Analysis of zz-www.sudokuoftheday.co.uk-20060729-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: ..2.....7......1.9...13..5.1.....79....74...88..2.95...2.8..9...6.9.1...58...4.6. initial
Autosolve
position: .12.9...7.....71299..132.5.1.....79229.74..188..2195...218..9...6.921..5589374261 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 4,6 => CTR => A2: 3 * DIS # D1: 4,6 => CTR => D1: 5 * PRF # C3: 4,7 => SOL * DIS # C3: 8 => CTR => C3: 4,7 * DIS # D1: 4,6 => CTR => D1: 5 * DIS # A2: 4,6 => CTR => A2: 3 * DIS # F1: 5 => CTR => F1: 6,8 * DIS # E4: 5 => CTR => E4: 6,8 * DIS # G3: 4,6 => CTR => G3: 8 * PRF # G3: 8 => SOL * DIS # I6: 3 => CTR => I6: 4,6 * DIS # C6: 3,7 => CTR => C6: 6 * PRF # C6: 6 => SOL * DIS # E4: 5,6 => CTR => E4: 8 * PRF # E4: 8 => SOL * PRF # F4: 5,6 => SOL * DIS # F5: 5,6 => CTR => F5: 3 * PRF # F5: 3 => SOL * DIS # C4: 5,6 => CTR => C4: 3,4 * DIS # D1: 4 => CTR => D1: 5,6 * PRF # I6: 4 => SOL * DIS # C5: 3,6 => CTR => C5: 5 * PRF # I6: 3,4 => SOL * DIS # I6: 6 => CTR => I6: 3,4 * DIS # H7: 3,4 => CTR => H7: 7 * DIS # H8: 3,4 => CTR => H8: 7,8 * DIS # A8: 3,4 => CTR => A8: 7 * DIS # H8: 3,4 => CTR => H8: 7,8 * DIS # C2: 3,4 => CTR => C2: 5,8 * DIS # E4: 5,6 => CTR => E4: 8 * PRF # E4: 8 => SOL * DIS # F1: 5,6 => CTR => F1: 8 * PRF # F1: 8 => SOL * PRF # F4: 5,6 => SOL * DIS # F5: 5,6 => CTR => F5: 3 * PRF # F5: 3 => SOL * DIS # H7: 3,4 => CTR => H7: 7 * DIS # H8: 3,4 => CTR => H8: 7,8 * DIS # A7: 7 => CTR => A7: 3,4 * PRF # I6: 3,4 => SOL * DIS # I6: 6 => CTR => I6: 3,4 * CNT 41 HDP CHAINS / 68 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 4,6 => CTR => A2: 3 * PRF A2: 3 # C3: 4,7 => SOL * STA A2: 3 + C3: 4,7 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..2.....7......1.9...13..5.1.....79....74...88..2.95...2.8..9...6.9.1...58...4.6. | initial |
| .12.9...7.....71299..132.5.1.....79229.74..188..2195...218..9...6.921..5589374261 | autosolve |
| 612598347358467129947132856134685792295743618876219534421856973763921485589374261 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A1: 4,6 B3: 4,7 D2: 4,6 E2: 6,8 I3: 4,6 B6: 3,7 D4: 5,6 G5: 3,6 H6: 3,4 C8: 3,4 E7: 5,6 F7: 5,6 I7: 3,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,H1: 3.. / G1 = 3 => 0 pairs (*) / H1 = 3 => 0 pairs (X) F4,F5: 3.. / F4 = 3 => 0 pairs (X) / F5 = 3 => 0 pairs (_) I6,I7: 3.. / I6 = 3 => 0 pairs (X) / I7 = 3 => 16 pairs (_) D1,D2: 4.. / D1 = 4 => 0 pairs (X) / D2 = 4 => 15 pairs (_) B4,C4: 4.. / B4 = 4 => 0 pairs (X) / C4 = 4 => 23 pairs (_) H6,I6: 4.. / H6 = 4 => 15 pairs (_) / I6 = 4 => 0 pairs (*) B2,C2: 5.. / B2 = 5 => 16 pairs (_) / C2 = 5 => 0 pairs (X) D1,F1: 5.. / D1 = 5 => 16 pairs (_) / F1 = 5 => 0 pairs (X) E7,F7: 5.. / E7 = 5 => 14 pairs (_) / F7 = 5 => 0 pairs (X) C5,F5: 5.. / C5 = 5 => 17 pairs (_) / F5 = 5 => 0 pairs (X) B2,B4: 5.. / B2 = 5 => 16 pairs (_) / B4 = 5 => 0 pairs (X) D1,D4: 5.. / D1 = 5 => 16 pairs (_) / D4 = 5 => 0 pairs (X) E4,E7: 5.. / E4 = 5 => 0 pairs (X) / E7 = 5 => 14 pairs (_) A1,A2: 6.. / A1 = 6 => 15 pairs (_) / A2 = 6 => 0 pairs (X) G3,I3: 6.. / G3 = 6 => 0 pairs (X) / I3 = 6 => 0 pairs (_) G5,I6: 6.. / G5 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) E7,F7: 6.. / E7 = 6 => 0 pairs (X) / F7 = 6 => 14 pairs (_) C6,I6: 6.. / C6 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) G3,G5: 6.. / G3 = 6 => 0 pairs (X) / G5 = 6 => 0 pairs (_) I3,I6: 6.. / I3 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) B3,C3: 7.. / B3 = 7 => 0 pairs (X) / C3 = 7 => 0 pairs (_) B6,C6: 7.. / B6 = 7 => 0 pairs (*) / C6 = 7 => 0 pairs (X) A7,A8: 7.. / A7 = 7 => 0 pairs (X) / A8 = 7 => 14 pairs (_) H7,H8: 7.. / H7 = 7 => 14 pairs (_) / H8 = 7 => 0 pairs (X) A7,H7: 7.. / A7 = 7 => 0 pairs (X) / H7 = 7 => 14 pairs (_) A8,H8: 7.. / A8 = 7 => 14 pairs (_) / H8 = 7 => 0 pairs (X) B3,B6: 7.. / B3 = 7 => 0 pairs (X) / B6 = 7 => 0 pairs (_) C3,C6: 7.. / C3 = 7 => 0 pairs (*) / C6 = 7 => 0 pairs (X) C2,C3: 8.. / C2 = 8 => 0 pairs (*) / C3 = 8 => 0 pairs (X) F1,E2: 8.. / F1 = 8 => 0 pairs (*) / E2 = 8 => 0 pairs (X) E4,F4: 8.. / E4 = 8 => 0 pairs (*) / F4 = 8 => 0 pairs (X) G8,H8: 8.. / G8 = 8 => 0 pairs (X) / H8 = 8 => 16 pairs (_) C2,E2: 8.. / C2 = 8 => 0 pairs (*) / E2 = 8 => 0 pairs (X) C3,G3: 8.. / C3 = 8 => 0 pairs (X) / G3 = 8 => 0 pairs (_) E2,E4: 8.. / E2 = 8 => 0 pairs (X) / E4 = 8 => 0 pairs (_) F1,F4: 8.. / F1 = 8 => 0 pairs (*) / F4 = 8 => 0 pairs (X) H1,H8: 8.. / H1 = 8 => 0 pairs (X) / H8 = 8 => 16 pairs (_) * DURATION: 0:00:44.615226 START: 01:23:20.584294 END: 01:24:05.199520 2019-05-01 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B3,B6,C8,D2,D4,E2,E7,F7,G5,H6,I3,I7) * .12.9...7.....71299..132.5.1.....79229.74..188..2195...218..9...6.921..5589374261 * PAIR A1: 4,6 BLK 1 A2: 4,6,3 # reduction candidate for 4,6 A2: 4,6 => CTR * .12.9...7.53.87129978132.5.14....79229.74..188..2195...218..9...64921..5589374261 A2: 3 # 19 pairs * PAIR A1: 4,6 ROW 1 D1: 4,6,5 # reduction candidate for 4,6 D1: 4,6 => CTR * .12.95..7....871299.8132.5.1..5687922957436188..2195...218..9...6.921..5589374261 D1: 5 # 16 pairs * PAIR B3: 4,7 BLK 1 C3: 4,7,8 # reduction candidate for 4,7 C3: 4,7 => SOLVED * 