Analysis of zz-www.sudokuoftheday.co.uk-20190317-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019

position: 6..8.......5..28.9.39..1..7...........8.....33...25.6.1..5.....2...1..7..7..3...4 initial

Autosolve

position: 6..8.......5..28.9839451627...........8.....33...25.681..5.....2...1..7..7623...4 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B1: 1,4 => CTR => B1: 2
* PRF # B1: 2 => SOL
* PRF # H2: 3 => SOL
* DIS # B4: 1,4 => CTR => B4: 2,5,6,9
* DIS # B5: 1,4 => CTR => B5: 2,5,6,9
* PRF # B6: 1,4 => SOL
* DIS # B6: 9 => CTR => B6: 1,4
* PRF # F1: 3 => SOL
* DIS # E4: 7,9 => CTR => E4: 4,6,8
* DIS # E5: 7,9 => CTR => E5: 4,6
* PRF # D2: 6,7 => SOL
* DIS # E4: 6,7 => CTR => E4: 4,8,9
* DIS # E5: 6,7 => CTR => E5: 4,9
* PRF # I4: 1,5 => SOL
* DIS # I4: 2 => CTR => I4: 1,5
* DIS # C4: 1,7 => CTR => C4: 2
* PRF # C4: 2 => SOL
* DIS # G6: 1,7 => CTR => G6: 4,9
* PRF # C1: 1,7 => SOL
* DIS # C1: 2 => CTR => C1: 1,7
* PRF # B8: 8,9 => SOL
* DIS # B8: 5 => CTR => B8: 8,9
* DIS # E7: 8,9 => CTR => E7: 4,6,7
* DIS # F7: 8,9 => CTR => F7: 4,6,7
* DIS # B8: 5,9 => CTR => B8: 8
* PRF # B8: 8 => SOL
* DIS # G9: 5,9 => CTR => G9: 1
* PRF # H9: 5,9 => SOL
* PRF # E7: 6,9 => SOL
* DIS # F7: 6,9 => CTR => F7: 4,7,8
* DIS # F8: 6,9 => CTR => F8: 4,8
* DIS # D4: 6,9 => CTR => D4: 1,3,7
* DIS # E7: 8,9 => CTR => E7: 4,6,7
* DIS # F7: 8,9 => CTR => F7: 4,6,7
* DIS # F8: 8,9 => CTR => F8: 4,6
* PRF # F8: 4,6 => SOL
* PRF # H9: 8,9 => SOL
* DIS # H9: 1,5 => CTR => H9: 8,9
* DIS # F4: 8,9 => CTR => F4: 3,4,6,7
* CNT  39 HDP CHAINS /  71 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 # B1: 1,4 => CTR => B1: 2
* PRF B1: 2 => SOL
* STA B1: 2
* CNT   2 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

6..8.......5..28.9.39..1..7...........8.....33...25.6.1..5.....2...1..7..7..3...4 initial
6..8.......5..28.9839451627...........8.....33...25.681..5.....2...1..7..7623...4 autosolve
627893415415672839839451627952386741768149253341725968194567382283914576576238194 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
A2: 4,7
B2: 1,4
E1: 7,9
E2: 6,7
I1: 1,5
C6: 1,7
B7: 8,9
C7: 3,4
C8: 3,4
A9: 5,9
D8: 6,9
F9: 8,9
I7: 2,6
I8: 5,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G9,H9: 1.. / G9 = 1  => 14 pairs (_) / H9 = 1  =>  0 pairs (X)
B2,H2: 1.. / B2 = 1  => 17 pairs (_) / H2 = 1  =>  0 pairs (X)
I1,I4: 1.. / I1 = 1  => 17 pairs (_) / I4 = 1  =>  0 pairs (*)
B1,C1: 2.. / B1 = 2  =>  0 pairs (*) / C1 = 2  =>  0 pairs (X)
G7,I7: 2.. / G7 = 2  =>  0 pairs (X) / I7 = 2  =>  0 pairs (_)
B5,G5: 2.. / B5 = 2  =>  0 pairs (X) / G5 = 2  =>  0 pairs (_)
C1,C4: 2.. / C1 = 2  =>  0 pairs (X) / C4 = 2  =>  0 pairs (_)
I4,I7: 2.. / I4 = 2  =>  0 pairs (X) / I7 = 2  =>  0 pairs (_)
F1,D2: 3.. / F1 = 3  =>  0 pairs (*) / D2 = 3  =>  0 pairs (X)
D4,F4: 3.. / D4 = 3  =>  0 pairs (*) / F4 = 3  =>  0 pairs (X)
C7,C8: 3.. / C7 = 3  =>  0 pairs (X) / C8 = 3  =>  0 pairs (_)
D2,H2: 3.. / D2 = 3  => 18 pairs (_) / H2 = 3  =>  0 pairs (*)
C8,G8: 3.. / C8 = 3  =>  0 pairs (*) / G8 = 3  =>  0 pairs (X)
