Analysis of zz-www.sudokuoftheday.co.uk-20190107-absurd-base.sdk

Contents

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

level: medium

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

position: ...3.129..728.....31..42....9..8.5.3..6.5.1.........4......7...64.....8..3..1.9.. initial

Autosolve

position: .6437129..728.....31..42....9..845.34.6.531....3....4......7...64.....8..3..189.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # C3: 5,8 => SOL
* DIS # C3: 9 => CTR => C3: 5,8
* DIS # A6: 5,8 => CTR => A6: 1,2,7
* PRF # A6: 1,2,7 => SOL
* PRF # A7: 5,8 => SOL
* DIS # C3: 5,9 => CTR => C3: 8
* PRF # C3: 8 => SOL
* DIS # F2: 6 => CTR => F2: 5,9
* DIS # A7: 5,9 => CTR => A7: 1,2,8
* PRF # A7: 1,2,8 => SOL
* DIS # F2: 6,9 => CTR => F2: 5
* PRF # F2: 5 => SOL
* PRF # E6: 6,9 => SOL
* DIS # F2: 6 => CTR => F2: 5,9
* DIS # C3: 5,9 => CTR => C3: 8
* PRF # C3: 8 => SOL
* DIS # D7: 5,9 => CTR => D7: 2,4,6
* PRF # D8: 5,9 => SOL
* DIS # I3: 5,8 => CTR => I3: 6,7
* PRF # G7: 6 => SOL
* DIS # I7: 1,4 => CTR => I7: 2,5,6
* DIS # A4: 1,7 => CTR => A4: 2
* PRF # A4: 2 => SOL
* PRF # A6: 1,7 => SOL
* DIS # A6: 2,5,8 => CTR => A6: 1,7
* PRF # D4: 1,7 => SOL
* PRF # C8: 1,7 => SOL
* DIS # A6: 2,8 => CTR => A6: 1,5,7
* DIS # B6: 2,8 => CTR => B6: 5
* DIS # I5: 2,8 => CTR => I5: 7,9
* DIS # B7: 5 => CTR => B7: 2,8
* DIS # D6: 6,9 => CTR => D6: 1,2,7
* PRF # E6: 6,9 => SOL
* DIS # F2: 6,9 => CTR => F2: 5
* PRF # F2: 5 => SOL
* DIS # H4: 2,7 => CTR => H4: 6
* DIS # I5: 2,7 => CTR => I5: 8,9
* DIS # D5: 9 => CTR => D5: 2,7
* PRF # H9: 2,7 => SOL
* DIS # C8: 5,7 => CTR => C8: 1,9
* PRF # A9: 5,7 => SOL
* DIS # A9: 2 => CTR => A9: 5,7
* DIS # H9: 5,7 => CTR => H9: 2,6
* PRF # H9: 2,6 => SOL
* DIS # I9: 5,7 => CTR => I9: 2,4,6
* DIS # D7: 5,9 => CTR => D7: 2,4,6
* PRF # D8: 5,9 => SOL
* PRF # C8: 1,7 => SOL
* DIS # F2: 6 => CTR => F2: 5,9
* CNT  49 HDP CHAINS /  80 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # C3: 5,8 => SOL
* STA C3: 5,8
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

...3.129..728.....31..42....9..8.5.3..6.5.1.........4......7...64.....8..3..1.9.. initial
.6437129..728.....31..42....9..845.34.6.531....3....4......7...64.....8..3..189.. autosolve
564371298972865431318942756297184563486253179153796842829437615641529387735618924 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
A1: 5,8
A2: 5,9
E2: 6,9
D3: 5,9
I1: 5,8
G2: 3,4
H2: 1,3
I2: 1,4
C4: 1,7
B5: 2,8
F6: 6,9
H5: 2,7
