Analysis of zz-werner-guess-000-base.sdk
Contents
Original Sudoku
level: medium
position: 521...7.3.6.....5...8...4.1...7...4.....21....72.85...1.3.69..5...13...9..6.7.... initial
Autosolve
position: 521.4.7.3.6..1..5...8.5.4.1.1579..4.....215.7.72.85..6143.69.75.571346.9..657...4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 4,9 => CTR => A2: 3,7 * DIS # D3: 3,9 => CTR => D3: 2,6 * DIS # B5: 3,9 => CTR => B5: 8 * DIS # D1: 6,8 => CTR => D1: 9 * DIS # H1: 9 => CTR => H1: 6,8 * DIS # G2: 2,8 => CTR => G2: 9 * PRF # D2: 2,8 => SOL * DIS # F2: 2,8 => CTR => F2: 3,7 * DIS # A5: 4,9 => CTR => A5: 3,6,8 * PRF # D5: 4 => SOL * DIS # A4: 8 => CTR => A4: 3,6 * DIS # F3: 3,6 => CTR => F3: 2,7 * PRF # D5: 3,4 => SOL * DIS # D5: 6 => CTR => D5: 3,4 * DIS # A6: 9 => CTR => A6: 3,4 * DIS # G4: 3 => CTR => G4: 2,8 * DIS # A9: 9 => CTR => A9: 2,8 * PRF # A9: 8,9 => SOL * DIS # A9: 2 => CTR => A9: 8,9 * DIS # B5: 3 => CTR => B5: 8,9 * PRF # D2: 2,8 => SOL * DIS # A9: 9 => CTR => A9: 2,8 * DIS # F2: 2,8 => CTR => F2: 3,7 * DIS # G2: 2,8 => CTR => G2: 9 * DIS # G6: 9 => CTR => G6: 1,3 * CNT 25 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 4,9 => CTR => A2: 3,7 * DIS A2: 3,7 # A3: 7 => CTR => A3: 3,9 * DIS A2: 3,7 + A3: 3,9 # D1: 6,8 => CTR => D1: 9 * PRF A2: 3,7 + A3: 3,9 + D1: 9 # D2: 2,8 => SOL * STA A2: 3,7 + A3: 3,9 + D1: 9 + D2: 2,8 * CNT 4 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 521...7.3.6.....5...8...4.1...7...4.....21....72.85...1.3.69..5...13...9..6.7.... | initial |
| 521.4.7.3.6..1..5...8.5.4.1.1579..4.....215.7.72.85..6143.69.75.571346.9..657...4 | autosolve |
| 521948763764213958938657421315796842689421537472385196143869275257134689896572314 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) C2: 4,9 B3: 3,9 F1: 6,8 I2: 2,8 C5: 4,9 F4: 3,6 D6: 3,4 I4: 2,8 A8: 2,8 B9: 8,9 D7: 2,8 F9: 2,8 G7: 2,8 H8: 2,8 G9: 1,3 H9: 1,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G6,H6: 1.. / G6 = 1 => 19 pairs (_) / H6 = 1 => 16 pairs (_) G9,H9: 1.. / G9 = 1 => 16 pairs (_) / H9 = 1 => 19 pairs (_) G6,G9: 1.. / G6 = 1 => 19 pairs (_) / G9 = 1 => 16 pairs (_) H6,H9: 1.. / H6 = 1 => 16 pairs (_) / H9 = 1 => 19 pairs (_) G4,I4: 2.. / G4 = 2 => 0 pairs (X) / I4 = 2 => 17 pairs (_) A8,A9: 2.. / A8 = 2 => 0 pairs (*) / A9 = 2 => 0 pairs (X) D7,F9: 2.. / D7 = 2 => 0 pairs (X) / F9 = 2 => 0 pairs (_) G7,H8: 2.. / G7 = 2 => 0 pairs (*) / H8 = 2 => 0 pairs (X) D7,G7: 2.. / D7 = 2 => 0 pairs (X) / G7 = 2 => 0 pairs (_) A8,H8: 2.. / A8 = 2 => 0 pairs (*) / H8 = 