612598347358467129947132856134685792295743618876219534421856973763921485589374261 C3: 8 => CTR * .12.9.837....871299781326541.....79229.74..18837219546.218..9.3.6.921485589374261 * PAIR D2: 4,6 BLK 2 D1: 4,6,5 # reduction candidate for 4,6 D1: 4,6 => CTR * .12.95..7....871299.8132.5.1..5687922957436188..2195...218..9...6.921..5589374261 D1: 5 # 16 pairs * PAIR D2: 4,6 ROW 2 A2: 4,6,3 # reduction candidate for 4,6 A2: 4,6 => CTR * .12.9...7.53.87129978132.5.14....79229.74..188..2195...218..9...64921..5589374261 A2: 3 # 19 pairs * PAIR E2: 6,8 BLK 2 F1: 6,8,5 # reduction candidate for 6,8 F1: 5 => CTR * .12.95..7....871299.8132.5.1..5687922957436188..2195...218..9...6.921..5589374261 F1: 6,8 # 16 pairs * PAIR E2: 6,8 COL E E4: 6,8,5 # reduction candidate for 6,8 E4: 5 => CTR * .12.9...7....871299.8132.5.1...587922957436188..2195...218..9...6.921..5589374261 E4: 6,8 # 14 pairs * PAIR I3: 4,6 BLK 3 G3: 4,6,8 # reduction candidate for 4,6 G3: 4,6 => CTR * .12.9...7....871299781326541....879229.743.188.72195.6.218..9.3.6.921..5589374261 G3: 8 => SOLVED * 612598347358467129947132856134685792295743618876219534421856973763921485589374261 * PAIR I3: 4,6 COL I I6: 4,6,3 # reduction candidate for 4,6 I6: 3 => CTR * .12.98437..84671299471328561.4...79229.74.618876219543.218..9.4.6.921385589374261 I6: 4,6 # 16 pairs * PAIR B6: 3,7 BLK 4 C6: 3,7,6 # reduction candidate for 3,7 C6: 3,7 => CTR * 6124958373..6871299781326541..5..79229.74.3188..2195464218..973763921485589374261 C6: 6 => SOLVED * 612598347358467129947132856134685792295743618876219534421856973763921485589374261 * PAIR D4: 5,6 BLK 5 E4: 5,6,8 # reduction candidate for 5,6 E4: 5,6 => CTR * .12.9...7....871299.8132.5.1....879229.7436188..2195...218..9...6.921..5589374261 E4: 8 => SOLVED * 612598347358467129947132856134685792295743618876219534421856973763921485589374261 F4: 5,6,3,8 # reduction candidate for 5,6 F4: 5,6 => SOLVED * 612598347358467129947132856134685792295743618876219534421856973763921485589374261 F4: 3,8 # 14 pairs F5: 5,6,3 # reduction candidate for 5,6 F5: 5,6 => CTR * 612598..7.584671299.713285614.68379229.7456188.62195...218569...6.921.85589374261 F5: 3 => SOLVED * 612598347358467129947132856134685792295743618876219534421856973763921485589374261 * PAIR D4: 5,6 ROW 4 C4: 5,6,3,4 # reduction candidate for 5,6 C4: 5,6 => CTR * .12.98..7.58.6712997413285614.68379229.74561883.2195...218..9...6.921..5589374261 C4: 3,4 # 19 pairs * PAIR D4: 5,6 COL D D1: 5,6,4 # reduction candidate for 5,6 D1: 4 => CTR * .12495..7...6871299.8132.5.1..5687922957436188..2195...218..9...6.921..5589374261 D1: 5,6 # 15 pairs * PAIR G5: 3,6 BLK 6 I6: 