Analysis of zz-www.sudokuoftheday.co.uk-20060705-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006
level: medium
position: ...21...617..5..3..9..7..4...3......78.......4.5...6..2...6.4.....53.27....72.1.. initial
Autosolve
position: ...21.7.617.45..32.9287.541..3......78....3..4.53..6..2.796.4.....53.27....72.16. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C8: 4,8 => CTR => C8: 1,6,9 * DIS # C9: 4,8 => CTR => C9: 9 * PRF # C9: 9 => SOL * DIS # C8: 6,8 => CTR => C8: 1,4,9 * DIS # H4: 8,9 => CTR => H4: 1,2,5 * PRF # H6: 8,9 => SOL * DIS # H6: 1,2 => CTR => H6: 8,9 * DIS # C5: 1 => CTR => C5: 6,9 * DIS # A8: 6,9 => CTR => A8: 8 * DIS # B4: 6 => CTR => B4: 1,2 * DIS # H6: 1,2 => CTR => H6: 8,9 * PRF # H6: 8,9 => SOL * DIS # B4: 1,6 => CTR => B4: 2 * PRF # C5: 1,6 => SOL * DIS # C5: 9 => CTR => C5: 1,6 * PRF # E4: 4,9 => SOL * DIS # E4: 8 => CTR => E4: 4,9 * DIS # F4: 2,5 => CTR => F4: 7 * PRF # F4: 7 => SOL * PRF # H5: 2,5 => SOL * DIS # H5: 1,9 => CTR => H5: 2,5 * DIS # E4: 8,9 => CTR => E4: 4 * PRF # E4: 4 => SOL * PRF # H6: 8,9 => SOL * DIS # H6: 1,2 => CTR => H6: 8,9 * PRF # F4: 2,7 => SOL * DIS # F4: 5 => CTR => F4: 2,7 * DIS # H4: 8,9 => CTR => H4: 1,2,5 * PRF # H6: 8,9 => SOL * DIS # H6: 1,2 => CTR => H6: 8,9 * DIS # E4: 8,9 => CTR => E4: 4 * PRF # E4: 4 => SOL * PRF # I4: 4,5 => SOL * DIS # I4: 7,8 => CTR => I4: 4,5 * DIS # I4: 7,8 => CTR => I4: 4,5 * PRF # I4: 4,5 => SOL * DIS # F8: 1 => CTR => F8: 4,8 * DIS # C9: 4,8 => CTR => C9: 9 * PRF # C9: 9 => SOL * DIS # H4: 5,8 => CTR => H4: 1,2,9 * PRF # H4: 1,2,9 => SOL * DIS # I9: 8,9 => CTR => I9: 3,5 * DIS # C8: 8,9 => CTR => C8: 1,4,6 * CNT 43 HDP CHAINS / 59 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C8: 4,8 => CTR => C8: 1,6,9 * DIS C8: 1,6,9 # C9: 4,8 => CTR => C9: 9 * PRF C8: 1,6,9 + C9: 9 => SOL * STA C8: 1,6,9 + C9: 9 * CNT 3 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...21...617..5..3..9..7..4...3......78.......4.5...6..2...6.4.....53.27....72.1.. | initial |
| ...21.7.617.45..32.9287.541..3......78....3..4.53..6..2.796.4.....53.27....72.16. | autosolve |
| 354219786178456932692873541923647815786195324415382697237961458861534279549728163 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (23) C1: 4,8 C2: 6,8 A3: 3,6 F1: 3,9 F2: 6,9 F3: 3,6 H1: 8,9 G2: 8,9 A4: 6,9 B6: 1,2 D4: 1,6 D5: 1,6 E5: 4,9 F5: 2,5 E6: 8,9 F6: 2,7 G4: 8,9 I5: 4,5 I6: 7,8 F7: 1,8 F9: 4,8 H7: 5,8 I8: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D4,D5: 1.. / D4 = 1 => 23 pairs (_) / D5 = 1 => 0 pairs (*) F7,F8: 1.. / F7 = 1 => 25 pairs (_) / F8 = 1 => 0 pairs (X) B6,H6: 1.. / B6 = 1 => 25 pairs (_) / H6 = 1 => 0 pairs (X) B7,F7: 1.. / B7 = 1 => 0 pairs (X) / F7 = 1 => 25 pairs (_) C5,C8: 1.. / C5 = 1 => 0 pairs (X) / C8 = 1 => 26 pairs (_) B4,B6: 2.. / B4 = 2 => 25 pairs (_) / B6 = 2 => 0 pairs (X) F5,H5: 2.. / F5 = 2 => 0 pairs (X) / H5 = 2 => 0 pairs (_) F1,F3: 3.. / F1 = 3 => 0 pairs (X) / F3 = 3 => 0 pairs (_) I7,I9: 3.. / I7 = 3 => 24 pairs (_) / I9 = 3 => 27 pairs (_) A3,F3: 3.. / A3 = 3 => 0 pairs (X) / F3 = 3 => 0 pairs (_) B7,I7: 3.. / B7 = 3 => 27 pairs (_) / I7 = 3 => 24 pairs (_) B1,C1: 4.. / B1 = 4 => 0 pairs (X) / C1 = 4 => 24 pairs (_) E4,E5: 4.. / E4 = 4 => 0 pairs (*) / E5 = 4 => 0 pairs (X) I4,I5: 4.. / I4 = 4 => 0 pairs (X) / I5 = 4 => 0 pairs (_) F8,F9: 4.. / F8 = 4 => 25 pairs (_) / F9 = 4 => 25 pairs (_) E4,I4: 4.. / E4 = 4 => 0 pairs (*) / I4 = 4 => 0 pairs (X) E5,I5: 4.. / E5 = 4 => 0 pairs (X) / I5 = 4 => 0 pairs (_) A1,B1: 5.. / A1 = 5 => 25 pairs (_) / B1 = 5 => 26 pairs (_) F4,F5: 5.. / F4 = 5 => 0 pairs (X) / F5 = 5 => 0 pairs (_) A1,A9: 5.. / A1 = 5 => 25 pairs (_) / A9 = 5 => 26 pairs (_) C2,A3: 6.. / C2 = 6 => 0 pairs (X) / A3 = 6 => 0 pairs (_) F2,F3: 6.. / F2 = 6 => 0 pairs (*) / F3 = 6 => 0 pairs (X) D4,D5: 6.. / D4 = 6 => 0 pairs (*) / D5 = 6 => 0 pairs (X) C2,F2: 6.. / C2 = 6 => 0 pairs (X) / F2 = 6 => 0 pairs (_) A3,F3: 6.. / A3 = 6 => 0 pairs (*) / F3 = 6 => 0 pairs (X) C5,D5: 6.. / C5 = 6 => 0 pairs (*) / D5 = 6 => 0 pairs (X) B4,B8: 6.. / B4 = 6 => 0 pairs (X) / B8 = 6 => 26 pairs (_) F4,F6: 7.. / F4 = 7 => 0 pairs (*) / F6 = 7 => 0 pairs (X) I4,I6: 7.. / I4 = 7 => 0 pairs (X) / I6 = 7 => 0 pairs (_) F4,I4: 7.. / F4 = 7 => 0 pairs (*) / I4 = 7 => 0 pairs (X) F6,I6: 7.. / F6 = 7 => 0 pairs (X) / I6 = 7 => 0 pairs (_) H1,G2: 8.. / H1 = 8 => 0 pairs (*) / G2 = 8 => 0 pairs (X) E4,E6: 8.. / E4 = 8 => 0 pairs (X) / E6 = 8 => 0 pairs (_) C2,G2: 8.. / C2 = 8 => 0 pairs (*) / G2 = 8 => 0 pairs (X) G2,G4: 8.. / G2 = 8 => 0 pairs (X) / G4 = 8 => 0 pairs (_) F1,F2: 9.. / F1 = 9 => 0 pairs (*) / F2 = 9 => 0 pairs (X) H1,G2: 9.. / H1 = 9 => 0 pairs (X) / G2 = 9 => 0 pairs (_) A4,C5: 9.. / A4 = 9 => 0 pairs (*) / C5 = 9 => 0 pairs (X) I8,I9: 9.. / I8 = 9 => 23 pairs (_) / I9 = 9 => 0 pairs (X) F1,H1: 9.. / F1 = 9 => 0 pairs (*) / H1 = 9 => 0 pairs (X) F2,G2: 9.. / F2 = 9 => 0 pairs (X) / G2 = 9 => 0 pairs (_) E6,H6: 9.. / E6 = 9 => 0 pairs (X) / H6 = 9 => 0 pairs (_) G2,G4: 9.. / G2 = 9 => 0 pairs (*) / G4 = 9 => 0 pairs (X) * DURATION: 0:00:58.414208 START: 00:20:46.531146 END: 00:21:44.945354 2019-05-01 