C9: 5,7
F8: 5,9
H7: 1,3
G8: 3,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H2,I2: 1.. / H2 = 1  => 13 pairs (_) / I2 = 1  =>  0 pairs (*)
D4,D6: 1.. / D4 = 1  =>  0 pairs (*) / D6 = 1  =>  0 pairs (X)
A6,D6: 1.. / A6 = 1  =>  0 pairs (*) / D6 = 1  =>  0 pairs (X)
C8,I8: 1.. / C8 = 1  =>  0 pairs (*) / I8 = 1  =>  0 pairs (X)
H2,H7: 1.. / H2 = 1  => 13 pairs (_) / H7 = 1  =>  0 pairs (*)
G2,H2: 3.. / G2 = 3  => 13 pairs (_) / H2 = 3  =>  0 pairs (*)
E7,E8: 3.. / E7 = 3  =>  0 pairs (*) / E8 = 3  =>  0 pairs (X)
E8,G8: 3.. / E8 = 3  => 18 pairs (_) / G8 = 3  =>  0 pairs (*)
H2,H7: 3.. / H2 = 3  =>  0 pairs (*) / H7 = 3  =>  0 pairs (X)
G2,I2: 4.. / G2 = 4  =>  0 pairs (*) / I2 = 4  =>  0 pairs (X)
D7,D9: 4.. / D7 = 4  =>  0 pairs (*) / D9 = 4  =>  0 pairs (X)
D9,I9: 4.. / D9 = 4  => 18 pairs (_) / I9 = 4  =>  0 pairs (*)
G2,G7: 4.. / G2 = 4  =>  0 pairs (*) / G7 = 4  =>  0 pairs (X)
F2,D3: 5.. / F2 = 5  =>  0 pairs (*) / D3 = 5  =>  0 pairs (X)
A6,B6: 5.. / A6 = 5  =>  0 pairs (X) / B6 = 5  => 17 pairs (_)
A1,I1: 5.. / A1 = 5  =>  0 pairs (*) / I1 = 5  =>  0 pairs (X)
A2,F2: 5.. / A2 = 5  =>  0 pairs (X) / F2 = 5  =>  0 pairs (_)
B6,B7: 5.. / B6 = 5  => 17 pairs (_) / B7 = 5  =>  0 pairs (X)
F2,F8: 5.. / F2 = 5  =>  0 pairs (*) / F8 = 5  =>  0 pairs (X)
H3,H9: 5.. / H3 = 5  =>  0 pairs (*) / H9 = 5  =>  0 pairs (X)
E2,F2: 6.. / E2 = 6  => 21 pairs (_) / F2 = 6  =>  0 pairs (X)
D4,H4: 6.. / D4 = 6  =>  0 pairs (X) / H4 = 6  => 20 pairs (_)
F2,F6: 6.. / F2 = 6  =>  0 pairs (X) / F6 = 6  => 21 pairs (_)
A1,C3: 8.. / A1 = 8  =>  0 pairs (X) / C3 = 8  =>  0 pairs (_)
A1,I1: 8.. / A1 = 8  =>  0 pairs (X) / I1 = 8  =>  0 pairs (_)
B5,I5: 8.. / B5 = 8  => 18 pairs (_) / I5 = 8  =>  0 pairs (X)
C3,C7: 8.. / C3 = 8  =>  0 pairs (*) / C7 = 8  =>  0 pairs (X)
G3,G6: 8.. / G3 = 8  =>  0 pairs (X) / G6 = 8  => 19 pairs (_)
A2,C3: 9.. / A2 = 9  =>  0 pairs (*) / C3 = 9  =>  0 pairs (X)
I5,I6: 9.. / I5 = 9  => 19 pairs (_) / I6 = 9  =>  0 pairs (X)
C3,D3: 9.. / C3 = 9  =>  0 pairs (X) / D3 = 9  =>  0 pairs (_)
D5,I5: 9.. / D5 = 9  =>  0 pairs (X) / I5 = 9  => 19 pairs (_)
A2,A7: 9.. / A2 = 9  =>  0 pairs (*) / A7 = 9  =>  0 pairs (X)
* DURATION: 0:00:36.823015  START: 02:46:12.737235  END: 02:46:49.560250 2019-05-01
* CP COUNT: (33)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,B5,C4,C9,D3,E2,F6,F8,G2,G8,H2,H5,H7,I1,I2)
* .6437129..728.....31..42....9..845.34.6.531....3....4......7...64.....8..3..189..