3,6,4 # reduction candidate for 3,6 I6: 4 => SOLVED * 612598347358467129947132856134685792295743618876219534421856973763921485589374261 I6: 3,6 # 15 pairs * PAIR G5: 3,6 ROW 5 C5: 3,6,5 # reduction candidate for 3,6 C5: 3,6 => CTR * 612598..73584671299..1328561.568379229.7456188.62195...218569...6.921.85589374261 C5: 5 # 17 pairs F5: 3,6,5 # reduction candidate for 3,6 F5: 3,6 # 17 pairs * PAIR H6: 3,4 BLK 6 I6: 3,4,6 # reduction candidate for 3,4 I6: 3,4 => SOLVED * 612598347358467129947132856134685792295743618876219534421856973763921485589374261 I6: 6 => CTR * 6124958373..6871299781326541..5..79229.74.3188..2195464218..973763921485589374261 * PAIR H6: 3,4 COL H H1: 3,4,8 # reduction candidate for 3,4 H1: 3,4 # 16 pairs H7: 3,4,7 # reduction candidate for 3,4 H7: 3,4 => CTR * .12.9..87....871299.8132.5.1....879229.7436188..2195..7218..9...6.921.75589374261 H7: 7 # 14 pairs H8: 3,4,7,8 # reduction candidate for 3,4 H8: 3,4 => CTR * .12.9..87....871299.8132.5.1....879229.7436188..2195...218..9...6.921..5589374261 H8: 7,8 # 14 pairs * PAIR C8: 3,4 BLK 7 A7: 3,4,7 # reduction candidate for 3,4 A7: 3,4 # 14 pairs A8: 3,4,7 # reduction candidate for 3,4 A8: 3,4 => CTR * .12.9..87....871299.8132.5.1....879229.7436188..2195..7218..9...6.921.75589374261 A8: 7 # 14 pairs * PAIR C8: 3,4 ROW 8 G8: 3,4,8 # reduction candidate for 3,4 G8: 3,4 # 16 pairs H8: 3,4,7,8 # reduction candidate for 3,4 H8: 3,4 => CTR * .12.9..87....871299.8132.5.1....879229.7436188..2195...218..9...6.921..5589374261 H8: 7,8 # 14 pairs * PAIR C8: 3,4 COL C C2: 3,4,5,8 # reduction candidate for 3,4 C2: 3,4 => CTR * .12.9...7.5..871299.8132.5.1....879229.7436188..2195...218..9...6.921..5589374261 C2: 5,8 # 14 pairs C4: 3,4,5,6 # reduction candidate for 3,4 C4: 3,4 # 19 pairs * PAIR E7: 5,6 COL E E4: 5,6,8 # reduction candidate for 5,6 E4: 5,6 => CTR * .12.9...7....871299.8132.5.1....879229.7436188..2195...218..9...6.921..5589374261 E4: 8 => SOLVED * 612598347358467129947132856134685792295743618876219534421856973763921485589374261 * PAIR F7: 5,6 COL F F1: 5,6,8 # reduction candidate for 5,6 F1: 5,6 => CTR * .12.9...7....871299.8132.5.1....879229.7436188..2195...218..9...6.921..5589374261 F1: 8 => SOLVED * 612598347358467129947132856134685792295743618876219534421856973763921485589374261 F4: 5,6,3,8 # reduction candidate for 5,6 F4: 5,6 => SOLVED * 612598347358467129947132856134685792295743618876219534421856973763921485589374261 F4: 3,8 # 14 pairs F5: 5,6,3 # reduction candidate for 5,6 F5: 5,6 => CTR * 612598..7.584671299.713285614.68379229.7456188.62195...218569...6.921.85589374261 F5: 