2 => 0 pairs (X) A9,F9: 2.. / A9 = 2 => 0 pairs (X) / F9 = 2 => 0 pairs (_) H3,H8: 2.. / H3 = 2 => 0 pairs (*) / H8 = 2 => 0 pairs (X) I2,I4: 2.. / I2 = 2 => 0 pairs (X) / I4 = 2 => 17 pairs (_) G9,H9: 3.. / G9 = 3 => 19 pairs (_) / H9 = 3 => 16 pairs (_) B3,B5: 3.. / B3 = 3 => 17 pairs (_) / B5 = 3 => 0 pairs (X) A2,C2: 4.. / A2 = 4 => 0 pairs (X) / C2 = 4 => 21 pairs (_) D5,D6: 4.. / D5 = 4 => 0 pairs (*) / D6 = 4 => 0 pairs (X) A6,D6: 4.. / A6 = 4 => 0 pairs (*) / D6 = 4 => 0 pairs (X) C2,C5: 4.. / C2 = 4 => 21 pairs (_) / C5 = 4 => 0 pairs (X) H1,H3: 6.. / H1 = 6 => 0 pairs (*) / H3 = 6 => 0 pairs (X) A4,A5: 6.. / A4 = 6 => 0 pairs (X) / A5 = 6 => 0 pairs (_) F4,D5: 6.. / F4 = 6 => 0 pairs (*) / D5 = 6 => 0 pairs (X) A4,F4: 6.. / A4 = 6 => 0 pairs (X) / F4 = 6 => 0 pairs (_) A5,D5: 6.. / A5 = 6 => 0 pairs (*) / D5 = 6 => 0 pairs (X) A2,A3: 7.. / A2 = 7 => 24 pairs (_) / A3 = 7 => 16 pairs (_) F2,F3: 7.. / F2 = 7 => 16 pairs (_) / F3 = 7 => 24 pairs (_) A2,F2: 7.. / A2 = 7 => 24 pairs (_) / F2 = 7 => 16 pairs (_) A3,F3: 7.. / A3 = 7 => 16 pairs (_) / F3 = 7 => 24 pairs (_) D7,F9: 8.. / D7 = 8 => 0 pairs (*) / F9 = 8 => 0 pairs (X) G7,H8: 8.. / G7 = 8 => 0 pairs (X) / H8 = 8 => 0 pairs (_) D7,G7: 8.. / D7 = 8 => 0 pairs (*) / G7 = 8 => 0 pairs (X) A8,H8: 8.. / A8 = 8 => 0 pairs (X) / H8 = 8 => 0 pairs (_) B5,B9: 8.. / B5 = 8 => 19 pairs (_) / B9 = 8 => 0 pairs (X) I2,I4: 8.. / I2 = 8 => 17 pairs (_) / I4 = 8 => 0 pairs (X) A9,B9: 9.. / A9 = 9 => 0 pairs (X) / B9 = 9 => 19 pairs (_) D1,H1: 9.. / D1 = 9 => 17 pairs (_) / H1 = 9 => 0 pairs (X) C2,C5: 9.. / C2 = 9 => 0 pairs (X) / C5 = 9 => 21 pairs (_) G2,G6: 9.. / G2 = 9 => 19 pairs (_) / G6 = 9 => 0 pairs (X) * DURATION: 0:01:01.757229 START: 03:15:46.951951 END: 03:16:48.709180 2017-05-01 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B3,B9,C2,C5,D6,D7,F1,F4,F9,G7,G9,H8,H9,I2,I4) * 521.4.7.3.6..1..5...8.5.4.1.1579..4.....215.7.72.85..6143.69.75.571346.9..657...4 * PAIR C2: 4,9 BLK 1 A2: 4,9,3,7 # reduction candidate for 4,9 A2: 4,9 => CTR * 521.4.7.3.6.317.5.738.5.4.1615793.4....6215.7.72485..6143.69.75.571346.9..657...4 A2: 3,7 # 23 pairs * PAIR B3: 3,9 BLK 1 A2: 3,9,4,7 # reduction candidate for 3,9 A2: 3,9 # 22 pairs A3: 3,9,7 # reduction candidate for 3,9 A3: 3,9 # 24 pairs * PAIR B3: 3,9 ROW 3 D3: 3,9,2,6 # reduction candidate for 3,9 D3: 3,9 => CTR * 521.4.7.3.6..1795.79835.4.1615793.4..396215.7.72485..6143.69.75.571346.9..657...4 D3: 2,6 # 17 pairs * PAIR B3: 3,9 COL B B5: 3,9,8 # reduction candidate