Analysis of zz-www.sudokuwiki.org-nine-empty-units.sdk
Contents
http://www.sudokuwiki.org/Interesting_Sudokus
level: medium
position: 2.71.4............6.43.8...5.8...1.4.........7.6...5.9...4.19.5............9.57.6 initial
Autosolve
position: 2.71.4............6.43.82..5.8...1.4...5.....7.68..5.9...4.19.59.5.8.......9.57.6 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H2: 5,9 => CTR => H2: 1,4 * DIS # I2: 3,8 => CTR => I2: 1,7 * DIS # I5: 3,8 => CTR => I5: 2 * DIS # I2: 3,8 => CTR => I2: 1,7 * DIS # B5: 1,4 => CTR => B5: 2,3,9 * DIS # B5: 1,4 => CTR => B5: 2,3,9 * DIS # E4: 6,7 => CTR => E4: 2,3,9 * DIS # F4: 6,7 => CTR => F4: 2,3,9 * DIS # E4: 6,7 => CTR => E4: 2,3,9 * DIS # F4: 6,7 => CTR => F4: 2,3,9 * DIS # I5: 3,8 => CTR => I5: 2 * DIS # I5: 8 => CTR => I5: 2,3 * DIS # E4: 6,7 => CTR => E4: 2,3,9 * DIS # H2: 5,9 => CTR => H2: 1,4 * CNT 14 HDP CHAINS / 83 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H2: 5,9 => CTR => H2: 1,4 * DIS H2: 1,4 # I2: 3,8 => CTR => I2: 1,7 * DIS H2: 1,4 + I2: 1,7 # I5: 3,8 => CTR => I5: 2 * PRF H2: 1,4 + I2: 1,7 + I5: 2 => SOL * STA H2: 1,4 + I2: 1,7 + I5: 2 * CNT 4 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2.71.4............6.43.8...5.8...1.4.........7.6...5.9...4.19.5............9.57.6 | initial |
| 2.71.4............6.43.82..5.8...1.4...5.....7.68..5.9...4.19.59.5.8.......9.57.6 | autosolve |
| 297164358853729641614358297528693174139547862746812539362471985975286413481935726 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (21) H1: 5,9 I1: 3,8 I3: 1,7 B4: 2,3 B6: 1,4 E5: 1,4 F5: 6,7 E6: 1,4 F6: 2,3 H4: 6,7 G5: 3,8 H5: 6,7 H6: 2,3 A7: 3,8 B7: 6,7 C7: 2,3 B8: 6,7 E7: 6,7 E9: 2,3 G8: 3,4 H8: 1,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E5,E6: 1.. / E5 = 1 => 20 pairs (_) / E6 = 1 => 19 pairs (_) H8,I8: 1.. / H8 = 1 => 22 pairs (_) / I8 = 1 => 0 pairs (X) B6,E6: 1.. / B6 = 1 => 20 pairs (_) / E6 = 1 => 19 pairs (_) I5,H6: 2.. / I5 = 2 => 27 pairs (_) / H6 = 2 => 0 pairs (X) F6,H6: 2.. / F6 = 2 => 27 pairs (_) / H6 = 2 => 0 pairs (X) C7,H7: 2.. / C7 = 2 => 22 pairs (_) / H7 = 2 => 29 pairs (_) I5,I8: 2.. / I5 = 2 => 27 pairs (_) / I8 = 2 => 0 pairs (X) F8,E9: 3.. / F8 = 3 => 0 pairs (X) / E9 = 3 => 27 pairs (_) F6,H6: 3.. / F6 = 3 => 0 pairs (X) / H6 = 3 => 27 pairs (_) E4,E9: 3.. / E4 = 3 => 0 pairs (X) / E9 = 3 => 27 pairs (_) G2,H2: 4.. / G2 = 4 => 0 pairs (X) / H2 = 4 => 22 pairs (_) E5,E6: 4.. / E5 = 4 => 19 pairs (_) / E6 = 4 => 20 pairs (_) A9,B9: 4.. / A9 = 4 => 22 pairs (_) / B9 = 4 => 21 pairs (_) G8,H8: 4.. / G8 = 4 => 22 pairs (_) / H8 = 4 => 0 pairs (X) B6,E6: 4.. / B6 = 4 => 19 pairs (_) / E6 = 4 => 20 pairs (_) A5,A9: 4.. / A5 = 4 => 21 pairs (_) / A9 = 4 => 22 pairs (_) G2,G8: 4.. / G2 = 4 => 0 pairs (X) / G8 = 4 => 22 pairs (_) H2,H8: 4.. / H2 = 4 => 22 pairs (_) / H8 = 4 => 0 pairs (X) G1,G2: 6.. / G1 = 6 => 23 pairs (_) / G2 = 6 => 21 pairs (_) H4,H5: 6.. / H4 = 6 => 19 pairs (_) / H5 = 6 => 19 pairs (_) B7,B8: 6.. / B7 = 6 => 19 pairs (_) / B8 = 6 => 21 pairs (_) E1,G1: 6.. / E1 = 6 => 21 pairs (_) / G1 = 6 => 23 pairs (_) F5,H5: 6.. / F5 = 6 => 19 pairs (_) / H5 = 6 => 19 pairs (_) B7,E7: 6.. / B7 = 6 => 19 pairs (_) / E7 = 6 => 21 pairs (_) I2,I3: 7.. / I2 = 7 => 23 pairs (_) / I3 = 7 => 21 pairs (_) H4,H5: 7.. / H4 = 7 => 19 pairs (_) / H5 = 7 => 19 pairs (_) B7,B8: 7.. / B7 = 7 => 21 pairs (_) / B8 = 7 => 19 pairs (_) E3,I3: 7.. / E3 = 7 => 23 pairs (_) / I3 = 7 => 21 pairs (_) F5,H5: 7.. / F5 = 7 => 19 pairs (_) / H5 = 7 => 19 pairs (_) B7,E7: 7.. / B7 = 7 => 21 pairs (_) / E7 = 7 => 19 pairs (_) G5,I5: 8.. / G5 = 8 => 22 pairs (_) / I5 = 8 => 0 pairs (X) H7,H9: 8.. / H7 = 8 => 26 pairs (_) / H9 = 8 => 22 pairs (_) A7,H7: 8.. / A7 = 8 => 22 pairs (_) / H7 = 8 => 26 pairs (_) B5,C5: 9.. / B5 = 9 => 22 pairs (_) / C5 = 9 => 22 pairs (_) E4,F4: 9.. / E4 = 9 => 27 pairs (_) / F4 = 9 => 21 pairs (_) C2,C5: 9.. / C2 = 9 => 22 pairs (_) / C5 = 9 => 22 pairs (_) F2,F4: 9.. / F2 = 9 => 27 pairs (_) / F4 = 9 => 21 pairs (_) * DURATION: 0:00:57.623102 START: 02:32:37.947159 END: 02:33:35.570261 2019-05-02 * CP COUNT: (37) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B4,B6,B7,B8,C7,E5,E6,E7,E9,F5,F6,G5,G8,H1,H4,H5,H6,H8,I1,I3) * 2.71.4............6.43.82..5.8...1.4...5.....7.68..5.9...4.19.59.5.8.......9.57.6 * PAIR H1: 5,9 BLK 3 H2: 5,9,1,4 # reduction candidate for 5,9 H2: 5,9 => CTR * 2.71.46......2945.6.43.8217528..31.4...5..8.27.68.2539...4.19.59.528.341...9357.6 H2: 1,4 # 23 pairs H3: 5,9,1 # reduction candidate for 5,9 H3: 5,9 # 23 pairs * PAIR H1: 5,9 ROW 1 B1: 5,9,3,8 # reduction candidate for 5,9 B1: 5,9 # 21 pairs E1: 5,9,6 # reduction candidate for 5,9 E1: 5,9 # 23 pairs * PAIR I1: 3,8 BLK 3 G1: 3,8,6 # reduction candidate for 3,8 G1: 3,8 # 21 pairs G2: 3,8,4,6 # reduction candidate for 3,8 G2: 3,8 # 25 pairs I2: 3,8,1,7 # reduction candidate for 3,8 I2: 3,8 => CTR * 2.71.46......294..6.43582.7528..31.4...5..8.27.68.2539...4.19.59.528.341...9357.6 I2: 1,7 # 22 pairs * PAIR I1: 3,8 ROW 1 B1: 3,8,5,9 # reduction candidate for 3,8 B1: 3,8 # 23 pairs B1: 5,9 # 21 pairs * PAIR I1: 