Analysis of zz-menneske-no-06908688-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .253..........4...3...1.5....1.8.7.4.5.....9.....7...8.....7..2.4.9.....1.3...8.. initial

Autosolve

position: .253......1...4...3...1.5....1.8.7.4.5.....9.....7...8.....7..2.4.9.....1.3...8.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # E2: 6,9 => CTR => E2: 2,5
* DIS # A1: 6,9 => CTR => A1: 4,7,8
* DIS # G1: 6,9 => CTR => G1: 1,4
* DIS # I1: 6,9 => CTR => I1: 1,7
* DIS # F3: 6,8 => CTR => F3: 2
* DIS # C3: 7,8 => CTR => C3: 4,6,9
* CNT   6 HDP CHAINS /  21 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 # E2: 6,9 => CTR => E2: 2,5
* DIS E2: 2,5 # F3: 6,8 => CTR => F3: 2
* DIS E2: 2,5 + F3: 2 # C3: 7,8 => CTR => C3: 4,6,9
* DIS E2: 2,5 + F3: 2 + C3: 4,6,9 # H8: 3,6 => CTR => H8: 1,7
* DIS E2: 2,5 + F3: 2 + C3: 4,6,9 + H8: 1,7 # G8: 1 => CTR => G8: 3,6
* DIS E2: 2,5 + F3: 2 + C3: 4,6,9 + H8: 1,7 + G8: 3,6 # F4: 5,6 => CTR => F4: 3,9
* DIS E2: 2,5 + F3: 2 + C3: 4,6,9 + H8: 1,7 + G8: 3,6 + F4: 3,9 # F6: 5,6 => CTR => F6: 1,3,9
* DIS E2: 2,5 + F3: 2 + C3: 4,6,9 + H8: 1,7 + G8: 3,6 + F4: 3,9 + F6: 1,3,9 # D2: 6,8 => CTR => D2: 7
* PRF E2: 2,5 + F3: 2 + C3: 4,6,9 + H8: 1,7 + G8: 3,6 + F4: 3,9 + F6: 1,3,9 + D2: 7 # A1: 6,8 => SOL
* STA E2: 2,5 + F3: 2 + C3: 4,6,9 + H8: 1,7 + G8: 3,6 + F4: 3,9 + F6: 1,3,9 + D2: 7 + A1: 6,8
* CNT   9 HDP CHAINS /  41 HYP OPENED

