Analysis of zz-www.sudokuoftheday.co.uk-20060903-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Sep&YEAR=2006
level: medium
position: ......13...2.....49.......6.437.2.9.....34..1..81.9...6.........8.5.....794....2. initial
Autosolve
position: 456..813.8.2.....49.7.....61437.2.9...9.34..1..81.9...625....1.38152....794....2. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F2: 1,3 => CTR => F2: 5,6 * PRF # F3: 1,3 => SOL * DIS # F3: 5 => CTR => F3: 1,3 * DIS # I1: 7 => CTR => I1: 2,9 * DIS # E2: 7,9 => CTR => E2: 1,6 * DIS # I1: 7,9 => CTR => I1: 2 * PRF # I1: 2 => SOL * DIS # G2: 5,7 => CTR => G2: 9 * DIS # H6: 5,7 => CTR => H6: 4,6 * PRF # G3: 5,8 => SOL * DIS # G3: 2 => CTR => G3: 5,8 * PRF # H5: 5,8 => SOL * DIS # H5: 6,7 => CTR => H5: 5,8 * DIS # G5: 6,7,8 => CTR => G5: 2,5 * DIS # G5: 6,7 => CTR => G5: 2,5,8 * DIS # H5: 6,7 => CTR => H5: 5,8 * PRF # H5: 5,8 => SOL * DIS # G6: 2,5 => CTR => G6: 3,4,6,7 * DIS # I6: 2,5 => CTR => I6: 3,7 * PRF # I6: 3,7 => SOL * DIS # G6: 6,7 => CTR => G6: 2,3,4,5 * DIS # H6: 6,7 => CTR => H6: 4,5 * PRF # E4: 6,8 => SOL * DIS # E4: 5 => CTR => E4: 6,8 * DIS # G5: 6,8 => CTR => G5: 2,5,7 * PRF # H5: 6,8 => SOL * DIS # D9: 3 => CTR => D9: 6,8 * PRF # E4: 8 => SOL * DIS # G6: 5,6 => CTR => G6: 2,3,4,7 * DIS # H6: 5,6 => CTR => H6: 4,7 * DIS # G4: 5,8 => CTR => G4: 6 * DIS # G5: 5,8 => CTR => G5: 2,6,7 * PRF # H5: 5,8 => SOL * DIS # H5: 6,7 => CTR => H5: 5,8 * DIS # E4: 6 => CTR => E4: 5,8 * PRF # G7: 3,7 => SOL * DIS # G8: 6,7 => CTR => G8: 4,9 * DIS # G8: 7,9 => CTR => G8: 4,6 * DIS # I1: 7,9 => CTR => I1: 2 * PRF # I1: 2 => SOL * DIS # G9: 6 => CTR => G9: 3,5 * DIS # I6: 3,5 => CTR => I6: 2,7 * CNT 42 HDP CHAINS / 69 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F2: 1,3 => CTR => F2: 5,6 * PRF F2: 5,6 # F3: 1,3 => SOL * STA F2: 5,6 + F3: 1,3 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ......13...2.....49.......6.437.2.9.....34..1..81.9...6.........8.5.....794....2. | initial |
| 456..813.8.2.....49.7.....61437.2.9...9.34..1..81.9...625....1.38152....794....2. | autosolve |
| 456978132812365974937241856143782695579634281268159347625493718381527469794816523 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) B2: 1,3 B3: 1,3 D1: 2,9 E1: 7,9 E3: 1,4 H2: 5,7 H3: 5,8 A5: 2,5 B5: 6,7 A6: 2,5 B6: 6,7 D5: 6,8 E6: 5,6 I4: 5,8 D7: 4,9 E7: 4,9 F7: 3,7 F8: 6,7 I8: 7,9 I9: 3,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,B3: 1.. / B2 = 1 => 20 pairs (_) / B3 = 1 => 19 pairs (_) E9,F9: 1.. / E9 = 1 => 0 pairs (*) / F9 = 1 => 0 pairs (X) D1,D3: 2.. / D1 = 2 => 0 pairs (X) / D3 = 2 => 0 pairs (_) I1,G3: 2.. / I1 = 2 => 0 pairs (*) / G3 = 2 => 0 pairs (X) A5,A6: 2.. / A5 = 2 => 0 pairs (X) / A6 = 2 => 0 pairs (_) D1,I1: 2.. / D1 = 2 => 0 pairs (X) / I1 = 2 => 0 pairs (_) D3,G3: 2.. / D3 = 2 => 0 pairs (*) / G3 = 2 => 0 pairs (X) A5,G5: 2.. / A5 = 2 => 0 pairs (X) / G5 = 2 => 0 pairs (_) I1,I6: 2.. / I1 = 2 => 0 pairs (*) / I6 = 2 => 0 pairs (X) B2,B3: 3.. / B2 = 3 => 19 pairs (_) / B3 = 3 => 20 pairs (_) G6,I6: 3.. / G6 = 3 => 24 pairs (_) / I6 = 3 => 0 pairs (X) D3,E3: 4.. / D3 = 4 => 0 pairs (X) / E3 = 4 => 19 pairs (_) G6,H6: 4.. / G6 = 4 => 0 pairs (X) / H6 = 4 => 22 pairs (_) D7,E7: 4.. / D7 = 4 => 19 pairs (_) / E7 = 4 => 0 pairs (X) G8,H8: 4.. / G8 = 4 => 22 pairs (_) / H8 = 4 => 0 pairs (X) D3,D7: 4.. / D3 = 4 => 0 pairs (X) / D7 = 4 => 19 pairs (_) E3,E7: 4.. / E3 = 4 => 19 pairs (_) / E7 = 4 => 0 pairs (X) G6,G8: 4.. / G6 = 4 => 0 pairs (X) / G8 = 4 => 22 pairs (_) H6,H8: 4.. / H6 = 4 => 22 pairs (_) / H8 = 4 => 0 pairs (X) F2,F3: 5.. / F2 = 5 => 0 pairs (*) / F3 = 5 => 0 pairs (X) A5,A6: 5.. / A5 = 5 => 0 pairs (*) / A6 = 5 => 0 pairs (X) E4,E6: 5.. / E4 = 5 => 0 pairs (X) / E6 = 5 => 0 pairs (_) G9,I9: 5.. / G9 = 5 => 0 pairs (*) / I9 = 5 => 0 pairs (X) B5,B6: 6.. / B5 = 6 => 23 pairs (_) / B6 = 6 => 0 pairs (*) E4,G4: 6.. / E4 = 6 => 0 pairs (X) / G4 = 6 => 26 pairs (_) E1,E2: 7.. / E1 = 7 => 20 pairs (_) / E2 = 7 => 0 pairs (X) B5,B6: 7.. / B5 = 7 => 0 pairs (*) / B6 = 7 => 0 pairs (X) F7,F8: 7.. / F7 = 7 => 0 pairs (X) / F8 = 7 => 27 pairs (_) E1,I1: 7.. / E1 = 7 => 20 pairs (_) / I1 = 7 => 0 pairs (X) G3,H3: 8.. / G3 = 8 => 0 pairs (*) / H3 = 8 => 0 pairs (X) E4,D5: 8.. / E4 = 8 => 0 pairs (*) / D5 = 8 => 0 pairs (X) D9,E9: 8.. / D9 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) G7,I7: 8.. / G7 = 8 => 23 pairs (_) / I7 = 8 => 0 pairs (*) D5,D9: 8.. / D5 = 8 => 22 pairs (_) / D9 = 8 => 0 pairs (*) E4,E9: 8.. / E4 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) H3,H5: 8.. / H3 = 8 => 20 pairs (_) / H5 = 8 => 0 pairs (*) I4,I7: 8.. / I4 = 8 => 23 pairs (_) / I7 = 8 => 0 pairs (*) I1,G2: 9.. / I1 = 9 => 0 pairs (X) / G2 = 9 => 21 pairs (_) D7,E7: 9.. / D7 = 9 => 0 pairs (X) / E7 = 9 => 19 pairs (_) G8,I8: 9.. / G8 = 9 => 0 pairs (X) / I8 = 9 => 21 pairs (_) G2,G8: 9.. / G2 = 9 => 21 pairs (_) / G8 = 9 => 0 pairs (X) I1,I8: 9.. / I1 = 9 => 0 pairs (X) / I8 = 9 => 21 pairs (_) * DURATION: 0:00:51.803808 START: 02:19:31.435670 END: 02:20:23.239478 2019-05-01 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B2,B3,B5,B6,D1,D5,D7,E1,E3,E6,E7,F7,F8,H2,H3,I4,I8,I9) * 456..813.8.2.....49.7.....61437.2.9...9.34..1..81.9...625....1.38152....794....2. * PAIR B2: 1,3 ROW 2 F2: 1,3,5,6 # reduction candidate for 1,3 F2: 1,3 => CTR * 4562.813.8.26....49.7..5286143752698269834..157816934262594.81.38152.46979438..2. F2: 5,6 # 21 pairs * PAIR B3: 1,3 ROW 3 F3: 1,3,5 # reduction candidate for 1,3 F3: 1,3 => SOLVED * 