* PAIR A1: 5,8 BLK 1
C3: 5,8,9                                # reduction candidate for 5,8
C3: 5,8 => SOLVED
* 564371298972865431318942756297184563486253179153796842829437615641529387735618924
C3: 9 => CTR
* 8643712955728.....319542....9..845.34.6.531...53....4.9....7...64.....8..3..189..
* PAIR A1: 5,8 COL A
A6: 5,8,1,2,7                            # reduction candidate for 5,8
A6: 5,8 => CTR
* 864371295972865...315942.7.791284563486753129523196.4.15...7...64.....8..37.1895.
A6: 1,2,7 => SOLVED
* 564371298972865431318942756297184563486253179153796842829437615641529387735618924
A7: 5,8,1,2,9                            # reduction candidate for 5,8
A7: 5,8 => SOLVED
* 564371298972865431318942756297184563486253179153796842829437615641529387735618924
A7: 1,2,9                                # 16 pairs
* PAIR A2: 5,9 BLK 1
C3: 5,9,8                                # reduction candidate for 5,9
C3: 5,9 => CTR
* 864371295.728.....31..42....91.845.34.6.531....31...4.1.8..7.3.649.35781237.1895.
C3: 8 => SOLVED
* 564371298972865431318942756297184563486253179153796842829437615641529387735618924
* PAIR A2: 5,9 ROW 2
F2: 5,9,6                                # reduction candidate for 5,9
F2: 6 => CTR
* .6437129.572896...319542....9..845.34.6.531...53..9.4.9.8..7..56419.5.8..35.189..
F2: 5,9                                  # 21 pairs
* PAIR A2: 5,9 COL A
A7: 5,9,1,2,8                            # reduction candidate for 5,9
A7: 5,9 => CTR
* .6437129..728.....31..42.5..97.845.34.6.5317..537...4.928..7...641....8.735.189..
A7: 1,2,8 => SOLVED
* 564371298972865431318942756297184563486253179153796842829437615641529387735618924
* PAIR E2: 6,9 BLK 2
F2: 6,9,5                                # reduction candidate for 6,9
F2: 6,9 => CTR
* .6437129.5728.....319542....9..845.34.6.531...53....4.9.8..7..5641..5.8..35.189..
F2: 5 => SOLVED
* 564371298972865431318942756297184563486253179153796842829437615641529387735618924
* PAIR E2: 6,9 COL E
E6: 6,9,2                                # reduction candidate for 6,9
E6: 6,9 => SOLVED
* 564371298972865431318942756297184563486253179153796842829437615641529387735618924
E6: 2                                    # 19 pairs
E7: 6,9,2,3                              # reduction candidate for 6,9
E7: 6,9                                  # 21 pairs
* PAIR D3: 5,9 BLK 2
F2: 5,9,6                                # reduction candidate for 5,9
F2: 6 => CTR
* .6437129.572896...319542....9..845.34.6.531...53..9.4.9.8..7..56419.5.8..35.189..
F2: 5,9                                  # 21 pairs
* PAIR D3: 5,9 ROW 3
C3: 5,9,8                                # reduction candidate for 5,9
C3: 5,9 => CTR
* 864371295.728.....31..42....91.845.34.6.531....31...4.1.8..7.3.649.35781237.1895.
C3: 8 => SOLVED
* 564371298972865431318942756297184563486253179153796842829437615641529387735618924
* PAIR D3: 5,9 COL D
D7: 5,9,2,4,6                            # reduction candidate for 5,9
D7: 5,9 => CTR
* .6437129..72896...319542....9..845.34.6.531....3.29.4.9...67...64..3.78..3.4189..