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

Details

Positions

.253..........4...3...1.5....1.8.7.4.5.....9.....7...8.....7..2.4.9.....1.3...8.. initial
.253......1...4...3...1.5....1.8.7.4.5.....9.....7...8.....7..2.4.9.....1.3...8.. autosolve
825396471619754283374812569961583724758421396432679158586147932247938615193265847 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (6)
E1: 6,9
F1: 6,8
A5: 7,8
C5: 7,8
D7: 1,8
F8: 1,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D7,F8: 1.. / D7 = 1  =>  9 pairs (_) / F8 = 1  =>  0 pairs (X)
A8,C8: 2.. / A8 = 2  =>  7 pairs (_) / C8 = 2  =>  6 pairs (_)
C6,C8: 2.. / C6 = 2  =>  7 pairs (_) / C8 = 2  =>  6 pairs (_)
B4,B6: 3.. / B4 = 3  =>  7 pairs (_) / B6 = 3  =>  7 pairs (_)
E7,E8: 3.. / E7 = 3  =>  8 pairs (_) / E8 = 3  =>  7 pairs (_)
A1,C3: 4.. / A1 = 4  =>  0 pairs (X) / C3 = 4  =>  6 pairs (_)
A6,C6: 4.. / A6 = 4  =>  6 pairs (_) / C6 = 4  =>  0 pairs (X)
D5,E5: 4.. / D5 = 4  =>  7 pairs (_) / E5 = 4  =>  7 pairs (_)
C3,H3: 4.. / C3 = 4  =>  6 pairs (_) / H3 = 4  =>  0 pairs (X)
A1,A6: 4.. / A1 = 4  =>  0 pairs (X) / A6 = 4  =>  6 pairs (_)
C3,C6: 4.. / C3 = 4  =>  6 pairs (_) / C6 = 4  =>  0 pairs (X)
D5,D9: 4.. / D5 = 4  =>  7 pairs (_) / D9 = 4  =>  7 pairs (_)
G1,G7: 4.. / G1 = 4  =>  6 pairs (_) / G7 = 4  => 24 pairs (_)
D2,E2: 5.. / D2 = 5  =>  0 pairs (X) / E2 = 5  =>  6 pairs (_)
H4,H6: 5.. / H4 = 5  =>  7 pairs (_) / H6 = 5  =>  6 pairs (_)
A7,A8: 5.. / A7 = 5  =>  6 pairs (_) / A8 = 5  =>  0 pairs (X)
I8,I9: 5.. / I8 = 5  =>  7 pairs (_) / I9 = 5  =>  0 pairs (X)
A7,E7: 5.. / A7 = 5  =>  6 pairs (_) / E7 = 5  =>  0 pairs (X)
D2,D3: 7.. / D2 = 7  =>  6 pairs (_) / D3 = 7  => 18 pairs (_)
A5,C5: 7.. / A5 = 7  =>  6 pairs (_) / C5 = 7  =>  4 pairs (_)
B3,B9: 7.. / B3 = 7  => 14 pairs (_) / B9 = 7  => 15 pairs (_)
A5,C5: 8.. / A5 = 8  =>  4 pairs (_) / C5 = 8  =>  6 pairs (_)
D7,F8: 8.. / D7 = 8  =>  0 pairs (X) / F8 = 8  =>  9 pairs (_)
B3,B7: 8.. / B3 = 8  =>  0 pairs (X) / B7 = 8  => 10 pairs (_)
E1,E2: 9.. / E1 = 9  =>  5 pairs (_) / E2 = 9  =>  0 pairs (X)
F4,F6: 9.. / F4 = 9  =>  8 pairs (_) / F6 = 9  =>  7 pairs (_)
G7,I9: 9.. / G7 = 9  =>  0 pairs (*) / I9 = 9  =>  0 pairs (X)
B9,I9: 9.. / B9 = 9  =>  0 pairs (*) / I9 = 9  =>  0 pairs (X)
* DURATION: 0:00:38.104187  START: 06:43:35.562853  END: 06:44:13.667040 2017-05-01
* CP COUNT: (28)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,C5,D7,E1,F1,F8)
* .253......1...4...3...1.5....1.8.7.4.5.....9.....7...8.....7..2.4.9.....1.3...8..
* PAIR E1: 6,9 BLK 2
E2: 6,9,2,5                              # reduction candidate for 6,9
E2: 6,9 => CTR
* 425368971617594.83389712546..1.8.7.4.5.....9...4.7...8..68.7412.429.1..5173...869
E2: 2,5                                  #  6 pairs
* PAIR E1: 6,9 ROW 1
A1: 6,9,4,7,8                            # reduction candidate for 6,9
A1: 6,9 => CTR
* .253.8....1...4...38471.5.9..1.8.7.4.5.....9.4...7...8...8.7912.4.9.1...1.3...8..
A1: 4,7,8                                #  6 pairs
G1: 6,9,1,4                              # reduction candidate for 6,9
G1: 6,9 => CTR
* 725398641.1.75492338..1.5.7..1.8.7.4.5.....96....7...85..8.7412.4.9.13.5173...869
G1: 1,4                                  #  7 pairs
I1: 6,9,1,7                              # reduction candidate for 6,9
I1: 6,9 => CTR
* .25398..6.1...4983389.1.5....1.8.7.4.5.....91...17...8...8.7..2.4.9.1...173...8.9
I1: 1,7                                  #  7 pairs
* PAIR F1: 6,8 BLK 2
D2: 6,8,2,5,7                            # reduction candidate for 6,8
D2: 6,8                                  # 18 pairs
D3: 6,8,2,7                              # reduction candidate for 6,8
D3: 6,8                                  #  8 pairs
F3: 6,8,2                                # reduction candidate for 6,8
F3: 6,8 => CTR
* .25398....1...4983389.165....1.8.7.4.5.....9.....7...8...8.7..2.4.9.1...173...8.9
F3: 2                                    #  7 pairs
* PAIR F1: 6,8 ROW 1
A1: 6,8,4,7,9                            # reduction candidate for 6,8
A1: 6,8                                  #  9 pairs