D2,D4: 3.. / D2 = 3  => 18 pairs (_) / D4 = 3  =>  0 pairs (*)
F1,F4: 3.. / F1 = 3  =>  0 pairs (*) / F4 = 3  =>  0 pairs (X)
C7,C8: 4.. / C7 = 4  =>  0 pairs (*) / C8 = 4  =>  0 pairs (X)
B6,G6: 4.. / B6 = 4  =>  0 pairs (*) / G6 = 4  =>  0 pairs (X)
C8,F8: 4.. / C8 = 4  =>  0 pairs (X) / F8 = 4  =>  0 pairs (_)
B8,A9: 5.. / B8 = 5  =>  0 pairs (X) / A9 = 5  =>  0 pairs (_)
D2,E2: 6.. / D2 = 6  =>  0 pairs (*) / E2 = 6  =>  0 pairs (X)
B4,B5: 6.. / B4 = 6  => 14 pairs (_) / B5 = 6  =>  0 pairs (*)
I7,I8: 6.. / I7 = 6  =>  0 pairs (X) / I8 = 6  =>  0 pairs (_)
C1,A2: 7.. / C1 = 7  =>  0 pairs (*) / A2 = 7  =>  0 pairs (X)
E7,F7: 7.. / E7 = 7  => 14 pairs (_) / F7 = 7  => 15 pairs (_)
E4,F4: 8.. / E4 = 8  => 14 pairs (_) / F4 = 8  =>  0 pairs (X)
B7,B8: 8.. / B7 = 8  =>  0 pairs (X) / B8 = 8  =>  0 pairs (_)
H7,H9: 8.. / H7 = 8  =>  0 pairs (*) / H9 = 8  =>  0 pairs (X)
B8,F8: 8.. / B8 = 8  =>  0 pairs (*) / F8 = 8  =>  0 pairs (X)
F9,H9: 8.. / F9 = 8  =>  0 pairs (*) / H9 = 8  =>  0 pairs (X)
E4,E7: 8.. / E4 = 8  => 14 pairs (_) / E7 = 8  =>  0 pairs (X)
E1,F1: 9.. / E1 = 9  => 14 pairs (_) / F1 = 9  =>  0 pairs (X)
* DURATION: 0:00:34.801467  START: 04:35:41.490625  END: 04:36:16.292092 2019-05-01
* CP COUNT: (31)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,B2,B7,C6,C7,C8,D8,E1,E2,F9,I1,I7,I8)
* 6..8.......5..28.9839451627...........8.....33...25.681..5.....2...1..7..7623...4
* PAIR A2: 4,7 COL A
A4: 4,7,5,9                              # reduction candidate for 4,7
A4: 4,7                                  # 16 pairs
A5: 4,7,5,9                              # reduction candidate for 4,7
A5: 4,7                                  # 16 pairs
* PAIR B2: 1,4 BLK 1
B1: 1,4,2                                # reduction candidate for 1,4
B1: 1,4 => CTR
* 6.28.....7.53628.98394516274...83.....8.....339..2546818.5.....25..18.7697623...4
B1: 2 => SOLVED
* 627893415415672839839451627952386741768149253341725968194567382283914576576238194
* PAIR B2: 1,4 ROW 2
H2: 1,4,3                                # reduction candidate for 1,4
H2: 3 => SOLVED
* 627893415415672839839451627952386741768149253341725968194567382283914576576238194
H2: 1,4                                  # 18 pairs
* PAIR B2: 1,4 COL B
B4: 1,4,2,5,6,9                          # reduction candidate for 1,4
B4: 1,4 => CTR
* 6..8.......5..28.9839451627..........68...2.33...25.681..5....225..18.7697623...4
B4: 2,5,6,9                              # 14 pairs
B5: 1,4,2,5,6,9                          # reduction candidate for 1,4
B5: 1,4 => CTR
* 6..8.......5..28.9839451627.62........8...2.33...25.681..5....225..18.7697623...4
B5: 2,5,6,9                              # 14 pairs
B6: 1,4,9                                # reduction candidate for 1,4
B6: 1,4 => SOLVED
* 627893415415672839839451627952386741768149253341725968194567382283914576576238194
B6: 9 => CTR
* 6..8.......5..28.9839451627...........8.....339..2546818.5.....25..18.7697623...4
* PAIR E1: 7,9 BLK 2