D7: 2,4,6                                # 16 pairs
D8: 5,9,2                                # reduction candidate for 5,9
D8: 5,9 => SOLVED
* 564371298972865431318942756297184563486253179153796842829437615641529387735618924
D8: 2                                    # 19 pairs
* PAIR I1: 5,8 BLK 3
I3: 5,8,6,7                              # reduction candidate for 5,8
I3: 5,8 => CTR
* .6437129..728.....31..42....91.845.3486.531....31..84.1.8..7.3.649.35781237.1895.
I3: 6,7                                  # 17 pairs
* PAIR G2: 3,4 COL G
G7: 3,4,6                                # reduction candidate for 3,4
G7: 6 => SOLVED
* 564371298972865431318942756297184563486253179153796842829437615641529387735618924
G7: 3,4                                  # 18 pairs
* PAIR I2: 1,4 COL I
I7: 1,4,2,5,6                            # reduction candidate for 1,4
I7: 1,4 => CTR
* .6437129..728.....31..42.5..97.845.34.6.5317..537...4....567...641.39.8.7354189..
I7: 2,5,6                                # 16 pairs
* PAIR C4: 1,7 BLK 4
A4: 1,7,2                                # reduction candidate for 1,7
A4: 1,7 => CTR
* .6437129..728.....31..42....9.284563486753129..31...4......7...64.....8..3..189..
A4: 2 => SOLVED
* 564371298972865431318942756297184563486253179153796842829437615641529387735618924
A6: 1,7,2,5,8                            # reduction candidate for 1,7
A6: 1,7 => SOLVED
* 564371298972865431318942756297184563486253179153796842829437615641529387735618924
A6: 2,5,8 => CTR
* .6437129..728.....31..42....9.284563486753129..31...4......7...64.....8..3..189..
* PAIR C4: 1,7 ROW 4
D4: 1,7,2,6                              # reduction candidate for 1,7
D4: 1,7 => SOLVED
* 564371298972865431318942756297184563486253179153796842829437615641529387735618924
D4: 2,6                                  # 20 pairs
* PAIR C4: 1,7 COL C
C8: 1,7,5,9                              # reduction candidate for 1,7
C8: 1,7 => SOLVED
* 564371298972865431318942756297184563486253179153796842829437615641529387735618924
C8: 5,9                                  # 18 pairs
* PAIR B5: 2,8 BLK 4
A6: 2,8,1,5,7                            # reduction candidate for 2,8
A6: 2,8 => CTR
* .6437129..728.....31..42....9..845634867531292531...4..2...7...64..2.38..3..189.2
A6: 1,5,7                                # 18 pairs
B6: 2,8,5                                # reduction candidate for 2,8
B6: 2,8 => CTR
* 864371295972865...315942...791.845.34.6753129523196.4.15...7...64.....8..37.189..
B6: 5                                    # 17 pairs
* PAIR B5: 2,8 ROW 5
I5: 2,8,7,9                              # reduction candidate for 2,8
I5: 2,8 => CTR
* .6437129..72869...319542.68.9..845234.695317...3..6849.....7...64.....8..3..189..
I5: 7,9                                  # 19 pairs
* PAIR B5: 2,8 COL B
B7: 2,8,5                                # reduction candidate for 2,8
B7: 5 => CTR
* .6437129..728.....315942....91.845.34.6.531.95.31...4.158.97.3.649.35781237.1895.
B7: 2,8                                  # 17 pairs
* PAIR F6: 6,9 BLK 5
D6: 6,9,1,2,7                            # reduction candidate for 6,9
D6: 6,9 => CTR
* .6437129..728.....31..42...297184563486753129153.2..4..2...7...64.....8.735.189..