3,8 COL I I5: 3,8,2 # reduction candidate for 3,8 I5: 3,8 => CTR * 2.71.4............6.43.82..5.8.3.1.4...5.....7.68..529..24.19.59.5.8...2...9257.6 I5: 2 # 27 pairs * PAIR I3: 1,7 BLK 3 I2: 1,7,3,8 # reduction candidate for 1,7 I2: 3,8 => CTR * 2.71.46......294..6.43582.7528..31.4...5..8.27.68.2539...4.19.59.528.341...9357.6 I2: 1,7 # 22 pairs * PAIR B4: 2,3 BLK 4 B5: 2,3,1,4,9 # reduction candidate for 2,3 B5: 2,3 # 24 pairs C5: 2,3,1,9 # reduction candidate for 2,3 C5: 2,3 # 24 pairs * PAIR B4: 2,3 ROW 4 E4: 2,3,6,7,9 # reduction candidate for 2,3 E4: 2,3 # 23 pairs F4: 2,3,6,7,9 # reduction candidate for 2,3 F4: 2,3 # 27 pairs * PAIR B4: 2,3 COL B B9: 2,3,1,4,8 # reduction candidate for 2,3 B9: 2,3 # 25 pairs B9: 1,4,8 # 21 pairs * PAIR B6: 1,4 BLK 4 A5: 1,4,3 # reduction candidate for 1,4 A5: 1,4 # 22 pairs B5: 1,4,2,3,9 # reduction candidate for 1,4 B5: 1,4 => CTR * 2.71.4.......2....6.43.82..528..31.43.95..8.27.68.25398.34.19259.528....412935786 B5: 2,3,9 # 21 pairs * PAIR B6: 1,4 COL B B9: 1,4,2,3,8 # reduction candidate for 1,4 B9: 1,4 # 24 pairs B9: 2,3,8 # 23 pairs * PAIR E5: 1,4 ROW 5 A5: 1,4,3 # reduction candidate for 1,4 A5: 1,4 # 22 pairs B5: 1,4,2,3,9 # reduction candidate for 1,4 B5: 1,4 => CTR * 2.71.4.......2....6.43.82..528..31.43.95..8.27.68.25398.34.19259.528....412935786 B5: 2,3,9 # 21 pairs * PAIR F5: 6,7 BLK 5 D4: 6,7,2 # reduction candidate for 6,7 D4: 6,7 # 22 pairs E4: 6,7,2,3,9 # reduction candidate for 6,7 E4: 6,7 => CTR * 2.71.4............6.43.82..5.8..91.4...5.....7.68.3529..24.19.59.5.8...2...9.57.6 E4: 2,3,9 # 21 pairs F4: 6,7,2,3,9 # reduction candidate for 6,7 F4: 6,7 => CTR * 2.71.4........9...6.43.82..5.8.9.1.4..95.....7.68.3529..24.19.59.5.82......9.57.6 F4: 2,3,9 # 21 pairs * PAIR F5: 6,7 COL F F2: 6,7,2,9 # reduction candidate for 6,7 F2: 6,7 # 24 pairs F8: 6,7,2,3 # reduction candidate for 6,7 F8: 6,7 # 27 pairs * PAIR F6: 2,3 BLK 5 E4: 2,3,6,7,9 # reduction candidate for 2,3 E4: 2,3 # 23 pairs F4: 2,3,6,7,9 # reduction candidate for 2,3 F4: 2,3 # 27 pairs * PAIR F6: 2,3 COL F F8: 2,3,6,7 # reduction candidate for 2,3 F8: 6,7 # 27 pairs F8: 2,3 # 23 pairs * PAIR H4: 6,7 ROW 4 D4: 6,7,2 # reduction candidate for 6,7 D4: 6,7 # 22 pairs E4: 6,7,2,3,9 # reduction candidate for 6,7 E4: 6,7 => CTR * 2.71.4............6.43.82..5.8..91.4...5.....7.68.3529..24.19.59.5.8...2...9.57.6 E4: 2,3,9 # 21 pairs F4: 6,7,2,3,9 # reduction candidate for 6,7 F4: 6,7 => CTR * 2.71.4........9...6.43.82..5.8.9.1.4..95.....7.68.3529..24.19.59.5.82......9.57.6 F4: 2,3,9 # 