H1: 6,8,1,4,7                            # reduction candidate for 6,8
H1: 6,8                                  #  9 pairs
* PAIR A5: 7,8 COL A
A1: 7,8,4,6,9                            # reduction candidate for 7,8
A1: 7,8                                  #  8 pairs
A2: 7,8,6,9                              # reduction candidate for 7,8
A2: 7,8                                  #  8 pairs
A8: 7,8,2,5,6                            # reduction candidate for 7,8
A8: 7,8                                  #  9 pairs
* PAIR C5: 7,8 COL C
C2: 7,8,6,9                              # reduction candidate for 7,8
C2: 7,8                                  #  9 pairs
C3: 7,8,4,6,9                            # reduction candidate for 7,8
C3: 7,8 => CTR
* 4253.6.87.16..4..339..12546..1.8.7.4.5.....91..4.71..8589167432.429.8..5173...869
C3: 4,6,9                                #  6 pairs
C8: 7,8,2,6                              # reduction candidate for 7,8
C8: 7,8                                  # 10 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-menneske-no-06908688-base-pr-000.dot
* REASONING
* DIS # E2: 6,9 => CTR => E2: 2,5
* DIS # A1: 6,9 => CTR => A1: 4,7,8
* DIS # G1: 6,9 => CTR => G1: 1,4
* DIS # I1: 6,9 => CTR => I1: 1,7
* DIS # F3: 6,8 => CTR => F3: 2
* DIS # C3: 7,8 => CTR => C3: 4,6,9
* CNT   6 HDP CHAINS /  21 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,C5,D7,E1,F1,F8)
* .253......1...4...3...1.5....1.8.7.4.5.....9.....7...8.....7..2.4.9.....1.3...8..
* PAIR E1: 6,9 BLK 2
E2: 6,9,2,5                              # reduction candidate for 6,9
E2: 6,9 => CTR
* 425368971617594.83389712546..1.8.7.4.5.....9...4.7...8..68.7412.429.1..5173...869
* PAIR F1: 6,8 BLK 2
D2: 6,8,2,5,7                            # reduction candidate for 6,8
D2: 6,8                                  # 18 pairs
D3: 6,8,2,7                              # reduction candidate for 6,8
D3: 6,8                                  #  8 pairs
F3: 6,8,2                                # reduction candidate for 6,8
F3: 6,8 => CTR
* .25398....1...4983389.165....1.8.7.4.5.....9.....7...8...8.7..2.4.9.1...173...8.9
* PAIR F1: 6,8 ROW 1
A1: 6,8,4,7                              # reduction candidate for 6,8
A1: 6,8                                  # 12 pairs
H1: 6,8,1,4,7                            # reduction candidate for 6,8
H1: 6,8                                  # 11 pairs
* PAIR RESTART
* PAIR F1: 6,8 BLK 2
D2: 6,8,7                                # reduction candidate for 6,8
D2: 6,8                                  # 18 pairs
D3: 6,8,7                                # reduction candidate for 6,8
D3: 6,8                                  #  8 pairs
* PAIR F1: 6,8 ROW 1
A1: 6,8,4,7                              # reduction candidate for 6,8
A1: 6,8                                  # 12 pairs
H1: 6,8,1,4,7                            # reduction candidate for 6,8
H1: 6,8                                  # 11 pairs
* PAIR A5: 7,8 COL A
A1: 7,8,4,6                              # reduction candidate for 7,8
A1: 7,8                                  # 10 pairs
A2: 7,8,6,9                              # reduction candidate for 7,8
A2: 7,8                                  # 17 pairs
A8: 7,8,2,6                              # reduction candidate for 7,8
A8: 7,8                                  # 11 pairs
* PAIR C5: 7,8 COL C
C2: 7,8,6,9                              # reduction candidate for 7,8
C2: 7,8                                  # 10 pairs
C3: 7,8,4,6,9                            # reduction candidate for 7,8
C3: 7,8 => CTR
* 42539618..1..5492339..1254...1.8.7.4.5.....9...4.7...85891.74.2.429.8..5173...869
C8: 7,8,2,6                              # reduction candidate for 7,8
C8: 7,8                                  # 11 pairs
* PAIR RESTART
* PAIR C5: 7,8 COL C
C2: 7,8,6,9                              # reduction candidate for 7,8
C2: 7,8                                  # 10 pairs
C8: 7,8,2,6                              # reduction candidate for 7,8
C8: 7,8                                  # 11 pairs