for 3,9 B5: 3,9 => CTR * 52194876346921..5...8.5.421.1579..428..6215.7.72485..6143869275257134689986572..4 B5: 8 # 19 pairs * PAIR F1: 6,8 BLK 2 D1: 6,8,9 # reduction candidate for 6,8 D1: 6,8 => CTR * 521846793.6..1..5..38.5.461615793.4.38..215.7.72.85916143.69.75.57134629296578134 D1: 9 # 17 pairs * PAIR F1: 6,8 ROW 1 H1: 6,8,9 # reduction candidate for 6,8 H1: 9 => CTR * 521846793.6..1..5..38.5.461615793.4.38..215.7.72.85916143.69.75.57134629296578134 H1: 6,8 # 17 pairs * PAIR I2: 2,8 BLK 3 G2: 2,8,9 # reduction candidate for 2,8 G2: 2,8 => CTR * 521.4.7.3.6..1..5...8.5.4.1.1579.342....21587.72.85916143.69875857134629296578134 G2: 9 # 19 pairs * PAIR I2: 2,8 ROW 2 D2: 2,8,3,9 # reduction candidate for 2,8 D2: 2,8 => SOLVED * 521948763764213958938657421315796842689421537472385196143869275257134689896572314 D2: 3,9 # 17 pairs F2: 2,8,3,7 # reduction candidate for 2,8 F2: 2,8 => CTR * 521946783764318952..825746161579324...96215.7.72485.96143.69.75.571346.9..657..14 F2: 3,7 # 17 pairs * PAIR C5: 4,9 BLK 4 A5: 4,9,3,6,8 # reduction candidate for 4,9 A5: 4,9 => CTR * 52194.7.3.6.31.95.938257461615793.4.489621537372485196143869275.571346.9.9657.314 A5: 3,6,8 # 16 pairs A6: 4,9,3 # reduction candidate for 4,9 A6: 4,9 # 18 pairs * PAIR F4: 3,6 BLK 5 D5: 3,6,4 # reduction candidate for 3,6 D5: 4 => SOLVED * 521948763764213958938657421315796842689421537472385196143869275257134689896572314 D5: 3,6 # 17 pairs * PAIR F4: 3,6 ROW 4 A4: 3,6,8 # reduction candidate for 3,6 A4: 8 => CTR * 521.4.7.3.6..1..5...8.5.4.18157963426...21587.72.85..6143.698752571346.9..657...4 A4: 3,6 # 19 pairs * PAIR F4: 3,6 COL F F3: 3,6,2,7 # reduction candidate for 3,6 F3: 3,6 => CTR * 521.48763.6.217958798.5.421.1579.842.39.215.7.72.85..6143869275257134689..6572..4 F3: 2,7 # 17 pairs * PAIR D6: 3,4 BLK 5 D5: 3,4,6 # reduction candidate for 3,4 D5: 3,4 => SOLVED * 521948763764213958938657421315796842689421537472385196143869275257134689896572314 D5: 6 => CTR * 52194.7.3.6431.95..3825.461615793.4.489621537372485196143869275.571346.9..657.314 * PAIR D6: 3,4 ROW 6 A6: 3,4,9 # reduction candidate for 3,4 A6: 9 => CTR * 521.4.7.3.69.1..5..38.5.4.1.1579..4..84.21597972485..6143.69.75.571346.9.9657...4 A6: 3,4 # 20 pairs * PAIR I4: 2,8 BLK 6 G4: 2,8,3 # reduction candidate for 2,8 G4: 3 => CTR * 521.4.7.3.6..1..5...8.5.4.1.1579.342....21587.72.85..6143.69875857134629296578134 G4: 2,8 # 19 pairs * PAIR A8: 2,8 BLK 7 A9: 2,8,9 # reduction candidate for 2,8 A9: 9 => CTR * 52194876346921..5...8.5.421.1579..428..6215.7.72485..6143869275257134689986572..4 