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B6,C1,C2,D4,D5,E5,E6,F1,F2,F3,F5,F6,F7,F9,G2,G4,H1,H7,I5,I6,I8) * ...21.7.617.45..32.9287.541..3......78....3..4.53..6..2.796.4.....53.27....72.16. * PAIR C1: 4,8 COL C C8: 4,8,1,6,9 # reduction candidate for 4,8 C8: 4,8 => CTR * ...21.7961764598323928765419.3......7816..3..4253.76182.796.48....53.279..972.16. C8: 1,6,9 # 23 pairs C9: 4,8,9 # reduction candidate for 4,8 C9: 4,8 => CTR * 54821379617645983239287654162318.9..78964.31541539.6..2.7961458..153.27995.72.163 C9: 9 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 * PAIR C2: 6,8 COL C C8: 6,8,1,4,9 # reduction candidate for 6,8 C8: 6,8 => CTR * ..421.79617.459832.928765419.3......7816..3..4253.76182.796.48....53.279..972.16. C8: 1,4,9 # 23 pairs * PAIR H1: 8,9 COL H H4: 8,9,1,2,5 # reduction candidate for 8,9 H4: 8,9 => CTR * ...21.7.617.45..32.9287.541..3......78....3..4.53..6..2.796.4.....53.27....72.16. H4: 1,2,5 # 23 pairs H6: 8,9,1,2 # reduction candidate for 8,9 H6: 8,9 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 H6: 1,2 => CTR * ...21.79617.459832.92876541..3.8.9..78....3..4.539.6.82.796.48....53.279...72.16. * PAIR A4: 6,9 BLK 4 C5: 6,9,1 # reduction candidate for 6,9 C5: 1 => CTR * ...21.7.617.45..32.9287.5419631..8..7816..3..4253876..2.796.4.....53.27....72.16. C5: 6,9 # 26 pairs * PAIR A4: 6,9 COL A A8: 6,9,8 # reduction candidate for 6,9 A8: 6,9 => CTR * ...21.7.6176459832392876541..3...9..78964.31541539.6..2.79614589..53.27....72.16. A8: 8 # 25 pairs * PAIR B6: 1,2 BLK 4 B4: 1,2,6 # reduction candidate for 1,2 B4: 6 => CTR * ...21.7.617.45..32.9287.541.631.....78.6..3..4253.76182.796.48....53.279...72.16. B4: 1,2 # 26 pairs * PAIR B6: 1,2 ROW 6 H6: 1,2,8,9 # reduction candidate for 1,2 H6: 1,2 => CTR * ...21.79617.459832.92876541..3.8.9..78....3..4.539.6.82.796.48....53.279...72.16. H6: 8,9 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 * PAIR D4: 1,6 ROW 4 B4: 1,6,2 # reduction candidate for 1,6 B4: 1,6 => CTR * ...21.79617.459832.92876541..3.8.9..78....3..4253.76182.796.48....53.279...72.16. B4: 2 # 25 pairs * PAIR D5: 1,6 ROW 5 C5: 1,6,9 # reduction candidate for 1,6 C5: 1,6 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 C5: 9 => CTR * 5..21.7.61764598323928765416231.59..78964.3154153..6..2.7961458..153.27995.72.163 * PAIR E5: 4,9 BLK 5 E4: 4,9,8 # reduction candidate for 4,9 E4: 4,9 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 E4: 8 => CTR * ...21.7.617.45..32.9287.541..3.8.9.478964.31541539.6..2.796.4.....53.27....72.16. * PAIR F5: 2,5 BLK 5 F4: 2,5,7 # reduction candidate for 2,5 F4: 2,5 => CTR * ...21.7.617.45..32.9287.541..3.....778....3.44.53.76.82.796.48....53.279...72.16. F4: 7 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 * PAIR F5: 2,5 ROW 5 H5: 2,5,1,9 # reduction candidate for 2,5 H5: 2,5 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 H5: 1,9 => CTR * ...21.7.617.45..32.9287.541..3......78...23.54.53.76.82.796.4.....53.27....72.16. * PAIR E6: 8,9 BLK 5 E4: 8,9,4 # reduction candidate for 8,9 E4: 8,9 => CTR * ...21.7.617.45..32.9287.541..3.....478..4.3.54.53..6.72.796.45....53.27....72.16. E4: 4 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 * PAIR E6: 8,9 ROW 6 H6: 8,9,1,2 # reduction candidate for 8,9 H6: 8,9 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 H6: 1,2 => CTR * ...21.79617.459832.92876541..3.8.9..78....3..4.539.6.82.796.48....53.279...72.16. * PAIR F6: 2,7 BLK 5 F4: 2,7,5 # reduction candidate for 2,7 F4: 2,7 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 F4: 5 => CTR * ...21.7.617.45..32.9287.541..3..5..778...23.44.53.76.82.796.48....53.279...72.16. * PAIR G4: 8,9 BLK 6 H4: 8,9,1,2,5 # reduction candidate for 8,9 H4: 8,9 => CTR * ...21.7.617.45..32.9287.541..3......78....3..4.53..6..2.796.4.....53.27....72.16. H4: 1,2,5 # 23 pairs H6: 8,9,1,2 # reduction candidate for 8,9 H6: 8,9 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 H6: 1,2 => CTR * ...21.79617.459832.92876541..3.8.9..78....3..4.539.6.82.796.48....53.279...72.16. * PAIR G4: 8,9 ROW 4 E4: 8,9,4 # reduction candidate for 8,9 E4: 8,9 => CTR * ...21.7.617.45..32.9287.541..3.....478..4.3.54.53..6.72.796.45....53.27....72.16. E4: 4 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 * PAIR I5: 4,5 BLK 6 I4: 4,5,7,8 # reduction candidate for 4,5 I4: 4,5 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 I4: 7,8 => CTR * ...21.7.617.45..32.9287.541..3.4....78..9.3.44.538.6972.796.4.....53.27....72.16. * PAIR I6: 7,8 BLK 6 I4: 7,8,4,5 # reduction candidate for 7,8 I4: 7,8 => CTR * ...21.7.617.45..32.9287.541..3.4....78..9.3.44.538.6972.796.4.....53.27....72.16. I4: 4,5 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 * PAIR F7: 1,8 BLK 8 F8: 1,8,4 # reduction candidate for 1,8 F8: 4 # 25 pairs F8: 1,8 # 25 pairs * PAIR F9: 4,8 BLK 8 F8: 4,8,1 # reduction candidate for 4,8 F8: 1 => CTR * ...21.7.617.45..32.9287.541..3......7816..3..4253.7618217968453...531279...72416. F8: 4,8 # 25 pairs * PAIR F9: 4,8 ROW 9 C9: 4,8,9 # reduction candidate for 4,8 C9: 4,8 => CTR * 54821379617645983239287654162318.9..78964.31541539.6..2.7961458..153.27995.72.163 C9: 9 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 * PAIR H7: 5,8 BLK 9 I7: 