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A5,C5,D7,E8,F1,F8,F9)
* .2539.....1..54...3...125....1.8.7.4.5.....9.....7...85....7..2.4.9....51.3...8..
* PAIR F1: 6,8 BLK 2
D2: 6,8,7                                # reduction candidate for 6,8
D2: 6,8                                  # 19 pairs
D3: 6,8,7                                # reduction candidate for 6,8
D3: 6,8                                  #  8 pairs
* PAIR F1: 6,8 ROW 1
A1: 6,8,4,7                              # reduction candidate for 6,8
A1: 6,8                                  # 12 pairs
H1: 6,8,1,4,7                            # reduction candidate for 6,8
H1: 6,8                                  # 11 pairs
* PAIR A5: 7,8 COL A
A1: 7,8,4,6                              # reduction candidate for 7,8
A1: 7,8                                  # 10 pairs
A2: 7,8,6,9                              # reduction candidate for 7,8
A2: 7,8                                  # 17 pairs
A8: 7,8,2,6                              # reduction candidate for 7,8
A8: 7,8                                  # 14 pairs
* PAIR C5: 7,8 COL C
C2: 7,8,6,9                              # reduction candidate for 7,8
C2: 7,8                                  # 10 pairs
C8: 7,8,2,6                              # reduction candidate for 7,8
C8: 7,8                                  # 11 pairs
* PAIR E8: 3,6 BLK 8
E7: 3,6,4                                # reduction candidate for 3,6
E7: 4                                    # 11 pairs
E7: 3,6                                  # 11 pairs
* PAIR E8: 3,6 ROW 8
G8: 3,6,1                                # reduction candidate for 3,6
G8: 3,6                                  #  9 pairs
H8: 3,6,1,7                              # reduction candidate for 3,6
H8: 3,6 => CTR
* 8253964.7.1.754.83374812569..1.8.7.4758....914...71..85861379422479.8135193..58.6
* RESTART
* PAIR E8: 3,6 ROW 8
G8: 3,6,1                                # reduction candidate for 3,6
G8: 1 => CTR
* .253964...1..54923394.125..9.1283754.5.....9.4...7...85..1.7..2.4.938175173..58.9
* PAIR RESTART
* PAIR E8: 3,6 BLK 8
E7: 3,6,4                                # reduction candidate for 3,6
E7: 3,6                                  # 13 pairs
E7: 4                                    # 12 pairs
* PAIR F9: 5,6 BLK 8
D9: 5,6,2,4                              # reduction candidate for 5,6
D9: 5,6                                  # 19 pairs
D9: 2,4                                  # 10 pairs
* PAIR F9: 5,6 COL F
F4: 5,6,3,9                              # reduction candidate for 5,6
F4: 5,6 => CTR
* .25398....1..549233...1258.9.128.7.4.5...329.....79..858...7..2.4.9.1.75173...8.9
F6: 5,6,1,3,9                            # reduction candidate for 5,6
F6: 5,6 => CTR
* .25398....1..549233...1258...1.897.4.5...3.9.9.4.7...858...7..2.4.9.1.75173...8.9
* PAIR RESTART