F1: 7,9,3                                # reduction candidate for 7,9
F1: 3 => SOLVED
* 627893415415672839839451627952386741768149253341725968194567382283914576576238194
F1: 7,9                                  # 18 pairs
* PAIR E1: 7,9 COL E
E4: 7,9,4,6,8                            # reduction candidate for 7,9
E4: 7,9 => CTR
* 6..893..1.15..2839839451627...378..2.28.46..33...25.6819.587..628..14.75576239184
E4: 4,6,8                                # 14 pairs
E5: 7,9,4,6                              # reduction candidate for 7,9
E5: 7,9 => CTR
* 6..8....1.15.628.9839451627........2.28.....33...25.681..5.72.62...1..7557623...4
E5: 4,6                                  # 15 pairs
E7: 7,9,4,6,8                            # reduction candidate for 7,9
E7: 7,9                                  # 15 pairs
* PAIR E2: 6,7 BLK 2
D2: 6,7,3                                # reduction candidate for 6,7
D2: 6,7 => SOLVED
* 627893415415672839839451627952386741768149253341725968194567382283914576576238194
D2: 3                                    # 18 pairs
* PAIR E2: 6,7 COL E
E4: 6,7,4,8,9                            # reduction candidate for 6,7
E4: 6,7 => CTR
* 6..893..1.15..2839839451627...3.8..2.28.46..33...25.6819.587..628..14.75576239184
E4: 4,8,9                                # 14 pairs
E5: 6,7,4,9                              # reduction candidate for 6,7
E5: 6,7 => CTR
* 6.7893..1415..2839839451627..2........8.....33...25.681..5.7..62...1..7557623...4
E5: 4,9                                  # 15 pairs
E7: 6,7,4,8,9                            # reduction candidate for 6,7
E7: 6,7                                  # 15 pairs
* PAIR I1: 1,5 BLK 3
G1: 1,5,3,4                              # reduction candidate for 1,5
G1: 1,5                                  # 21 pairs
H1: 1,5,3,4                              # reduction candidate for 1,5
H1: 1,5                                  # 19 pairs
* PAIR I1: 1,5 COL I
I4: 1,5,2                                # reduction candidate for 1,5
I4: 1,5 => SOLVED
* 627893415415672839839451627952386741768149253341725968194567382283914576576238194
I4: 2 => CTR
* 6..8....1.15..28.9839451627........2.28.....33...25.681..5..2.62...1..7557623...4
* PAIR C6: 1,7 BLK 4
C4: 1,7,2                                # reduction candidate for 1,7
C4: 1,7 => CTR
* 6.28.....7.53628.98394516274...83.....8.....339..2546818.5.....25..18.7697623...4
C4: 2 => SOLVED
* 627893415415672839839451627952386741768149253341725968194567382283914576576238194
* PAIR C6: 1,7 ROW 6
D6: 1,7,9                                # reduction candidate for 1,7
D6: 1,7                                  # 17 pairs
G6: 1,7,4,9                              # reduction candidate for 1,7
G6: 1,7 => CTR
* 6..8....1415.62839839451627...3....2.28.....334.925.681..5.....2..61..7557623...4
G6: 4,9                                  # 15 pairs
* PAIR C6: 1,7 COL C
C1: 1,7,2                                # reduction candidate for 1,7
C1: 1,7 => SOLVED