D6: 1,2,7                                # 16 pairs
E6: 6,9,2                                # reduction candidate for 6,9
E6: 6,9 => SOLVED
* 564371298972865431318942756297184563486253179153796842829437615641529387735618924
E6: 2                                    # 19 pairs
* PAIR F6: 6,9 ROW 6
I6: 6,9,2,7,8                            # reduction candidate for 6,9
I6: 6,9                                  # 22 pairs
I6: 2,7,8                                # 19 pairs
* PAIR F6: 6,9 COL F
F2: 6,9,5                                # reduction candidate for 6,9
F2: 6,9 => CTR
* .6437129.5728.....319542....9..845.34.6.531...53....4.9.8..7..5641..5.8..35.189..
F2: 5 => SOLVED
* 564371298972865431318942756297184563486253179153796842829437615641529387735618924
* PAIR H5: 2,7 BLK 6
H4: 2,7,6                                # reduction candidate for 2,7
H4: 2,7 => CTR
* .6437129.572896...319542....9.6845.34.6753129.53129.4.92846731564193578273..189..
H4: 6                                    # 20 pairs
I5: 2,7,8,9                              # reduction candidate for 2,7
I5: 2,7 => CTR
* .6437129..72869...319542....9..845634869531....3.26849928.37.15641295387.35.1892.
I5: 8,9                                  # 17 pairs
I6: 2,7,6,8,9                            # reduction candidate for 2,7
I6: 2,7                                  # 25 pairs
* PAIR H5: 2,7 ROW 5
D5: 2,7,9                                # reduction candidate for 2,7
D5: 9 => CTR
* .6437129..72869...319542....9..845634.69531....3.26.499.8.37.1.641295387.35.1892.
D5: 2,7                                  # 19 pairs
* PAIR H5: 2,7 COL H
H9: 2,7,5,6                              # reduction candidate for 2,7
H9: 2,7 => SOLVED
* 564371298972865431318942756297184563486253179153796842829437615641529387735618924
H9: 5,6                                  # 17 pairs
* PAIR C9: 5,7 BLK 7
C8: 5,7,1,9                              # reduction candidate for 5,7
C8: 5,7 => CTR
* .6437129..728.531431.942....91.845.34.67531....3....4......743.645239781.374189..
C8: 1,9                                  # 17 pairs
A9: 5,7,2                                # reduction candidate for 5,7
A9: 5,7 => SOLVED
* 564371298972865431318942756297184563486253179153796842829437615641529387735618924
A9: 2 => CTR
* .6437129.97286531431.942...791.845.34.6753129.2319684715...7.3.64..3.781237.189..
* PAIR C9: 5,7 ROW 9
H9: 5,7,2,6                              # reduction candidate for 5,7
H9: 5,7 => CTR
* .6437129.97286531431.942...791.845.34.6753129.2319684715...7.3.64..3.781237.1895.
H9: 2,6 => SOLVED
* 564371298972865431318942756297184563486253179153796842829437615641529387735618924
I9: 5,7,2,4,6                            # reduction candidate for 5,7
I9: 5,7 => CTR
* .6437129..728.....31..42.5..9.6845.34.6.531....31.9.4......7...64.....8..3.41896.
I9: 2,4,6                                # 16 pairs
* PAIR F8: 5,9 BLK 8
D7: 5,9,2,4,6                            # reduction candidate for 5,9
D7: 5,9 => CTR
* .6437129..72896...319542....9..845.34.6.531....3.29.4.9...67...64..3.78..3.4189..
D7: 2,4,6                                # 16 pairs
D8: 5,9,2                                # reduction candidate for 5,9
D8: 5,9 => SOLVED
* 564371298972865431318942756297184563486253179153796842829437615641529387735618924
D8: 2                                    # 19 pairs
* PAIR F8: 5,9 ROW 8
C8: 5,9,1,7                              # reduction candidate for 5,9
C8: 1,7 => SOLVED
* 564371298972865431318942756297184563486253179153796842829437615641529387735618924
C8: 5,9                                  # 18 pairs
* PAIR F8: 5,9 COL F
F2: 5,9,6                                # reduction candidate for 5,9
F2: 6 => CTR
* .6437129.572896...319542....9..845.34.6.531...53..9.4.9.8..7..56419.5.8..35.189..