* LEVEL 0 PASS 1 ROUND 3 (AUTO SOLVE) (A5,C5,D7,E8,F1,F4,F8,G8,H8)
* .2539.....1..54...3...125....1.8.7.4.5.....9.....7...85....7..2.4.9....51.3..58..
* PAIR F1: 6,8 BLK 2
D2: 6,8,7                                # reduction candidate for 6,8
D2: 6,8 => CTR
* .25398..7.1.6549233..712586..1.8.7.4.5...6391...17.25858...7..2.4.9.1.75173..58.9
* RESTART
* PAIR F1: 6,8 ROW 1
A1: 6,8,4,7                              # reduction candidate for 6,8
A1: 6,8 => SOLVED
* 825396471619754283374812569961583724758421396432679158586147932247938615193265847
* DURATION: 0:00:38.352173  START: 06:44:29.236921  END: 06:45:07.589094 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-menneske-no-06908688-base-pr-001.dot
* REASONING
* DIS # E2: 6,9 => CTR => E2: 2,5
* DIS E2: 2,5 # F3: 6,8 => CTR => F3: 2
* DIS E2: 2,5 + F3: 2 # C3: 7,8 => CTR => C3: 4,6,9
* DIS E2: 2,5 + F3: 2 + C3: 4,6,9 # H8: 3,6 => CTR => H8: 1,7
* DIS E2: 2,5 + F3: 2 + C3: 4,6,9 + H8: 1,7 # G8: 1 => CTR => G8: 3,6
* DIS E2: 2,5 + F3: 2 + C3: 4,6,9 + H8: 1,7 + G8: 3,6 # F4: 5,6 => CTR => F4: 3,9
* DIS E2: 2,5 + F3: 2 + C3: 4,6,9 + H8: 1,7 + G8: 3,6 + F4: 3,9 # F6: 5,6 => CTR => F6: 1,3,9
* DIS E2: 2,5 + F3: 2 + C3: 4,6,9 + H8: 1,7 + G8: 3,6 + F4: 3,9 + F6: 1,3,9 # D2: 6,8 => CTR => D2: 7
* PRF E2: 2,5 + F3: 2 + C3: 4,6,9 + H8: 1,7 + G8: 3,6 + F4: 3,9 + F6: 1,3,9 + D2: 7 # A1: 6,8 => SOL
* STA E2: 2,5 + F3: 2 + C3: 4,6,9 + H8: 1,7 + G8: 3,6 + F4: 3,9 + F6: 1,3,9 + D2: 7 + A1: 6,8
* CNT   9 HDP CHAINS /  41 HYP OPENED