456978132812365974937241856143782695579634281268159347625493718381527469794816523 F3: 5 => CTR * 4562.813.8.2.....49.7..5286143752698269834..1578169342625...81.38152.469794.81523 * PAIR D1: 2,9 ROW 1 I1: 2,9,7 # reduction candidate for 2,9 I1: 7 => CTR * 4562981378.2.7.9549.74152861437526982698345715781693.262594..1.38152...9794....25 I1: 2,9 # 20 pairs * PAIR E1: 7,9 BLK 2 E2: 7,9,1,6 # reduction candidate for 7,9 E2: 7,9 => CTR * 4562.813.8.2.....49.7415286143752698269834..157816934262594.81.38152.469794.81523 E2: 1,6 # 19 pairs * PAIR E1: 7,9 ROW 1 I1: 7,9,2 # reduction candidate for 7,9 I1: 7,9 => CTR * 4562.813.8.2.....49.7..5286143752698269834..1578169342625...81.38152.469794.81523 I1: 2 => SOLVED * 456978132812365974937241856143782695579634281268159347625493718381527469794816523 * PAIR H2: 5,7 BLK 3 G2: 5,7,9 # reduction candidate for 5,7 G2: 5,7 => CTR * 456..81398.2.....49.7...2861437.2.9.2.9.34..15.8169..2625....1.38152.947794...62. G2: 9 # 21 pairs * PAIR H2: 5,7 COL H H5: 5,7,6,8 # reduction candidate for 5,7 H5: 5,7 # 23 pairs H6: 5,7,4,6 # reduction candidate for 5,7 H6: 5,7 => CTR * 456..81328.2...9749.724...61437.2.98..9.34..1..81.94.3625....1.38152..4.794....25 H6: 4,6 # 21 pairs * PAIR H3: 5,8 BLK 3 G3: 5,8,2 # reduction candidate for 5,8 G3: 5,8 => SOLVED * 456978132812365974937241856143782695579634281268159347625493718381527469794816523 G3: 2 => CTR * 4562.813.8.2.....49.7..5286143752698269834..1578169342625...81.38152.469794.81523 * PAIR H3: 5,8 COL H H5: 5,8,6,7 # reduction candidate for 5,8 H5: 5,8 => SOLVED * 456978132812365974937241856143782695579634281268159347625493718381527469794816523 H5: 6,7 => CTR * 456..813.8.2..6.549.7..5286143752698269834571.78169...625...81.38152..6.794681325 * PAIR A5: 2,5 ROW 5 G5: 2,5,6,7,8 # reduction candidate for 2,5 G5: 6,7,8 => CTR * 456.781328.2..6.749.7....86143752698269834751578169.4.625...81.381527469794.81325 G5: 2,5 # 21 pairs * PAIR B5: 6,7 ROW 5 G5: 6,7,2,5,8 # reduction candidate for 6,7 G5: 6,7 => CTR * 456.781328.2..6.749.7....86143752698269834751578169.4.625...81.381527469794.81325 G5: 2,5,8 # 20 pairs H5: 6,7,5,8 # reduction candidate for 6,7 H5: 6,7 => CTR * 456..813.8.2..6.549.7..5286143752698269834571.78169...625...81.38152..6.794681325 H5: 5,8 => SOLVED * 456978132812365974937241856143782695579634281268159347625493718381527469794816523 * PAIR A6: 2,5 ROW 6 G6: 2,5,3,4,6,7 # reduction candidate for 2,5 G6: 2,5 => CTR * 456..81328.2...9749.724...61437.2.98..98347.1.7816924362549.817381527469794.81325 G6: 3,4,6,7 # 20 pairs I6: 2,5,3,7 # reduction candidate for 2,5 I6: 2,5 => CTR * 456..813.8.2..69549.7..5286143752698.69834..1.7816934.625...81.38152.469794.81523 I6: 3,7 => SOLVED * 456978132812365974937241856143782695579634281268159347625493718381527469794816523 * PAIR B6: 6,7 ROW 6 G6: 6,7,2,3,4,5 # reduction candidate for 6,7 G6: 6,7 => CTR * 456..81328.2...9749.724...61437.2.98..98342.12.815974362549.817381527469794.81325 G6: 2,3,4,5 # 20 pairs H6: 6,7,4,5 # reduction candidate for 6,7 H6: 6,7 => CTR * 456..81328.2...9749.724...61437.2.98..9.34..1..81.94.3625....1.38152..4.794....25 H6: 4,5 # 21 pairs * PAIR D5: 6,8 BLK 5 E4: 6,8,5 # reduction candidate for 6,8 E4: 6,8 => SOLVED * 456978132812365974937241856143782695579634281268159347625493718381527469794816523 E4: 5 => CTR * 456..813.8.2..6..49.7..5286143752698269834..1578169.42625..381738152..6.794.81.2. * PAIR D5: 6,8 ROW 5 G5: 6,8,2,5,7 # reduction candidate for 6,8 G5: 6,8 => CTR * 456..813.8.2.....49.7.....61437.2.9.2.9.34.515.8169...625....1.38152..6.794....25 G5: 2,5,7 # 20 pairs H5: 6,8,5,7 # reduction candidate for 6,8 H5: 6,8 => SOLVED * 456978132812365974937241856143782695579634281268159347625493718381527469794816523 H5: 5,7 # 23 pairs * PAIR D5: 6,8 COL D D9: 6,8,3 # reduction candidate for 6,8 D9: 3 => CTR * 456..813.8.26....49.7....861437625985.98342.1..81.9...625....1.38152....794381625 D9: 6,8 # 23 pairs * PAIR E6: 5,6 BLK 5 E4: 5,6,8 # reduction candidate for 5,6 E4: 8 => SOLVED * 456978132812365974937241856143782695579634281268159347625493718381527469794816523 E4: 5,6 # 22 pairs * PAIR E6: 5,6 ROW 6 G6: 5,6,2,3,4,7 # reduction candidate for 5,6 G6: 5,6 => CTR * 456..81328.2...9749.724...61437.2.98..9.34..1..81.9.43625....1.38152.4.9794....25 G6: 2,3,4,7 # 20 pairs H6: 5,6,4,7 # reduction candidate for 5,6 H6: 5,6 => CTR * 456..81328.2...9749.724...61437.2.98..9.34..1..81.94.3625....1.38152..4.794....25 H6: 4,7 # 21 pairs * PAIR I4: 5,8 BLK 6 G4: 5,8,6 # reduction candidate for 5,8 G4: 5,8 => CTR * 456..81328.2...9.49.7....86143762.9.5.98342.12.8159...625....1.38152....794.81.2. G4: 6 # 26 pairs G5: 5,8,2,6,7 # reduction candidate for 5,8 G5: 5,8 => CTR * 456..813.8.2.....49.7.....6143752698269834571578169.4.625...81.38152.469794.8132. G5: 2,6,7 # 20 pairs H5: 5,8,6,7 # reduction candidate for 5,8 H5: 5,8 => SOLVED * 456978132812365974937241856143782695579634281268159347625493718381527469794816523 H5: 6,7 => CTR * 456..813.8.2..6.549.7..5286143752698269834571.78169...625...81.38152..6.794681325 * PAIR I4: 5,8 ROW 4 E4: 5,8,6 # reduction candidate for 5,8 E4: 6 => CTR * 456..81328.2...9.49.7....86143762.9.5.98342.12.8159...625....1.38152....794.81.2. E4: 5,8 # 26 pairs * PAIR F7: 3,7 ROW 7 G7: 3,7,8 # reduction candidate for 3,7 G7: 3,7 => SOLVED * 456978132812365974937241856143782695579634281268159347625493718381527469794816523 G7: 8 # 23 pairs I7: 3,7,8 # reduction candidate for 3,7 I7: 3,7 # 23 pairs * PAIR F8: 6,7 ROW 8 G8: 6,7,4,9 # reduction candidate for 6,7 G8: 6,7 => CTR * 456..81328.2...9749.724...61437.2.98..9.34..1..81.94.3625....1.38152..49794....25 G8: 4,9 # 21 pairs H8: 6,7,4 # reduction candidate for 6,7 H8: 6,7 # 22 pairs * PAIR I8: 7,9 BLK 9 G8: 7,9,4,6 # reduction candidate for 7,9 G8: 7,9 => CTR * 456..81328.2...9749.724...614376259...9.34..1..81.94.3625....1.38152..4.794...625 G8: 4,6 # 22 pairs * PAIR I8: 7,9 COL I I1: 7,9,2 # reduction candidate for 7,9 I1: 7,9 => CTR * 4562.813.8.2.....49.7..5286143752698269834..1578169342625...81.38152.469794.81523 I1: 2 => SOLVED * 456978132812365974937241856143782695579634281268159347625493718381527469794816523 * PAIR I9: 3,5 BLK 9 G9: 3,5,6 # reduction candidate for 3,5 G9: 6 => CTR * 456..813.8.2.....49.7.....61437625985.98342.12.8159...625...81.38152....794...625 G9: 3,5 # 27 pairs * PAIR I9: 3,5 COL I I6: 3,5,2,7 # reduction candidate for 3,5 I6: 3,5 => CTR * 4569781328.2..59749.7241..61437.2.98..9834..1..81.9...625493.17381527..9794..6.2. I6: 2,7 # 26 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060903-absurd-base-pr-000.dot * REASONING * DIS # F2: 1,3 => CTR => F2: 5,6 * PRF # F3: 1,3 => SOL * DIS # F3: 5 => CTR => F3: 1,3 * DIS # I1: 7 => CTR => I1: 2,9 * DIS # E2: 7,9 => CTR => E2: 1,6 * DIS # I1: 7,9 => CTR => I1: 2 * PRF # I1: 2 => SOL * DIS # G2: 5,7 => CTR => G2: 9 * DIS # H6: 5,7 => CTR => H6: 4,6 * PRF # G3: 5,8 => SOL * DIS # G3: 2 => CTR => G3: 5,8 * PRF # H5: 5,8 => SOL * DIS # H5: 6,7 => CTR => H5: 5,8 * DIS # G5: 6,7,8 => CTR => G5: 2,5 * DIS # G5: 6,7 => CTR => G5: 2,5,8 * DIS # H5: 6,7 => CTR => H5: 5,8 * PRF # H5: 5,8 => SOL * DIS # G6: 2,5 => CTR => G6: 3,4,6,7 * DIS # I6: 2,5 => CTR => I6: 3,7 * PRF # I6: 3,7 => SOL * DIS # G6: 6,7 => CTR => G6: 2,3,4,5 * DIS # H6: 6,7 => CTR => H6: 4,5 * PRF # E4: 6,8 => SOL * DIS # E4: 5 => CTR => E4: 6,8 * DIS # G5: 6,8 => CTR => G5: 2,5,7 * PRF # H5: 6,8 => SOL * DIS # D9: 3 => CTR => D9: 6,8 * PRF # E4: 8 => SOL * DIS # G6: 5,6 => CTR => G6: 2,3,4,7 * DIS # H6: 5,6 => CTR => H6: 4,7 * DIS # G4: 5,8 => CTR => G4: 6 * DIS # G5: 5,8 => CTR => G5: 2,6,7 * PRF # H5: 5,8 => SOL * DIS # H5: 6,7 => CTR => H5: 5,8 * DIS # E4: 6 => CTR => E4: 5,8 * PRF # G7: 3,7 => SOL * DIS # G8: 6,7 => CTR => G8: 4,9 * DIS # G8: 7,9 => CTR => G8: 4,6 * DIS # I1: 7,9 => CTR => I1: 2 * PRF # I1: 2 => SOL * DIS # G9: 6 => CTR => G9: 3,5 * DIS # I6: 3,5 => CTR => I6: 2,7 * CNT 42 HDP CHAINS / 69 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B2,B3,B5,B6,D1,D5,D7,E1,E3,E6,E7,F7,F8,H2,H3,I4,I8,I9) * 456..813.8.2.....49.7.....61437.2.9...9.34..1..81.9...625....1.38152....794....2. * PAIR B2: 1,3 ROW 2 F2: 1,3,5,6 # reduction candidate for 1,3 F2: 1,3 => CTR * 4562.813.8.26....49.7..5286143752698269834..157816934262594.81.38152.46979438..2. * PAIR RESTART * PAIR B3: 1,3 