F2: 5,9                                  # 21 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190107-absurd-base-pr-000.dot
* REASONING
* PRF # C3: 5,8 => SOL
* DIS # C3: 9 => CTR => C3: 5,8
* DIS # A6: 5,8 => CTR => A6: 1,2,7
* PRF # A6: 1,2,7 => SOL
* PRF # A7: 5,8 => SOL
* DIS # C3: 5,9 => CTR => C3: 8
* PRF # C3: 8 => SOL
* DIS # F2: 6 => CTR => F2: 5,9
* DIS # A7: 5,9 => CTR => A7: 1,2,8
* PRF # A7: 1,2,8 => SOL
* DIS # F2: 6,9 => CTR => F2: 5
* PRF # F2: 5 => SOL
* PRF # E6: 6,9 => SOL
* DIS # F2: 6 => CTR => F2: 5,9
* DIS # C3: 5,9 => CTR => C3: 8
* PRF # C3: 8 => SOL
* DIS # D7: 5,9 => CTR => D7: 2,4,6
* PRF # D8: 5,9 => SOL
* DIS # I3: 5,8 => CTR => I3: 6,7
* PRF # G7: 6 => SOL
* DIS # I7: 1,4 => CTR => I7: 2,5,6
* DIS # A4: 1,7 => CTR => A4: 2
* PRF # A4: 2 => SOL
* PRF # A6: 1,7 => SOL
* DIS # A6: 2,5,8 => CTR => A6: 1,7
* PRF # D4: 1,7 => SOL
* PRF # C8: 1,7 => SOL
* DIS # A6: 2,8 => CTR => A6: 1,5,7
* DIS # B6: 2,8 => CTR => B6: 5
* DIS # I5: 2,8 => CTR => I5: 7,9
* DIS # B7: 5 => CTR => B7: 2,8
* DIS # D6: 6,9 => CTR => D6: 1,2,7
* PRF # E6: 6,9 => SOL
* DIS # F2: 6,9 => CTR => F2: 5
* PRF # F2: 5 => SOL
* DIS # H4: 2,7 => CTR => H4: 6
* DIS # I5: 2,7 => CTR => I5: 8,9
* DIS # D5: 9 => CTR => D5: 2,7
* PRF # H9: 2,7 => SOL
* DIS # C8: 5,7 => CTR => C8: 1,9
* PRF # A9: 5,7 => SOL
* DIS # A9: 2 => CTR => A9: 5,7
* DIS # H9: 5,7 => CTR => H9: 2,6
* PRF # H9: 2,6 => SOL
* DIS # I9: 5,7 => CTR => I9: 2,4,6
* DIS # D7: 5,9 => CTR => D7: 2,4,6
* PRF # D8: 5,9 => SOL
* PRF # C8: 1,7 => SOL
* DIS # F2: 6 => CTR => F2: 5,9
* CNT  49 HDP CHAINS /  80 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,B5,C4,C9,D3,E2,F6,F8,G2,G8,H2,H5,H7,I1,I2)
* .6437129..728.....31..42....9..845.34.6.531....3....4......7...64.....8..3..189..
