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
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
Pair Reduction Variants
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
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
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