5,8,3 # reduction candidate for 5,8 I7: 5,8 # 27 pairs I9: 5,8,3,9 # reduction candidate for 5,8 I9: 5,8 # 25 pairs * PAIR H7: 5,8 COL H H4: 5,8,1,2,9 # reduction candidate for 5,8 H4: 5,8 => CTR * ...21.79617.459832.92876541..3...9.778964.3154153976282.796.4.....53.27....72.16. H4: 1,2,9 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 * PAIR I8: 8,9 BLK 9 I9: 8,9,3,5 # reduction candidate for 8,9 I9: 8,9 => CTR * ...21.7.617.45..32.9287.541..3......7816..3..4253.7618217968453...531279...72416. I9: 3,5 # 25 pairs * PAIR I8: 8,9 ROW 8 A8: 8,9,6 # reduction candidate for 8,9 A8: 8,9 # 25 pairs C8: 8,9,1,4,6 # reduction candidate for 8,9 C8: 8,9 => CTR * ..421.7961764598323928765419.3......7816..3..4253.76182.796.48....53.279..972.16. C8: 1,4,6 # 23 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060705-absurd-base-pr-000.dot * REASONING * DIS # C8: 4,8 => CTR => C8: 1,6,9 * DIS # C9: 4,8 => CTR => C9: 9 * PRF # C9: 9 => SOL * DIS # C8: 6,8 => CTR => C8: 1,4,9 * DIS # H4: 8,9 => CTR => H4: 1,2,5 * PRF # H6: 8,9 => SOL * DIS # H6: 1,2 => CTR => H6: 8,9 * DIS # C5: 1 => CTR => C5: 6,9 * DIS # A8: 6,9 => CTR => A8: 8 * DIS # B4: 6 => CTR => B4: 1,2 * DIS # H6: 1,2 => CTR => H6: 8,9 * PRF # H6: 8,9 => SOL * DIS # B4: 1,6 => CTR => B4: 2 * PRF # C5: 1,6 => SOL * DIS # C5: 9 => CTR => C5: 1,6 * PRF # E4: 4,9 => SOL * DIS # E4: 8 => CTR => E4: 4,9 * DIS # F4: 2,5 => CTR => F4: 7 * PRF # F4: 7 => SOL * PRF # H5: 2,5 => SOL * DIS # H5: 1,9 => CTR => H5: 2,5 * DIS # E4: 8,9 => CTR => E4: 4 * PRF # E4: 4 => SOL * PRF # H6: 8,9 => SOL * DIS # H6: 1,2 => CTR => H6: 8,9 * PRF # F4: 2,7 => SOL * DIS # F4: 5 => CTR => F4: 2,7 * DIS # H4: 8,9 => CTR => H4: 1,2,5 * PRF # H6: 8,9 => SOL * DIS # H6: 1,2 => CTR => H6: 8,9 * DIS # E4: 8,9 => CTR => E4: 4 * PRF # E4: 4 => SOL * PRF # I4: 4,5 => SOL * DIS # I4: 7,8 => CTR => I4: 4,5 * DIS # I4: 7,8 => CTR => I4: 4,5 * PRF # I4: 4,5 => SOL * DIS # F8: 1 => CTR => F8: 4,8 * DIS # C9: 4,8 => CTR => C9: 9 * PRF # C9: 9 => SOL * DIS # H4: 5,8 => CTR => H4: 1,2,9 * PRF # H4: 1,2,9 => SOL * DIS # I9: 8,9 => CTR => I9: 3,5 * DIS # C8: 8,9 => CTR => C8: 1,4,6 * CNT 43 HDP CHAINS / 59 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B6,C1,C2,D4,D5,E5,E6,F1,F2,F3,F5,F6,F7,F9,G2,G4,H1,H7,I5,I6,I8) * ...21.7.617.45..32.9287.541..3......78....3..4.53..6..2.796.4.....53.27....72.16. * PAIR C1: 4,8 COL C C8: 4,8,1,6,9 # reduction candidate for 4,8 C8: 4,8 => CTR * ...21.7961764598323928765419.3......7816..3..4253.76182.796.48....53.279..972.16. C9: 4,8,9 # reduction candidate for 4,8 C9: 4,8 => CTR * 