* PAIR A1: 5,8 BLK 1
C3: 5,8,9                                # reduction candidate for 5,8
C3: 5,8 => SOLVED
* 564371298972865431318942756297184563486253179153796842829437615641529387735618924
* DURATION: 0:00:01.675593  START: 02:47:42.069027  END: 02:47:43.744620 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190107-absurd-base-pr-001.dot
* REASONING
* PRF # C3: 5,8 => SOL
* STA C3: 5,8
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190107, absurd

Solution

position: 564371298972865431318942756297184563486253179153796842829437615641529387735618924 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:

* PRF # C3: 5,8 => SOL
* DIS # C3: 9 => CTR => C3: 5,8
* DIS # A6: 5,8 => CTR => A6: 1,2,7
* PRF # A6: 1,2,7 => SOL
* PRF # A7: 5,8 => SOL
* INC # A7: 1,2,9 => UNS
* DIS # C3: 5,9 => CTR => C3: 8
* PRF # C3: 8 => SOL
* INC # F2: 5,9 => UNS
* DIS # F2: 6 => CTR => F2: 5,9
* DIS # A7: 5,9 => CTR => A7: 1,2,8
* PRF # A7: 1,2,8 => SOL
* DIS # F2: 6,9 => CTR => F2: 5
* PRF # F2: 5 => SOL
* PRF # E6: 6,9 => SOL
* INC # E6: 2 => UNS
* INC # E7: 6,9 => UNS
* INC # F2: 5,9 => UNS
* DIS # F2: 6 => CTR => F2: 5,9
* DIS # C3: 5,9 => CTR => C3: 8
* PRF # C3: 8 => SOL
* DIS # D7: 5,9 => CTR => D7: 2,4,6
* INC # D7: 2,4,6 => UNS
* PRF # D8: 5,9 => SOL
* INC # D8: 2 => UNS
* DIS # I3: 5,8 => CTR => I3: 6,7
* INC # I3: 6,7 => UNS
* INC # G7: 3,4 => UNS
* PRF # G7: 6 => SOL
* DIS # I7: 1,4 => CTR => I7: 2,5,6
* INC # I7: 2,5,6 => UNS
* DIS # A4: 1,7 => CTR => A4: 2
* PRF # A4: 2 => SOL
* PRF # A6: 1,7 => SOL
* DIS # A6: 2,5,8 => CTR => A6: 1,7
* PRF # D4: 1,7 => SOL
* INC # D4: 2,6 => UNS
* PRF # C8: 1,7 => SOL
* INC # C8: 5,9 => UNS
* DIS # A6: 2,8 => CTR => A6: 1,5,7
* INC # A6: 1,5,7 => UNS
* DIS # B6: 2,8 => CTR => B6: 5
* INC # B6: 5 => UNS
* DIS # I5: 2,8 => CTR => I5: 7,9
* INC # I5: 7,9 => UNS
* INC # B7: 2,8 => UNS
* DIS # B7: 5 => CTR => B7: 2,8
* DIS # D6: 6,9 => CTR => D6: 1,2,7
* INC # D6: 1,2,7 => UNS
* PRF # E6: 6,9 => SOL
* INC # E6: 2 => UNS
* INC # I6: 6,9 => UNS
* INC # I6: 2,7,8 => UNS
* DIS # F2: 6,9 => CTR => F2: 5
* PRF # F2: 5 => SOL
* DIS # H4: 2,7 => CTR => H4: 6
* INC # H4: 6 => UNS
* DIS # I5: 2,7 => CTR => I5: 8,9
* INC # I5: 8,9 => UNS
* INC # I6: 2,7 => UNS
* INC # D5: 2,7 => UNS
* DIS # D5: 9 => CTR => D5: 2,7
* PRF # H9: 2,7 => SOL
* INC # H9: 5,6 => UNS
* DIS # C8: 5,7 => CTR => C8: 1,9
* INC # C8: 1,9 => UNS
* PRF # A9: 5,7 => SOL
* DIS # A9: 2 => CTR => A9: 5,7
* DIS # H9: 5,7 => CTR => H9: 2,6
* PRF # H9: 2,6 => SOL
* DIS # I9: 5,7 => CTR => I9: 2,4,6
* INC # I9: 2,4,6 => UNS
* DIS # D7: 5,9 => CTR => D7: 2,4,6
* INC # D7: 2,4,6 => UNS
* PRF # D8: 5,9 => SOL
* INC # D8: 2 => UNS
* INC # C8: 5,9 => UNS
* PRF # C8: 1,7 => SOL
* INC # F2: 5,9 => UNS
* DIS # F2: 6 => CTR => F2: 5,9
* CNT  80 HDP CHAINS /  80 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # C3: 5,8 => SOL
* STA C3: 5,8
* CNT   1 HDP CHAINS /   1 HYP OPENED