Header Info

http://www.menneske.no/sudoku/utskrift.html?number=6908688
umulig

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

* PAIR REDUCTION ..
* ROUND 1: .253......1...4...3...1.5....1.8.7.4.5.....9.....7...8.....7..2.4.9.....1.3...8..
E1: 6,9
E2: 2,5,6,9                              # reduction candidate for 6,9
E2: 6,9 => CTR
* 425368971617594.83389712546..1.8.7.4.5.....9...4.7...8..68.7412.429.1..5173...869
F1: 6,8
D2: 2,5,6,7,8                            # reduction candidate for 6,8
D3: 2,6,7,8                              # reduction candidate for 6,8
F3: 2,6,8                                # reduction candidate for 6,8
F3: 6,8 => CTR
* .25398....1...4983389.165....1.8.7.4.5.....9.....7...8...8.7..2.4.9.1...173...8.9
A1: 4,6,7,8                              # reduction candidate for 6,8
H1: 1,4,6,7,8                            # reduction candidate for 6,8
A5: 7,8
A1: 4,6,7,8                              # reduction candidate for 7,8
A2: 6,7,8,9                              # reduction candidate for 7,8
A8: 2,6,7,8                              # reduction candidate for 7,8
C5: 7,8
C2: 6,7,8,9                              # reduction candidate for 7,8
C3: 4,6,7,8,9                            # reduction candidate for 7,8
C3: 7,8 => CTR
* 42539618..1..5492339..1254...1.8.7.4.5.....9...4.7...85891.74.2.429.8..5173...869
C8: 2,6,7,8                              # reduction candidate for 7,8
D7: 1,8
F8: 1,8
* ROUND 2: .2539.....1..54...3...125....1.8.7.4.5.....9.....7...85....7..2.4.9....51.3...8..
F1: 6,8
D2: 6,7,8                                # reduction candidate for 6,8
D3: 6,7,8                                # reduction candidate for 6,8
A1: 4,6,7,8                              # reduction candidate for 6,8
H1: 1,4,6,7,8                            # reduction candidate for 6,8
A5: 7,8
A1: 4,6,7,8                              # reduction candidate for 7,8
A2: 6,7,8,9                              # reduction candidate for 7,8
A8: 2,6,7,8                              # reduction candidate for 7,8
C5: 7,8
C2: 6,7,8,9                              # reduction candidate for 7,8
C8: 2,6,7,8                              # reduction candidate for 7,8
D7: 1,8
E8: 3,6
E7: 3,4,6                                # reduction candidate for 3,6
G8: 1,3,6                                # reduction candidate for 3,6
H8: 1,3,6,7                              # reduction candidate for 3,6
H8: 3,6 => CTR
* 8253964.7.1.754.83374812569..1.8.7.4758....914...71..85861379422479.8135193..58.6
F8: 1,8
F9: 5,6
D9: 2,4,5,6                              # reduction candidate for 5,6
F4: 3,5,6,9                              # reduction candidate for 5,6
F4: 5,6 => CTR
* .25398....1..549233...1258.9.128.7.4.5...329.....79..858...7..2.4.9.1.75173...8.9
F6: 1,3,5,6,9                            # reduction candidate for 5,6
F6: 5,6 => CTR
* .25398....1..549233...1258...1.897.4.5...3.9.9.4.7...858...7..2.4.9.1.75173...8.9
* ROUND 3: .2539.....1..54...3...125....1.8.7.4.5.....9.....7...85....7..2.4.9....51.3..58..
F1: 6,8
D2: 6,7,8                                # reduction candidate for 6,8
D3: 6,7,8                                # reduction candidate for 6,8
A1: 4,6,7,8                              # reduction candidate for 6,8
H1: 1,4,6,7,8                            # reduction candidate for 6,8
A5: 7,8
A1: 4,6,7,8                              # reduction candidate for 7,8
A2: 6,7,8,9                              # reduction candidate for 7,8
A8: 2,6,7,8                              # reduction candidate for 7,8
C5: 7,8
C2: 6,7,8,9                              # reduction candidate for 7,8
C8: 2,6,7,8                              # reduction candidate for 7,8
F4: 3,9
F6: 1,3,9                                # reduction candidate for 3,9
B4: 3,6,9                                # reduction candidate for 3,9
D7: 1,8
E8: 3,6
E7: 3,4,6                                # reduction candidate for 3,6
G8: 1,3,6                                # reduction candidate for 3,6
G8: 1 => CTR
* .253964...1..54923394.125..9.1283754.5.....9.4...7...85..1.7..2.4.938175173..58.9
F8: 1,8
H8: 1,7
H1: 1,4,6,7,8                            # reduction candidate for 1,7
* ROUND 4: .2539.....1..54...3...125....1.8.7.4.5.....9.....7...85....7..2.4.9....51.3..58..
F1: 6,8
D2: 6,7,8                                # reduction candidate for 6,8
D2: 6,8 => CTR
* .25398..7.1.6549233..712586..1.8.7.4.5...6391...17.25858...7..2.4.9.1.75173..58.9
A1: 4,6,7,8                              # reduction candidate for 6,8
A1: 6,8 => SOLVED
* 825396471619754283374812569961583724758421396432679158586147932247938615193265847
* SOLVED!