* 627893415415672839839451627952386741768149253341725968194567382283914576576238194
C1: 2 => CTR
* 6.28.....7.53628.98394516274...83.....8.....339..2546818.5.....25..18.7697623...4
* PAIR B7: 8,9 BLK 7
B8: 8,9,5                                # reduction candidate for 8,9
B8: 8,9 => SOLVED
* 627893415415672839839451627952386741768149253341725968194567382283914576576238194
B8: 5 => CTR
* 6..8.......5..28.9839451627...........8.....33...25.6818.5.....25..18.7697623...4
* PAIR B7: 8,9 ROW 7
E7: 8,9,4,6,7                            # reduction candidate for 8,9
E7: 8,9 => CTR
* 6..8....1.15..28.9839451627........2.28.....33...25.681.45.723628..14.7557623...4
E7: 4,6,7                                # 14 pairs
F7: 8,9,4,6,7                            # reduction candidate for 8,9
F7: 8,9 => CTR
* 6..89...1.15.628.9839451627....8...2.28.4...33...25.681.457.23628..14.7557623...4
F7: 4,6,7                                # 14 pairs
H7: 8,9,3                                # reduction candidate for 8,9
H7: 8,9                                  # 16 pairs
* PAIR A9: 5,9 BLK 7
B8: 5,9,8                                # reduction candidate for 5,9
B8: 5,9 => CTR
* 6..89...1.15.628.9839451627....8...2.28..6..334..25.6818.5.....294618375576239184
B8: 8 => SOLVED
* 627893415415672839839451627952386741768149253341725968194567382283914576576238194
* PAIR A9: 5,9 ROW 9
G9: 5,9,1                                # reduction candidate for 5,9
G9: 5,9 => CTR
* 627893..1415762839839451627..2.8......8.....334.925.6819.5...8.28.619.75576238914
G9: 1                                    # 14 pairs
H9: 5,9,1,8                              # reduction candidate for 5,9
H9: 5,9 => SOLVED
* 627893415415672839839451627952386741768149253341725968194567382283914576576238194
H9: 1,8                                  # 15 pairs
* PAIR A9: 5,9 COL A
A4: 5,9,4,7                              # reduction candidate for 5,9
A4: 5,9                                  # 16 pairs
A5: 5,9,4,7                              # reduction candidate for 5,9
A5: 5,9                                  # 16 pairs
* PAIR D8: 6,9 BLK 8
E7: 6,9,4,7,8                            # reduction candidate for 6,9
E7: 6,9 => SOLVED
* 627893415415672839839451627952386741768149253341725968194567382283914576576238194
E7: 4,7,8                                # 14 pairs
F7: 6,9,4,7,8                            # reduction candidate for 6,9
F7: 6,9 => CTR
* 6..89.4..415762839839451627...38..4...864..13347125968194576382283914576576238194
F7: 4,7,8                                # 14 pairs
F8: 6,9,4,8                              # reduction candidate for 6,9
F8: 6,9 => CTR
* 6..8....1.15..28.9839451627........2.28.....33...25.6819.5.....284.1.37557623...4
F8: 4,8                                  # 15 pairs
* PAIR D8: 6,9 COL D
D4: 6,9,1,3,7                            # reduction candidate for 6,9
D4: 6,9 => CTR
* 6..8.....7.53628.98394516274...83...5.8.....339..2546818.5.....25..18.7697623...4
D4: 1,3,7                                # 14 pairs