A9: 2,8 # 19 pairs * PAIR B9: 8,9 BLK 7 A9: 8,9,2 # reduction candidate for 8,9 A9: 8,9 => SOLVED * 521948763764213958938657421315796842689421537472385196143869275257134689896572314 A9: 2 => CTR * 521.46783.6..1..5..38.5.461615793.4..8.6215.7.72485..6143269875857134629296578..4 * PAIR B9: 8,9 COL B B5: 8,9,3 # reduction candidate for 8,9 B5: 3 => CTR * 521.4.7.3.6..1..5..98.5.4.1.1579..4..39.21587472385..6143869.75.571346.9.86572..4 B5: 8,9 # 17 pairs * PAIR D7: 2,8 COL D D2: 2,8,3,9 # reduction candidate for 2,8 D2: 2,8 => SOLVED * 521948763764213958938657421315796842689421537472385196143869275257134689896572314 D2: 3,9 # 17 pairs * PAIR F9: 2,8 ROW 9 A9: 2,8,9 # reduction candidate for 2,8 A9: 9 => CTR * 52194876346921..5...8.5.421.1579..428..6215.7.72485..6143869275257134689986572..4 A9: 2,8 # 19 pairs * PAIR F9: 2,8 COL F F2: 2,8,3,7 # reduction candidate for 2,8 F2: 2,8 => CTR * 521946783764318952..825746161579324...96215.7.72485.96143.69.75.571346.9..657..14 F2: 3,7 # 17 pairs * PAIR G7: 2,8 COL G G2: 2,8,9 # reduction candidate for 2,8 G2: 2,8 => CTR * 521.4.7.3.6..1..5...8.5.4.1.1579.342....21587.72.85916143.69875857134629296578134 G2: 9 # 19 pairs G4: 2,8,3 # reduction candidate for 2,8 G4: 2,8 # 19 pairs * PAIR G9: 1,3 COL G G6: 1,3,9 # reduction candidate for 1,3 G6: 9 => CTR * 521.4.7.3.6..1..5...8.5.4.1.1579.342....21587.72.85916143.69875857134629296578134 G6: 1,3 # 19 pairs * PAIR H9: 1,3 COL H H6: 1,3,9 # reduction candidate for 1,3 H6: 9 # 19 pairs H6: 1,3 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-werner-guess-000-base-pr-000.dot * REASONING * DIS # A2: 4,9 => CTR => A2: 3,7 * DIS # D3: 3,9 => CTR => D3: 2,6 * DIS # B5: 3,9 => CTR => B5: 8 * DIS # D1: 6,8 => CTR => D1: 9 * DIS # H1: 9 => CTR => H1: 6,8 * DIS # G2: 2,8 => CTR => G2: 9 * PRF # D2: 2,8 => SOL * DIS # F2: 2,8 => CTR => F2: 3,7 * DIS # A5: 4,9 => CTR => A5: 3,6,8 * PRF # D5: 4 => SOL * DIS # A4: 8 => CTR => A4: 3,6 * DIS # F3: 3,6 => CTR => F3: 2,7 * PRF # D5: 3,4 => SOL * DIS # D5: 6 => CTR => D5: 3,4 * DIS # A6: 9 => CTR => A6: 3,4 * DIS # G4: 3 => CTR => G4: 2,8 * DIS # A9: 9 => CTR => A9: 2,8 * PRF # A9: 8,9 => SOL * DIS # A9: 2 => CTR => A9: 8,9 * DIS # B5: 3 => CTR => B5: 8,9 * PRF # D2: 2,8 => SOL * DIS # A9: 9 => CTR => A9: 2,8 * DIS # F2: 2,8 => CTR => F2: 3,7 * DIS # G2: 2,8 => CTR => G2: 9 * DIS # G6: 9 => CTR => G6: 1,3 * CNT 25 HDP CHAINS / 52 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B3,B9,C2,C5,D6,D7,F1,F4,F9,G7,G9,H8,H9,I2,I4) * 