Solution

position: 825396471619754283374812569961583724758421396432679158586147932247938615193265847 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 # E2: 6,9 => CTR => E2: 2,5
* INC # E2: 2,5 => UNS
* DIS # A1: 6,9 => CTR => A1: 4,7,8
* INC # A1: 4,7,8 => UNS
* DIS # G1: 6,9 => CTR => G1: 1,4
* INC # G1: 1,4 => UNS
* DIS # I1: 6,9 => CTR => I1: 1,7
* INC # I1: 1,7 => UNS
* INC # D2: 6,8 => UNS
* INC # D3: 6,8 => UNS
* DIS # F3: 6,8 => CTR => F3: 2
* INC # F3: 2 => UNS
* INC # A1: 6,8 => UNS
* INC # H1: 6,8 => UNS
* INC # A1: 7,8 => UNS
* INC # A2: 7,8 => UNS
* INC # A8: 7,8 => UNS
* INC # C2: 7,8 => UNS
* DIS # C3: 7,8 => CTR => C3: 4,6,9
* INC # C3: 4,6,9 => UNS
* INC # C8: 7,8 => UNS
* CNT  21 HDP CHAINS /  21 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # E2: 6,9 => CTR => E2: 2,5
* INC E2: 2,5 # D2: 6,8 => UNS
* INC E2: 2,5 # D3: 6,8 => UNS
* DIS E2: 2,5 # F3: 6,8 => CTR => F3: 2
* INC E2: 2,5 + F3: 2 # A1: 6,8 => UNS
* INC E2: 2,5 + F3: 2 # H1: 6,8 => UNS
* INC E2: 2,5 + F3: 2 # D2: 6,8 => UNS
* INC E2: 2,5 + F3: 2 # D3: 6,8 => UNS
* INC E2: 2,5 + F3: 2 # A1: 6,8 => UNS
* INC E2: 2,5 + F3: 2 # H1: 6,8 => UNS
* INC E2: 2,5 + F3: 2 # A1: 7,8 => UNS
* INC E2: 2,5 + F3: 2 # A2: 7,8 => UNS
* INC E2: 2,5 + F3: 2 # A8: 7,8 => UNS
* INC E2: 2,5 + F3: 2 # C2: 7,8 => UNS
* DIS E2: 2,5 + F3: 2 # C3: 7,8 => CTR => C3: 4,6,9
* INC E2: 2,5 + F3: 2 + C3: 4,6,9 # C8: 7,8 => UNS
* INC E2: 2,5 + F3: 2 + C3: 4,6,9 # C2: 7,8 => UNS
* INC E2: 2,5 + F3: 2 + C3: 4,6,9 # C8: 7,8 => UNS
* INC E2: 2,5 + F3: 2 + C3: 4,6,9 # D2: 6,8 => UNS
* INC E2: 2,5 + F3: 2 + C3: 4,6,9 # D3: 6,8 => UNS
* INC E2: 2,5 + F3: 2 + C3: 4,6,9 # A1: 6,8 => UNS
* INC E2: 2,5 + F3: 2 + C3: 4,6,9 # H1: 6,8 => UNS
* INC E2: 2,5 + F3: 2 + C3: 4,6,9 # A1: 7,8 => UNS
* INC E2: 2,5 + F3: 2 + C3: 4,6,9 # A2: 7,8 => UNS
* INC E2: 2,5 + F3: 2 + C3: 4,6,9 # A8: 7,8 => UNS
* INC E2: 2,5 + F3: 2 + C3: 4,6,9 # C2: 7,8 => UNS
* INC E2: 2,5 + F3: 2 + C3: 4,6,9 # C8: 7,8 => UNS
* INC E2: 2,5 + F3: 2 + C3: 4,6,9 # E7: 3,6 => UNS
* INC E2: 2,5 + F3: 2 + C3: 4,6,9 # E7: 4 => UNS
* INC E2: 2,5 + F3: 2 + C3: 4,6,9 # G8: 3,6 => UNS
* DIS E2: 2,5 + F3: 2 + C3: 4,6,9 # H8: 3,6 => CTR => H8: 1,7
* INC E2: 2,5 + F3: 2 + C3: 4,6,9 + H8: 1,7 # G8: 3,6 => UNS
* DIS E2: 2,5 + F3: 2 + C3: 4,6,9 + H8: 1,7 # G8: 1 => CTR => G8: 3,6
* INC E2: 2,5 + F3: 2 + C3: 4,6,9 + H8: 1,7 + G8: 3,6 # E7: 3,6 => UNS
* INC E2: 2,5 + F3: 2 + C3: 4,6,9 + H8: 1,7 + G8: 3,6 # E7: 4 => UNS
* INC E2: 2,5 + F3: 2 + C3: 4,6,9 + H8: 1,7 + G8: 3,6 # D9: 5,6 => UNS
* INC E2: 2,5 + F3: 2 + C3: 4,6,9 + H8: 1,7 + G8: 3,6 # D9: 2,4 => UNS
* DIS E2: 2,5 + F3: 2 + C3: 4,6,9 + H8: 1,7 + G8: 3,6 # F4: 5,6 => CTR => F4: 3,9
* DIS E2: 2,5 + F3: 2 + C3: 4,6,9 + H8: 1,7 + G8: 3,6 + F4: 3,9 # F6: 5,6 => CTR => F6: 1,3,9
* DIS E2: 2,5 + F3: 2 + C3: 4,6,9 + H8: 1,7 + G8: 3,6 + F4: 3,9 + F6: 1,3,9 # D2: 6,8 => CTR => D2: 7
* PRF E2: 2,5 + F3: 2 + C3: 4,6,9 + H8: 1,7 + G8: 3,6 + F4: 3,9 + F6: 1,3,9 + D2: 7 # A1: 6,8 => SOL
* STA E2: 2,5 + F3: 2 + C3: 4,6,9 + H8: 1,7 + G8: 3,6 + F4: 3,9 + F6: 1,3,9 + D2: 7 + A1: 6,8
* CNT  41 HDP CHAINS /  41 HYP OPENED