D5: 6,9,1,7                              # reduction candidate for 6,9
D5: 6,9                                  # 18 pairs
* PAIR F9: 8,9 BLK 8
E7: 8,9,4,6,7                            # reduction candidate for 8,9
E7: 8,9 => CTR
* 6..8....1.15..28.9839451627........2.28.....33...25.681.45.723628..14.7557623...4
E7: 4,6,7                                # 14 pairs
F7: 8,9,4,6,7                            # reduction candidate for 8,9
F7: 8,9 => CTR
* 6..89...1.15.628.9839451627....8...2.28.4...33...25.681.457.23628..14.7557623...4
F7: 4,6,7                                # 14 pairs
F8: 8,9,4,6                              # reduction candidate for 8,9
F8: 8,9 => CTR
* 6..89...1.15.628.9839451627....8...2.28..6..33...25.681.35..2.62.461.37557623...4
F8: 4,6 => SOLVED
* 627893415415672839839451627952386741768149253341725968194567382283914576576238194
* PAIR F9: 8,9 ROW 9
H9: 8,9,1,5                              # reduction candidate for 8,9
H9: 8,9 => SOLVED
* 627893415415672839839451627952386741768149253341725968194567382283914576576238194
H9: 1,5 => CTR
* 627893..1415762839839451627..2.8......8.....334.925.6819.5...8.28.619.75576238914
* PAIR F9: 8,9 COL F
F4: 8,9,3,4,6,7                          # reduction candidate for 8,9
F4: 8,9 => CTR
* 627893...415672839839451627..2389.....81..2.33.1725.681..5.7.8228.914576576238..4
F4: 3,4,6,7                              # 14 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190317-absurd-base-pr-000.dot
* REASONING
* DIS # B1: 1,4 => CTR => B1: 2
* PRF # B1: 2 => SOL
* PRF # H2: 3 => SOL
* DIS # B4: 1,4 => CTR => B4: 2,5,6,9
* DIS # B5: 1,4 => CTR => B5: 2,5,6,9
* PRF # B6: 1,4 => SOL
* DIS # B6: 9 => CTR => B6: 1,4
* PRF # F1: 3 => SOL
* DIS # E4: 7,9 => CTR => E4: 4,6,8
* DIS # E5: 7,9 => CTR => E5: 4,6
* PRF # D2: 6,7 => SOL
* DIS # E4: 6,7 => CTR => E4: 4,8,9
* DIS # E5: 6,7 => CTR => E5: 4,9
* PRF # I4: 1,5 => SOL
* DIS # I4: 2 => CTR => I4: 1,5
* DIS # C4: 1,7 => CTR => C4: 2
* PRF # C4: 2 => SOL
* DIS # G6: 1,7 => CTR => G6: 4,9
* PRF # C1: 1,7 => SOL
* DIS # C1: 2 => CTR => C1: 1,7
* PRF # B8: 8,9 => SOL
* DIS # B8: 5 => CTR => B8: 8,9
* DIS # E7: 8,9 => CTR => E7: 4,6,7
* DIS # F7: 8,9 => CTR => F7: 4,6,7
* DIS # B8: 5,9 => CTR => B8: 8
* PRF # B8: 8 => SOL
* DIS # G9: 5,9 => CTR => G9: 1
* PRF # H9: 5,9 => SOL
* PRF # E7: 6,9 => SOL
* DIS # F7: 6,9 => CTR => F7: 4,7,8
* DIS # F8: 6,9 => CTR => F8: 4,8
* DIS # D4: 6,9 => CTR => D4: 1,3,7
* DIS # E7: 8,9 => CTR => E7: 4,6,7
* DIS # F7: 8,9 => CTR => F7: 4,6,7
* DIS # F8: 8,9 => CTR => F8: 4,6
* PRF # F8: 4,6 => SOL
* PRF # H9: 8,9 => SOL
* DIS # H9: 1,5 => CTR => H9: 8,9
* DIS # F4: 8,9 => CTR => F4: 3,4,6,7
* CNT  39 HDP CHAINS /  71 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,B2,B7,C6,C7,C8,D8,E1,E2,F9,I1,I7,I8)
* 6..8.......5..28.9839451627...........8.....33...25.681..5.....2...1..7..7623...4
* PAIR A2: 4,7 COL A
A4: 4,7,5,9                              # reduction candidate for 4,7
A4: 4,7                                  # 16 pairs
