SOL
* INC # G3: 2,9 => UNS
* INC # B2: 5,8 => UNS
* DIS # B2: 1 => CTR => B2: 5,8
* INC # H9: 5,8 => UNS
* DIS # H9: 9 => CTR => H9: 5,8
* DIS # G1: 1,8 => CTR => G1: 2,4,5,9
* INC # G1: 2,4,5,9 => UNS
* DIS # I1: 1,8 => CTR => I1: 2,3,4,9
* INC # I1: 2,3,4,9 => UNS
* INC # B2: 1,8 => UNS
* INC # B2: 5 => UNS
* PRF # I7: 1,8 => SOL
* INC # I7: 4,6,9 => UNS
* DIS # I9: 1,8 => CTR => I9: 4,6,9
* INC # I9: 4,6,9 => UNS
* DIS # G6: 2,9 => CTR => G6: 8
* INC # G6: 8 => UNS
* INC # I6: 2,9 => UNS
* DIS # G6: 2,9 => CTR => G6: 8
* INC # G6: 8 => UNS
* INC # I6: 2,9 => UNS
* PRF # G1: 2,9 => SOL
* INC # G1: 1,4,5,8 => UNS
* INC # G3: 2,9 => UNS
* INC # C9: 6,9 => UNS
* DIS # C9: 3 => CTR => C9: 6,9
* DIS # I7: 6,9 => CTR => I7: 1,4,8
* INC # I7: 1,4,8 => UNS
* DIS # A7: 1,9 => CTR => A7: 4,8
* INC # A7: 4,8 => UNS
* DIS # A9: 1,9 => CTR => A9: 3,4,8
* INC # A9: 3,4,8 => UNS
* DIS # A1: 1,9 => CTR => A1: 3,8
* INC # A1: 3,8 => UNS
* DIS # A7: 1,8 => CTR => A7: 4,9
* INC # A7: 4,9 => UNS
* DIS # A9: 1,8 => CTR => A9: 3,4,9
* INC # A9: 3,4,9 => UNS
* DIS # G9: 1,8 => CTR => G9: 4,5,9
* INC # G9: 4,5,9 => UNS
* DIS # I9: 1,8 => CTR => I9: 4,6,9
* INC # I9: 4,6,9 => UNS
* INC # B1: 1,8 => UNS
* INC # B2: 1,8 => UNS
* PRF # D7: 5,9 => SOL
* INC # D7: 1 => UNS
* INC # D9: 5,9 => UNS
* INC # G7: 5,9 => UNS
* INC # G7: 1,4,8 => UNS
* PRF # G7: 1,9 => SOL
* INC # G7: 4,5,8 => UNS
* DIS # I7: 1,9 => CTR => I7: 4,6,8
* INC # I7: 4,6,8 => UNS
* DIS # G9: 1,9 => CTR => G9: 4,5,8
* INC # G9: 4,5,8 => UNS
* DIS # I9: 1,9 => CTR => I9: 4,6,8
* INC # I9: 4,6,8 => UNS
* DIS # I1: 1,9 => CTR => I1: 2,3,4,8
* INC # I1: 2,3,4,8 => UNS
* CNT  76 HDP CHAINS /  76 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A1: 3,9 => CTR => A1: 1,8
* DIS A1: 1,8 # I1: 3,9 => CTR => I1: 1,2,4,8
* DIS A1: 1,8 + I1: 1,2,4,8 # G6: 2,9 => CTR => G6: 8
* PRF A1: 1,8 + I1: 1,2,4,8 + G6: 8 => SOL
* STA A1: 1,8 + I1: 1,2,4,8 + G6: 8
* CNT   4 HDP CHAINS /   3 HYP OPENED