21 pairs * PAIR G5: 3,8 BLK 6 I5: 3,8,2 # reduction candidate for 3,8 I5: 3,8 => CTR * 2.71.4............6.43.82..5.8.3.1.4...5.....7.68..529..24.19.59.5.8...2...9257.6 I5: 2 # 27 pairs * PAIR G5: 3,8 COL G G1: 3,8,6 # reduction candidate for 3,8 G1: 3,8 # 21 pairs G2: 3,8,4,6 # reduction candidate for 3,8 G2: 3,8 # 25 pairs * PAIR H6: 2,3 BLK 6 I5: 2,3,8 # reduction candidate for 2,3 I5: 8 => CTR * 2.71.4..3.........6.43.82..5.8.3.1.4...5....87.68..529..24.19.59.5.8...2...9257.6 I5: 2,3 # 22 pairs * PAIR H6: 2,3 COL H H7: 2,3,8 # reduction candidate for 2,3 H7: 2,3 # 22 pairs H9: 2,3,8 # reduction candidate for 2,3 H9: 2,3 # 26 pairs * PAIR A7: 3,8 BLK 7 A9: 3,8,1,4 # reduction candidate for 3,8 A9: 3,8 # 22 pairs B9: 3,8,1,2,4 # reduction candidate for 3,8 B9: 3,8 # 25 pairs * PAIR A7: 3,8 ROW 7 H7: 3,8,2 # reduction candidate for 3,8 H7: 2 # 29 pairs H7: 3,8 # 22 pairs * PAIR A7: 3,8 COL A A2: 3,8,1 # reduction candidate for 3,8 A2: 3,8 # 24 pairs A2: 1 # 24 pairs * PAIR C7: 2,3 BLK 7 B9: 2,3,1,4,8 # reduction candidate for 2,3 B9: 2,3 # 25 pairs C9: 2,3,1 # reduction candidate for 2,3 C9: 2,3 # 28 pairs * PAIR C7: 2,3 ROW 7 H7: 2,3,8 # reduction candidate for 2,3 H7: 8 # 26 pairs H7: 2,3 # 22 pairs * PAIR C7: 2,3 COL C C5: 2,3,1,9 # reduction candidate for 2,3 C5: 2,3 # 24 pairs C5: 1,9 # 22 pairs * PAIR B8: 6,7 ROW 8 D8: 6,7,2 # reduction candidate for 6,7 D8: 6,7 # 23 pairs F8: 6,7,2,3 # reduction candidate for 6,7 F8: 6,7 # 27 pairs * PAIR E7: 6,7 BLK 8 D8: 6,7,2 # reduction candidate for 6,7 D8: 6,7 # 23 pairs F8: 6,7,2,3 # reduction candidate for 6,7 F8: 6,7 # 27 pairs * PAIR E7: 6,7 COL E E2: 6,7,2,5,9 # reduction candidate for 6,7 E2: 6,7 # 26 pairs E4: 6,7,2,3,9 # reduction candidate for 6,7 E4: 6,7 => CTR * 2.71.4............6.43.82..5.8..91.4...5.....7.68.3529..24.19.59.5.8...2...9.57.6 E4: 2,3,9 # 21 pairs * PAIR E9: 2,3 BLK 8 F8: 2,3,6,7 # reduction candidate for 2,3 F8: 6,7 # 27 pairs F8: 2,3 # 23 pairs * PAIR E9: 2,3 ROW 9 B9: 2,3,1,4,8 # reduction candidate for 2,3 B9: 2,3 # 25 pairs C9: 2,3,1 # reduction candidate for 2,3 C9: 2,3 # 28 pairs H9: 2,3,8 # reduction candidate for 2,3 H9: 2,3 # 26 pairs * PAIR E9: 2,3 COL E E4: 2,3,6,7,9 # reduction candidate for 2,3 E4: 6,7,9 # 27 pairs E4: 2,3 # 23 pairs * PAIR G8: 3,4 COL G G2: 3,4,6,8 # reduction candidate for 3,4 G2: 3,4 # 24 pairs G2: 6,8 # 23 pairs * PAIR H8: 1,4 COL H H2: 1,4,5,9 # reduction candidate for 1,4 H2: 5,9 => CTR * 2.71.46......2945.6.43.8217528..31.4...5..8.27.68.2539...4.19.59.528.341...9357.6 H2: 1,4 # 23 