3 => SOLVED * 612598347358467129947132856134685792295743618876219534421856973763921485589374261 * PAIR I7: 3,4 BLK 9 H7: 3,4,7 # reduction candidate for 3,4 H7: 3,4 => CTR * .12.9..87....871299.8132.5.1....879229.7436188..2195..7218..9...6.921.75589374261 H7: 7 # 14 pairs G8: 3,4,8 # reduction candidate for 3,4 G8: 3,4 # 16 pairs H8: 3,4,7,8 # reduction candidate for 3,4 H8: 3,4 => CTR * .12.9..87....871299.8132.5.1....879229.7436188..2195...218..9...6.921..5589374261 H8: 7,8 # 14 pairs * PAIR I7: 3,4 ROW 7 A7: 3,4,7 # reduction candidate for 3,4 A7: 7 => CTR * .12.9..87....871299.8132.5.1....879229.7436188..2195..7218..9...6.921.75589374261 A7: 3,4 # 14 pairs * PAIR I7: 3,4 COL I I6: 3,4,6 # reduction candidate for 3,4 I6: 3,4 => SOLVED * 612598347358467129947132856134685792295743618876219534421856973763921485589374261 I6: 6 => CTR * 6124958373..6871299781326541..5..79229.74.3188..2195464218..973763921485589374261 * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060729-absurd-base-pr-000.dot * REASONING * DIS # A2: 4,6 => CTR => A2: 3 * DIS # D1: 4,6 => CTR => D1: 5 * PRF # C3: 4,7 => SOL * DIS # C3: 8 => CTR => C3: 4,7 * DIS # D1: 4,6 => CTR => D1: 5 * DIS # A2: 4,6 => CTR => A2: 3 * DIS # F1: 5 => CTR => F1: 6,8 * DIS # E4: 5 => CTR => E4: 6,8 * DIS # G3: 4,6 => CTR => G3: 8 * PRF # G3: 8 => SOL * DIS # I6: 3 => CTR => I6: 4,6 * DIS # C6: 3,7 => CTR => C6: 6 * PRF # C6: 6 => SOL * DIS # E4: 5,6 => CTR => E4: 8 * PRF # E4: 8 => SOL * PRF # F4: 5,6 => SOL * DIS # F5: 5,6 => CTR => F5: 3 * PRF # F5: 3 => SOL * DIS # C4: 5,6 => CTR => C4: 3,4 * DIS # D1: 4 => CTR => D1: 5,6 * PRF # I6: 4 => SOL * DIS # C5: 3,6 => CTR => C5: 5 * PRF # I6: 3,4 => SOL * DIS # I6: 6 => CTR => I6: 3,4 * DIS # H7: 3,4 => CTR => H7: 7 * DIS # H8: 3,4 => CTR => H8: 7,8 * DIS # A8: 3,4 => CTR => A8: 7 * DIS # H8: 3,4 => CTR => H8: 7,8 * DIS # C2: 3,4 => CTR => C2: 5,8 * DIS # E4: 5,6 => CTR => E4: 8 * PRF # E4: 8 => SOL * DIS # F1: 5,6 => CTR => F1: 8 * PRF # F1: 8 => SOL * PRF # F4: 5,6 => SOL * DIS # F5: 5,6 => CTR => F5: 3 * PRF # F5: 3 => SOL * DIS # H7: 3,4 => CTR => H7: 7 * DIS # H8: 3,4 => CTR => H8: 7,8 * DIS # A7: 7 => CTR => A7: 3,4 * PRF # I6: 3,4 => SOL * DIS # I6: 6 => CTR => I6: 3,4 * CNT 41 HDP CHAINS / 68 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B3,B6,C8,D2,D4,E2,E7,F7,G5,H6,I3,I7) * .12.9...7.....71299..132.5.1.....79229.74..188..2195...218..9...6.921..5589374261 * PAIR A1: 4,6 BLK 1 A2: 4,6,3 # reduction candidate for 4,6 A2: 4,6 => CTR * .12.9...7.53.87129978132.5.14....79229.74..188..2195...218..9...64921..5589374261 * PAIR B3: 4,7 BLK 