521.4.7.3.6..1..5...8.5.4.1.1579..4.....215.7.72.85..6143.69.75.571346.9..657...4 * PAIR C2: 4,9 BLK 1 A2: 4,9,3,7 # reduction candidate for 4,9 A2: 4,9 => CTR * 521.4.7.3.6.317.5.738.5.4.1615793.4....6215.7.72485..6143.69.75.571346.9..657...4 * PAIR B3: 3,9 BLK 1 A3: 3,9,7 # reduction candidate for 3,9 A3: 7 => CTR * 521.4.7.3.64.1..5.798.5.4.1.1579..4..39.21587472385..6143.698758571346.9..657...4 * PAIR F1: 6,8 BLK 2 D1: 6,8,9 # reduction candidate for 6,8 D1: 6,8 => CTR * 521.4.793764913.5...8257461.15796.4.6.94215.7472385916143869275.571346.9..657...4 * PAIR I2: 2,8 ROW 2 D2: 2,8,3 # reduction candidate for 2,8 D2: 2,8 => SOLVED * 521948763764213958938657421315796842689421537472385196143869275257134689896572314 * DURATION: 0:00:08.832121 START: 03:17:38.716235 END: 03:17:47.548356 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-werner-guess-000-base-pr-001.dot * REASONING * DIS # A2: 4,9 => CTR => A2: 3,7 * DIS A2: 3,7 # A3: 7 => CTR => A3: 3,9 * DIS A2: 3,7 + A3: 3,9 # D1: 6,8 => CTR => D1: 9 * PRF A2: 3,7 + A3: 3,9 + D1: 9 # D2: 2,8 => SOL * STA A2: 3,7 + A3: 3,9 + D1: 9 + D2: 2,8 * CNT 4 HDP CHAINS / 5 HYP OPENED
Header Info
-------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 521.4.7.3.6..1..5...8.5.4.1.1579..4.....215.7.72.85..6143.69.75.571346.9..657...4 C2: 4,9 A2: 3,4,7,9 # reduction candidate for 4,9 A2: 4,9 => CTR * 521.4.7.3.6.317.5.738.5.4.1615793.4....6215.7.72485..6143.69.75.571346.9..657...4 B3: 3,9 A3: 3,7,9 # reduction candidate for 3,9 A3: 7 => CTR * 521.4.7.3.64.1..5.798.5.4.1.1579..4..39.21587472385..6143.698758571346.9..657...4 F1: 6,8 D1: 6,8,9 # reduction candidate for 6,8 D1: 6,8 => CTR * 521.4.793764913.5...8257461.15796.4.6.94215.7472385916143869275.571346.9..657...4 I2: 2,8 D2: 2,3,8 # reduction candidate for 2,8 D2: 2,8 => SOLVED * 521948763764213958938657421315796842689421537472385196143869275257134689896572314 * SOLVED! -------------------------------------------------- A single check of (all) 2-value alternatives detects the solution. Therefore, there is no need to guess. step-00 -------------------------------------------------- G7,H8: 2,8 => G9,H9 != 2,8 step-01 -------------------------------------------------- Highlight 1,3 to detect Pair-Square: G6,H6,G9,H9: 1,3.. Disable G6,H6: 9.. to show that at least one is needed: G6,H6 != 9 => H5 = 9 + G2 = 9 H5 = 9 => C5 = 4 => C2 = 9 => G2 != 9 => CTR => H5 != 9 => G6 = 9 or H6 = 9 auto .. Q6: 9.. = G6,H6: 9.. => A6 != 9 step-02 -------------------------------------------------- A6,D6: 4,3 => G6,H6 != 3 step-03 -------------------------------------------------- Interesting Pair-Square (highlight 2,8) shortcut conclusion: G2,I4,G4,I2: 2,8.. => G2 = 9 or G4 = 3 G4 = 3 has the same effect as G4 = 8, therefore G2 = 9! G4 = 3 => H5 = 8 => H8 = 2 => A8 = 8 G4 = 3 => F4 = 6 => A4 = 8 => A8 != 8 => CTR auto .. step-04 -------------------------------------------------- highlight 8 F1: 6,8 H1: 6,8 H8: 2,8 A8: 2,8 A9: 2,8 F9: 2,8 => F2 != 8 # swordfish D2: 2,3,8 I2: 2,8 F2: 2,3 D2 = 2 => I2 = 8 + F2 = 3 D2 = 8 => I2 = 2 + F2 = 3 F2 = 3 => F4 = 6 => D3 = 6 => F1 = 8 => D2 != 8 D2 = 8 => D2 = 2 => D2 != 8 turn off single/row column detection, auto .. reveals either single: D7 = 8 alternatively, a single row/column is found: Q2: 8.. = F1,F2: 8.. => F9 != 8 step-05 -------------------------------------------------- The long way ... from step-05 -------------------------------------------------- F2: 2,3,8 I2: 2,8 D2: 2,3 F2 = 2 => I2 = 8 + (F1 = 6 => D3 = 2) => D2 = 3 F2 = 8 => I2 = 2 + D2 = 3 D2 = 3 => F4 = 3 + D6 = 4 => D5 = 6 => D3 = 2 => F2 = 8 F2 = 2 => F2 = 8 => F2 != 2 step-10 -------------------------------------------------- Highlight implication chain 8 F2 = 8 => I2 != 8 => H1 = 8 => H8 != 8 => G7 = 8 => D7 != 8 => F9 = 8 => CTR => F2 != 8 => F2 = 3 Highlight implication chain 2 I2 = 2 => D2,F2 != 2 I2 = 2 => I4 != 2 => G4 = 2 => G7 != 2 => H8 = 2 => A8 != 2 => A9 = 2 => F9 != 2 => D7 = 2 => D3 != 2 => D2,F2,D3 != 2 => CTR => I2 != 2 step-11 -------------------------------------------------- auto .. solved. |:info:| XYZ-Wing: Z=8, X=2, Y= 3 (no effect) G4: 2,3,8 + H5: 3,8 + H8: 2,8 => no cells = 8.. * POSITIONS orig Original Sudoku d: 0 h: 0 521...7.3.6.....5...8...4.1...7...4.....21....72.85...1.3.69..5...13...9..6.7.... ===== ======================================== ===== ===== ================================================================================= 0 Solution d: 18 h: 0 521948763764213958938657421315796842689421537472385196143869275257134689896572314 1 Original Sudoku d: 0 h: 0 521...7.3.6.....5...8...4.1...7...4.....21....72.85...1.3.69..5...13...9..6.7.... 