A5: 4,7,5,9                              # reduction candidate for 4,7
A5: 4,7                                  # 16 pairs
* PAIR B2: 1,4 BLK 1
B1: 1,4,2                                # reduction candidate for 1,4
B1: 1,4 => CTR
* 6.28.....7.53628.98394516274...83.....8.....339..2546818.5.....25..18.7697623...4
B1: 2 => SOLVED
* 627893415415672839839451627952386741768149253341725968194567382283914576576238194
* DURATION: 0:00:03.280911  START: 04:36:57.533860  END: 04:37:00.814771 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190317-absurd-base-pr-001.dot
* REASONING
* DIS # B1: 1,4 => CTR => B1: 2
* PRF B1: 2 => SOL
* STA B1: 2
* CNT   2 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190317, absurd

Solution

position: 627893415415672839839451627952386741768149253341725968194567382283914576576238194 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 # A4: 4,7 => UNS
* INC # A5: 4,7 => UNS
* DIS # B1: 1,4 => CTR => B1: 2
* PRF # B1: 2 => SOL
* INC # H2: 1,4 => UNS
* PRF # H2: 3 => SOL
* DIS # B4: 1,4 => CTR => B4: 2,5,6,9
* INC # B4: 2,5,6,9 => UNS
* DIS # B5: 1,4 => CTR => B5: 2,5,6,9
* INC # B5: 2,5,6,9 => UNS
* PRF # B6: 1,4 => SOL
* DIS # B6: 9 => CTR => B6: 1,4
* INC # F1: 7,9 => UNS
* PRF # F1: 3 => SOL
* DIS # E4: 7,9 => CTR => E4: 4,6,8
* INC # E4: 4,6,8 => UNS
* DIS # E5: 7,9 => CTR => E5: 4,6
* INC # E5: 4,6 => UNS
* INC # E7: 7,9 => UNS
* PRF # D2: 6,7 => SOL
* INC # D2: 3 => UNS
* DIS # E4: 6,7 => CTR => E4: 4,8,9
* INC # E4: 4,8,9 => UNS
* DIS # E5: 6,7 => CTR => E5: 4,9
* INC # E5: 4,9 => UNS
* INC # E7: 6,7 => UNS
* INC # G1: 1,5 => UNS
* INC # H1: 1,5 => UNS
* PRF # I4: 1,5 => SOL
* DIS # I4: 2 => CTR => I4: 1,5
* DIS # C4: 1,7 => CTR => C4: 2
* PRF # C4: 2 => SOL
* INC # D6: 1,7 => UNS
* DIS # G6: 1,7 => CTR => G6: 4,9
* INC # G6: 4,9 => UNS
* PRF # C1: 1,7 => SOL
* DIS # C1: 2 => CTR => C1: 1,7
* PRF # B8: 8,9 => SOL
* DIS # B8: 5 => CTR => B8: 8,9
* DIS # E7: 8,9 => CTR => E7: 4,6,7
* INC # E7: 4,6,7 => UNS
* DIS # F7: 8,9 => CTR => F7: 4,6,7
* INC # F7: 4,6,7 => UNS
* INC # H7: 8,9 => UNS
* DIS # B8: 5,9 => CTR => B8: 8
* PRF # B8: 8 => SOL
* DIS # G9: 5,9 => CTR => G9: 1
* INC # G9: 1 => UNS
* PRF # H9: 5,9 => SOL
* INC # H9: 1,8 => UNS
* INC # A4: 5,9 => UNS
* INC # A5: 5,9 => UNS
* PRF # E7: 6,9 => SOL
* INC # E7: 4,7,8 => UNS
* DIS # F7: 6,9 => CTR => F7: 4,7,8
* INC # F7: 4,7,8 => UNS
* DIS # F8: 6,9 => CTR => F8: 4,8
* INC # F8: 4,8 => UNS
* DIS # D4: 6,9 => CTR => D4: 1,3,7
* INC # D4: 1,3,7 => UNS
* INC # D5: 6,9 => UNS
* DIS # E7: 8,9 => CTR => E7: 4,6,7
* INC # E7: 4,6,7 => UNS
* DIS # F7: 8,9 => CTR => F7: 4,6,7
* INC # F7: 4,6,7 => UNS
* DIS # F8: 8,9 => CTR => F8: 4,6
* PRF # F8: 4,6 => SOL
* PRF # H9: 8,9 => SOL
* DIS # H9: 1,5 => CTR => H9: 8,9
* DIS # F4: 8,9 => CTR => F4: 3,4,6,7
* INC # F4: 3,4,6,7 => UNS
* CNT  71 HDP CHAINS /  71 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A4: 4,7 => UNS
* INC # A5: 4,7 => UNS
* DIS # B1: 1,4 => CTR => B1: 2
* PRF B1: 2 => SOL
* STA B1: 2
* CNT   4 HDP CHAINS /   3 HYP OPENED