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-nine-empty-units-pr-000.dot * REASONING * DIS # H2: 5,9 => CTR => H2: 1,4 * DIS # I2: 3,8 => CTR => I2: 1,7 * DIS # I5: 3,8 => CTR => I5: 2 * DIS # I2: 3,8 => CTR => I2: 1,7 * DIS # B5: 1,4 => CTR => B5: 2,3,9 * DIS # B5: 1,4 => CTR => B5: 2,3,9 * DIS # E4: 6,7 => CTR => E4: 2,3,9 * DIS # F4: 6,7 => CTR => F4: 2,3,9 * DIS # E4: 6,7 => CTR => E4: 2,3,9 * DIS # F4: 6,7 => CTR => F4: 2,3,9 * DIS # I5: 3,8 => CTR => I5: 2 * DIS # I5: 8 => CTR => I5: 2,3 * DIS # E4: 6,7 => CTR => E4: 2,3,9 * DIS # H2: 5,9 => CTR => H2: 1,4 * CNT 14 HDP CHAINS / 83 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B4,B6,B7,B8,C7,E5,E6,E7,E9,F5,F6,G5,G8,H1,H4,H5,H6,H8,I1,I3) * 2.71.4............6.43.82..5.8...1.4...5.....7.68..5.9...4.19.59.5.8.......9.57.6 * PAIR H1: 5,9 BLK 3 H2: 5,9,1,4 # reduction candidate for 5,9 H2: 5,9 => CTR * 2.71.46......2945.6.43.8217528..31.4...5..8.27.68.2539...4.19.59.528.341...9357.6 * RESTART * PAIR H1: 5,9 ROW 1 B1: 5,9,3,8 # reduction candidate for 5,9 B1: 5,9 # 21 pairs E1: 5,9,6 # reduction candidate for 5,9 E1: 5,9 # 25 pairs * PAIR I1: 3,8 BLK 3 G1: 3,8,6 # reduction candidate for 3,8 G1: 3,8 # 21 pairs G2: 3,8,4,6 # reduction candidate for 3,8 G2: 3,8 # 25 pairs I2: 3,8,1,7 # reduction candidate for 3,8 I2: 3,8 => CTR * 2.71.46.885..294136143.82.7528..31.41..54.8.2746812539..24.19859.528.341481935726 * PAIR I1: 3,8 ROW 1 B1: 3,8,5,9 # reduction candidate for 3,8 B1: 3,8 # 25 pairs B1: 5,9 # 21 pairs * PAIR I1: 3,8 COL I I5: 3,8,2 # reduction candidate for 3,8 I5: 3,8 => CTR * 2.71.4..........4.6.43.82..5.8.3.1.4...5.....7.68..529..24.19.59.5.8.412...9257.6 I5: 2 => SOLVED * 297164358853729641614358297528693174139547862746812539362471985975286413481935726 * DURATION: 0:00:10.628427 START: 02:34:44.088051 END: 02:34:54.716478 2019-05-02 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-nine-empty-units-pr-001.dot * REASONING * DIS # H2: 5,9 => CTR => H2: 1,4 * DIS H2: 1,4 # I2: 3,8 => CTR => I2: 1,7 * DIS H2: 1,4 + I2: 1,7 # I5: 3,8 => CTR => I5: 2 * PRF H2: 1,4 + I2: 1,7 + I5: 2 => SOL * STA H2: 1,4 + I2: 1,7 + I5: 2 * CNT 4 HDP CHAINS / 9 HYP OPENED
Header Info
http://www.sudokuwiki.org/Interesting_Sudokus Nine empty units. Could be wrong, but I can't believe there can be more than nine. Discovered by Klaus Brenner
Solution