2 auto solve d: 4 h: 0 521.4.7.3.6..1..5...8.5.4.1.1579..4.....215.7.72.85..6143.69.75.571346.9..657...4 3 G6,H6,G9,H9: 1,3,9 => G7 = 9 or H7 = 9 d: 4 h: 26 521.4.7.3.6..1..5...8.5.4.1.1579..4.....215.7.72.85..6143.69.75.571346.9..657...4 ----- ---------------------------------------- ----- ----- --------------------------------------------------------------------------------- save => H5 != 9 and A6 != 9 d: 6 h: 26 521.4.7.3.6..1..5...8.5.4.1.1579..4.....215.7.72.85..6143.69.75.571346.9..657...4 ===== ======================================== ===== ===== ================================================================================= view* auto solve d: 8 h: 26 521.4.7.3.6..1..5...8.5.4.1.1579..4.....215.7.72.85..6143.69.75.571346.9..657...4 ===== ======================================== ===== ===== ================================================================================= 0 Solution d: 18 h: 0 521948763764213958938657421315796842689421537472385196143869275257134689896572314
Solution
position: 521948763764213958938657421315796842689421537472385196143869275257134689896572314 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: 4,9 => CTR => A2: 3,7 * INC # A2: 3,7 => UNS * INC # A2: 3,9 => UNS * INC # A3: 3,9 => UNS * DIS # D3: 3,9 => CTR => D3: 2,6 * INC # D3: 2,6 => UNS * DIS # B5: 3,9 => CTR => B5: 8 * INC # B5: 8 => UNS * DIS # D1: 6,8 => CTR => D1: 9 * INC # D1: 9 => UNS * INC # H1: 6,8 => UNS * DIS # H1: 9 => CTR => H1: 6,8 * DIS # G2: 2,8 => CTR => G2: 9 * INC # G2: 9 => UNS * PRF # D2: 2,8 => SOL * INC # D2: 3,9 => UNS * DIS # F2: 2,8 => CTR => F2: 3,7 * INC # F2: 3,7 => UNS * DIS # A5: 4,9 => CTR => A5: 3,6,8 * INC # A5: 3,6,8 => UNS * INC # A6: 4,9 => UNS * INC # D5: 3,6 => UNS * PRF # D5: 4 => SOL * INC # A4: 3,6 => UNS * DIS # A4: 8 => CTR => A4: 3,6 * DIS # F3: 3,6 => CTR => F3: 2,7 * INC # F3: 2,7 => UNS * PRF # D5: 3,4 => SOL * DIS # D5: 6 => CTR => D5: 3,4 * INC # A6: 3,4 => UNS * DIS # A6: 9 => CTR => A6: 3,4 * INC # G4: 2,8 => UNS * DIS # G4: 3 => CTR => G4: 2,8 * INC # A9: 2,8 => UNS * DIS # A9: 9 => CTR => A9: 2,8 * PRF # A9: 8,9 => SOL * DIS # A9: 2 => CTR => A9: 8,9 * INC # B5: 8,9 => UNS * DIS # B5: 3 => CTR => B5: 8,9 * PRF # D2: 2,8 => SOL * INC # D2: 3,9 => UNS * INC # A9: 2,8 => UNS * DIS # A9: 9 => CTR => A9: 2,8 * DIS # F2: 2,8 => CTR => F2: 3,7 * INC # F2: 3,7 => UNS * DIS # G2: 2,8 => CTR => G2: 9 * INC # G2: 9 => UNS * INC # G4: 2,8 => UNS * INC # G6: 1,3 => UNS * DIS # G6: 9 => CTR => G6: 1,3 * INC # H6: 1,3 => UNS * INC # H6: 9 => UNS * CNT 52 HDP CHAINS / 52 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A2: 4,9 => CTR => A2: 3,7 * INC A2: 3,7 # A3: 3,9 => UNS * DIS A2: 3,7 # A3: 7 => CTR => A3: 3,9 * DIS A2: 3,7 + A3: 3,9 # D1: 6,8 => CTR => D1: 9 * PRF A2: 3,7 + A3: 3,9 + D1: 9 # D2: 2,8 => SOL * STA A2: 3,7 + A3: 3,9 + D1: 9 + D2: 2,8 * CNT 5 HDP CHAINS / 5 HYP OPENED