1 C3: 4,7,8 # reduction candidate for 4,7 C3: 4,7 => SOLVED * 612598347358467129947132856134685792295743618876219534421856973763921485589374261 * DURATION: 0:00:02.987188 START: 01:24:53.314719 END: 01:24:56.301907 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060729-absurd-base-pr-001.dot * REASONING * DIS # A2: 4,6 => CTR => A2: 3 * PRF A2: 3 # C3: 4,7 => SOL * STA A2: 3 + C3: 4,7 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060729, absurd
Solution
position: 612598347358467129947132856134685792295743618876219534421856973763921485589374261 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 # A2: 4,6 => CTR => A2: 3 * INC # A2: 3 => UNS * DIS # D1: 4,6 => CTR => D1: 5 * INC # D1: 5 => UNS * PRF # C3: 4,7 => SOL * DIS # C3: 8 => CTR => C3: 4,7 * DIS # D1: 4,6 => CTR => D1: 5 * INC # D1: 5 => UNS * DIS # A2: 4,6 => CTR => A2: 3 * INC # A2: 3 => UNS * INC # F1: 6,8 => UNS * DIS # F1: 5 => CTR => F1: 6,8 * INC # E4: 6,8 => UNS * DIS # E4: 5 => CTR => E4: 6,8 * DIS # G3: 4,6 => CTR => G3: 8 * PRF # G3: 8 => SOL * INC # I6: 4,6 => UNS * DIS # I6: 3 => CTR => I6: 4,6 * DIS # C6: 3,7 => CTR => C6: 6 * PRF # C6: 6 => SOL * DIS # E4: 5,6 => CTR => E4: 8 * PRF # E4: 8 => SOL * PRF # F4: 5,6 => SOL * INC # F4: 3,8 => UNS * DIS # F5: 5,6 => CTR => F5: 3 * PRF # F5: 3 => SOL * DIS # C4: 5,6 => CTR => C4: 3,4 * INC # C4: 3,4 => UNS * INC # D1: 5,6 => UNS * DIS # D1: 4 => CTR => D1: 5,6 * INC # I6: 3,6 => UNS * PRF # I6: 4 => SOL * DIS # C5: 3,6 => CTR => C5: 5 * INC # C5: 5 => UNS * INC # F5: 3,6 => UNS * PRF # I6: 3,4 => SOL * DIS # I6: 6 => CTR => I6: 3,4 * INC # H1: 3,4 => UNS * DIS # H7: 3,4 => CTR => H7: 7 * INC # H7: 7 => UNS * DIS # H8: 3,4 => CTR => H8: 7,8 * INC # H8: 7,8 => UNS * INC # A7: 3,4 => UNS * DIS # A8: 3,4 => CTR => A8: 7 * INC # A8: 7 => UNS * INC # G8: 3,4 => UNS * DIS # H8: 3,4 => CTR => H8: 7,8 * INC # H8: 7,8 => UNS * DIS # C2: 3,4 => CTR => C2: 5,8 * INC # C2: 5,8 => UNS * INC # C4: 3,4 => UNS * DIS # E4: 5,6 => CTR => E4: 8 * PRF # E4: 8 => SOL * DIS # F1: 5,6 => CTR => F1: 8 * PRF # F1: 8 => SOL * PRF # F4: 5,6 => SOL * INC # F4: 3,8 => UNS * DIS # F5: 5,6 => CTR => F5: 3 * PRF # F5: 3 => SOL * DIS # H7: 3,4 => CTR => H7: 7 * INC # H7: 7 => UNS * INC # G8: 3,4 => UNS * DIS # H8: 3,4 => CTR => H8: 7,8 * INC # H8: 7,8 => UNS * INC # A7: 3,4 => UNS * DIS # A7: 7 => CTR => A7: 3,4 * PRF # I6: 3,4 => SOL * DIS # I6: 6 => CTR => I6: 3,4 * CNT 68 HDP CHAINS / 68 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A2: 4,6 => CTR => A2: 3 * PRF A2: 3 # C3: 4,7 => SOL * STA A2: 3 + C3: 4,7 * CNT 2 HDP CHAINS / 2 HYP OPENED