position: 297164358853729641614358297528693174139547862746812539362471985975286413481935726 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 # H2: 5,9 => CTR => H2: 1,4 * INC # H2: 1,4 => UNS * INC # H3: 5,9 => UNS * INC # B1: 5,9 => UNS * INC # E1: 5,9 => UNS * INC # G1: 3,8 => UNS * INC # G2: 3,8 => UNS * DIS # I2: 3,8 => CTR => I2: 1,7 * INC # I2: 1,7 => UNS * INC # B1: 3,8 => UNS * INC # B1: 5,9 => UNS * DIS # I5: 3,8 => CTR => I5: 2 * INC # I5: 2 => UNS * INC # I2: 1,7 => UNS * DIS # I2: 3,8 => CTR => I2: 1,7 * INC # B5: 2,3 => UNS * INC # C5: 2,3 => UNS * INC # E4: 2,3 => UNS * INC # F4: 2,3 => UNS * INC # B9: 2,3 => UNS * INC # B9: 1,4,8 => UNS * INC # A5: 1,4 => UNS * DIS # B5: 1,4 => CTR => B5: 2,3,9 * INC # B5: 2,3,9 => UNS * INC # B9: 1,4 => UNS * INC # B9: 2,3,8 => UNS * INC # A5: 1,4 => UNS * DIS # B5: 1,4 => CTR => B5: 2,3,9 * INC # B5: 2,3,9 => UNS * INC # D4: 6,7 => UNS * DIS # E4: 6,7 => CTR => E4: 2,3,9 * INC # E4: 2,3,9 => UNS * DIS # F4: 6,7 => CTR => F4: 2,3,9 * INC # F4: 2,3,9 => UNS * INC # F2: 6,7 => UNS * INC # F8: 6,7 => UNS * INC # E4: 2,3 => UNS * INC # F4: 2,3 => UNS * INC # F8: 2,3 => UNS * INC # F8: 6,7 => UNS * INC # D4: 6,7 => UNS * DIS # E4: 6,7 => CTR => E4: 2,3,9 * INC # E4: 2,3,9 => UNS * DIS # F4: 6,7 => CTR => F4: 2,3,9 * INC # F4: 2,3,9 => UNS * DIS # I5: 3,8 => CTR => I5: 2 * INC # I5: 2 => UNS * INC # G1: 3,8 => UNS * INC # G2: 3,8 => UNS * INC # I5: 2,3 => UNS * DIS # I5: 8 => CTR => I5: 2,3 * INC # H7: 2,3 => UNS * INC # H9: 2,3 => UNS * INC # A9: 3,8 => UNS * INC # B9: 3,8 => UNS * INC # H7: 3,8 => UNS * INC # H7: 2 => UNS * INC # A2: 3,8 => UNS * INC # A2: 1 => UNS * INC # B9: 2,3 => UNS * INC # C9: 2,3 => UNS * INC # H7: 2,3 => UNS * INC # H7: 8 => UNS * INC # C5: 2,3 => UNS * INC # C5: 1,9 => UNS * INC # D8: 6,7 => UNS * INC # F8: 6,7 => UNS * INC # D8: 6,7 => UNS * INC # F8: 6,7 => UNS * INC # E2: 6,7 => UNS * DIS # E4: 6,7 => CTR => E4: 2,3,9 * INC # E4: 2,3,9 => UNS * INC # F8: 2,3 => UNS * INC # F8: 6,7 => UNS * INC # B9: 2,3 => UNS * INC # C9: 2,3 => UNS * INC # H9: 2,3 => UNS * INC # E4: 2,3 => UNS * INC # E4: 6,7,9 => UNS * INC # G2: 3,4 => UNS * INC # G2: 6,8 => UNS * INC # H2: 1,4 => UNS * DIS # H2: 5,9 => CTR => H2: 1,4 * CNT 83 HDP CHAINS / 83 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # H2: 5,9 => CTR => H2: 1,4 * INC H2: 1,4 # B1: 5,9 => UNS * INC H2: 1,4 # E1: 5,9 => UNS * INC H2: 1,4 # G1: 3,8 => UNS * INC H2: 1,4 # G2: 3,8 => UNS * DIS H2: 1,4 # I2: 3,8 => CTR => I2: 1,7 * INC H2: 1,4 + I2: 1,7 # B1: 3,8 => UNS * INC H2: 1,4 + I2: 1,7 # B1: 5,9 => UNS * DIS H2: 1,4 + I2: 1,7 # I5: 3,8 => CTR => I5: 2 * PRF H2: 1,4 + I2: 1,7 + I5: 2 => SOL * STA H2: 1,4 + I2: 1,7 + I5: 2 * CNT 10 HDP CHAINS / 9 HYP OPENED