54821379617645983239287654162318.9..78964.31541539.6..2.7961458..153.27995.72.163 C9: 9 => SOLVED * 354219786178456932692873541923647815786195324415382697237961458861534279549728163 * DURATION: 0:00:02.467107 START: 00:22:31.330988 END: 00:22:33.798095 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060705-absurd-base-pr-001.dot * REASONING * DIS # C8: 4,8 => CTR => C8: 1,6,9 * DIS C8: 1,6,9 # C9: 4,8 => CTR => C9: 9 * PRF C8: 1,6,9 + C9: 9 => SOL * STA C8: 1,6,9 + C9: 9 * CNT 3 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060705, absurd
Solution
position: 354219786178456932692873541923647815786195324415382697237961458861534279549728163 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:
* DIS # C8: 4,8 => CTR => C8: 1,6,9 * INC # C8: 1,6,9 => UNS * DIS # C9: 4,8 => CTR => C9: 9 * PRF # C9: 9 => SOL * DIS # C8: 6,8 => CTR => C8: 1,4,9 * INC # C8: 1,4,9 => UNS * DIS # H4: 8,9 => CTR => H4: 1,2,5 * INC # H4: 1,2,5 => UNS * PRF # H6: 8,9 => SOL * DIS # H6: 1,2 => CTR => H6: 8,9 * INC # C5: 6,9 => UNS * DIS # C5: 1 => CTR => C5: 6,9 * DIS # A8: 6,9 => CTR => A8: 8 * INC # A8: 8 => UNS * INC # B4: 1,2 => UNS * DIS # B4: 6 => CTR => B4: 1,2 * DIS # H6: 1,2 => CTR => H6: 8,9 * PRF # H6: 8,9 => SOL * DIS # B4: 1,6 => CTR => B4: 2 * INC # B4: 2 => UNS * PRF # C5: 1,6 => SOL * DIS # C5: 9 => CTR => C5: 1,6 * PRF # E4: 4,9 => SOL * DIS # E4: 8 => CTR => E4: 4,9 * DIS # F4: 2,5 => CTR => F4: 7 * PRF # F4: 7 => SOL * PRF # H5: 2,5 => SOL * DIS # H5: 1,9 => CTR => H5: 2,5 * DIS # E4: 8,9 => CTR => E4: 4 * PRF # E4: 4 => SOL * PRF # H6: 8,9 => SOL * DIS # H6: 1,2 => CTR => H6: 8,9 * PRF # F4: 2,7 => SOL * DIS # F4: 5 => CTR => F4: 2,7 * DIS # H4: 8,9 => CTR => H4: 1,2,5 * INC # H4: 1,2,5 => UNS * PRF # H6: 8,9 => SOL * DIS # H6: 1,2 => CTR => H6: 8,9 * DIS # E4: 8,9 => CTR => E4: 4 * PRF # E4: 4 => SOL * PRF # I4: 4,5 => SOL * DIS # I4: 7,8 => CTR => I4: 4,5 * DIS # I4: 7,8 => CTR => I4: 4,5 * PRF # I4: 4,5 => SOL * INC # F8: 1,8 => UNS * INC # F8: 4 => UNS * INC # F8: 4,8 => UNS * DIS # F8: 1 => CTR => F8: 4,8 * DIS # C9: 4,8 => CTR => C9: 9 * PRF # C9: 9 => SOL * INC # I7: 5,8 => UNS * INC # I9: 5,8 => UNS * DIS # H4: 5,8 => CTR => H4: 1,2,9 * PRF # H4: 1,2,9 => SOL * DIS # I9: 8,9 => CTR => I9: 3,5 * INC # I9: 3,5 => UNS * INC # A8: 8,9 => UNS * DIS # C8: 8,9 => CTR => C8: 1,4,6 * INC # C8: 1,4,6 => UNS * CNT 59 HDP CHAINS / 59 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C8: 4,8 => CTR => C8: 1,6,9 * DIS C8: 1,6,9 # C9: 4,8 => CTR => C9: 9 * PRF C8: 1,6,9 + C9: 9 => SOL * STA C8: 1,6,9 + C9: 9 * CNT 3 HDP CHAINS / 2 HYP OPENED