ROW 3 F3: 1,3,5 # reduction candidate for 1,3 F3: 1,3 => SOLVED * 456978132812365974937241856143782695579634281268159347625493718381527469794816523 * DURATION: 0:00:03.320897 START: 02:21:13.096848 END: 02:21:16.417745 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060903-absurd-base-pr-001.dot * REASONING * DIS # F2: 1,3 => CTR => F2: 5,6 * PRF F2: 5,6 # F3: 1,3 => SOL * STA F2: 5,6 + F3: 1,3 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Sep&YEAR=2006, 20060903, absurd
Solution
position: 456978132812365974937241856143782695579634281268159347625493718381527469794816523 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 # F2: 1,3 => CTR => F2: 5,6 * INC # F2: 5,6 => UNS * PRF # F3: 1,3 => SOL * DIS # F3: 5 => CTR => F3: 1,3 * INC # I1: 2,9 => UNS * DIS # I1: 7 => CTR => I1: 2,9 * DIS # E2: 7,9 => CTR => E2: 1,6 * INC # E2: 1,6 => UNS * DIS # I1: 7,9 => CTR => I1: 2 * PRF # I1: 2 => SOL * DIS # G2: 5,7 => CTR => G2: 9 * INC # G2: 9 => UNS * INC # H5: 5,7 => UNS * DIS # H6: 5,7 => CTR => H6: 4,6 * INC # H6: 4,6 => UNS * PRF # G3: 5,8 => SOL * DIS # G3: 2 => CTR => G3: 5,8 * PRF # H5: 5,8 => SOL * DIS # H5: 6,7 => CTR => H5: 5,8 * INC # G5: 2,5 => UNS * DIS # G5: 6,7,8 => CTR => G5: 2,5 * DIS # G5: 6,7 => CTR => G5: 2,5,8 * INC # G5: 2,5,8 => UNS * DIS # H5: 6,7 => CTR => H5: 5,8 * PRF # H5: 5,8 => SOL * DIS # G6: 2,5 => CTR => G6: 3,4,6,7 * INC # G6: 3,4,6,7 => UNS * DIS # I6: 2,5 => CTR => I6: 3,7 * PRF # I6: 3,7 => SOL * DIS # G6: 6,7 => CTR => G6: 2,3,4,5 * INC # G6: 2,3,4,5 => UNS * DIS # H6: 6,7 => CTR => H6: 4,5 * INC # H6: 4,5 => UNS * PRF # E4: 6,8 => SOL * DIS # E4: 5 => CTR => E4: 6,8 * DIS # G5: 6,8 => CTR => G5: 2,5,7 * INC # G5: 2,5,7 => UNS * PRF # H5: 6,8 => SOL * INC # H5: 5,7 => UNS * INC # D9: 6,8 => UNS * DIS # D9: 3 => CTR => D9: 6,8 * INC # E4: 5,6 => UNS * PRF # E4: 8 => SOL * DIS # G6: 5,6 => CTR => G6: 2,3,4,7 * INC # G6: 2,3,4,7 => UNS * DIS # H6: 5,6 => CTR => H6: 4,7 * INC # H6: 4,7 => UNS * DIS # G4: 5,8 => CTR => G4: 6 * INC # G4: 6 => UNS * DIS # G5: 5,8 => CTR => G5: 2,6,7 * INC # G5: 2,6,7 => UNS * PRF # H5: 5,8 => SOL * DIS # H5: 6,7 => CTR => H5: 5,8 * INC # E4: 5,8 => UNS * DIS # E4: 6 => CTR => E4: 5,8 * PRF # G7: 3,7 => SOL * INC # G7: 8 => UNS * INC # I7: 3,7 => UNS * DIS # G8: 6,7 => CTR => G8: 4,9 * INC # G8: 4,9 => UNS * INC # H8: 6,7 => UNS * DIS # G8: 7,9 => CTR => G8: 4,6 * INC # G8: 4,6 => UNS * DIS # I1: 7,9 => CTR => I1: 2 * PRF # I1: 2 => SOL * INC # G9: 3,5 => UNS * DIS # G9: 6 => CTR => G9: 3,5 * DIS # I6: 3,5 => CTR => I6: 2,7 * INC # I6: 2,7 => UNS * CNT 69 HDP CHAINS / 69 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # F2: 1,3 => CTR => F2: 5,6 * PRF F2: 5,6 # F3: 1,3 => SOL * STA F2: 5,6 + F3: 1,3 * CNT 2 HDP CHAINS / 2 HYP OPENED