Analysis of zz-www.sudokuwiki.org-0087-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=87
level: medium
position: .......9.8....6..5..5.4.6...21.........3....1.....926..3.5.....48.1....9.6..9..8. initial
Autosolve
position: .......9.8....6..5..5.4.6...216........3....1.5..1926.1395....648.16...956..9.18. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H2: 3,4 => CTR => H2: 1,2,7 * DIS # G1: 4,7 => CTR => G1: 3,8 * DIS # G4: 4,7 => CTR => G4: 3,5,8,9 * DIS # G5: 4,7 => CTR => G5: 5,8,9 * CNT 4 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H2: 3,4 => CTR => H2: 1,2,7 * DIS H2: 1,2,7 # G1: 4,7 => CTR => G1: 3,8 * DIS H2: 1,2,7 + G1: 3,8 # G4: 4,7 => CTR => G4: 3,5,8,9 * DIS H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 # G5: 4,7 => CTR => G5: 5,8,9 * DIS H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 # G2: 3 => CTR => G2: 4,7 * DIS H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 # I1: 3,8 => CTR => I1: 2,4,7 * DIS H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 + I1: 2,4,7 # E1: 2,5,7 => CTR => E1: 3,8 * PRF H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 + I1: 2,4,7 + E1: 3,8 # I3: 2,7 => SOL * STA H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 + I1: 2,4,7 + E1: 3,8 + I3: 2,7 * CNT 8 HDP CHAINS / 53 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .......9.8....6..5..5.4.6...21.........3....1.....926..3.5.....48.1....9.6..9..8. | initial |
| .......9.8....6..5..5.4.6...216........3....1.5..1926.1395....648.16...956..9.18. | autosolve |
| 216735894843926715795841632921657348674382951358419267139578426482163579567294183 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) C2: 3,4 A6: 3,7 C8: 2,7 C9: 2,7 G7: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F1,F3: 1.. / F1 = 1 => 0 pairs (X) / F3 = 1 => 7 pairs (_) H2,H3: 1.. / H2 = 1 => 6 pairs (_) / H3 = 1 => 0 pairs (X) B1,F1: 1.. / B1 = 1 => 7 pairs (_) / F1 = 1 => 0 pairs (X) B2,H2: 1.. / B2 = 1 => 0 pairs (X) / H2 = 1 => 6 pairs (_) A1,A3: 2.. / A1 = 2 => 7 pairs (_) / A3 = 2 => 11 pairs (_) E5,F5: 2.. / E5 = 2 => 10 pairs (_) / F5 = 2 => 6 pairs (_) C8,C9: 2.. / C8 = 2 => 5 pairs (_) / C9 = 2 => 11 pairs (_) E1,E2: 3.. / E1 = 3 => 10 pairs (_) / E2 = 3 => 0 pairs (X) F8,F9: 3.. / F8 = 3 => 8 pairs (_) / F9 = 3 => 8 pairs (_) F9,I9: 3.. / F9 = 3 => 8 pairs (_) / I9 = 3 => 8 pairs (_) D6,D9: 4.. / D6 = 4 => 12 pairs (_) / D9 = 4 => 10 pairs (_) E1,F1: 5.. / E1 = 5 => 0 pairs (X) / F1 = 5 => 7 pairs (_) G8,H8: 5.. / G8 = 5 => 5 pairs (_) / H8 = 5 => 10 pairs (_) A1,C1: 6.. / A1 = 6 => 21 pairs (_) / C1 = 6 => 6 pairs (_) A5,C5: 6.. / A5 = 6 => 6 pairs (_) / C5 = 6 => 21 pairs (_) A1,A5: 6.. / A1 = 6 => 21 pairs (_) / A5 = 6 => 6 pairs (_) C1,C5: 6.. / C1 = 6 => 6 pairs (_) / C5 = 6 => 21 pairs (_) C8,C9: 7.. / C8 = 7 => 11 pairs (_) / C9 = 7 => 5 pairs (_) C5,C6: 8.. / C5 = 8 => 6 pairs (_) / C6 = 8 => 16 pairs (_) E7,F7: 8.. / E7 = 8 => 6 pairs (_) / F7 = 8 => 6 pairs (_) D2,D3: 9.. / D2 = 9 => 5 pairs (_) / D3 = 9 => 9 pairs (_) G4,G5: 9.. / G4 = 9 => 15 pairs (_) / G5 = 9 => 7 pairs (_) B2,D2: 9.. / B2 = 9 => 9 pairs (_) / D2 = 9 => 5 pairs (_) A4,G4: 9.. / A4 = 9 => 7 pairs (_) / G4 = 9 => 15 pairs (_) * DURATION: 0:00:32.800370 START: 04:59:46.781472 END: 05:00:19.581842 2017-05-01 * CP COUNT: (24) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,C2,C8,C9,G7) * .......9.8....6..5..5.4.6...216........3....1.5..1926.1395....648.16...956..9.18. * PAIR C2: 3,4 BLK 1 C1: 3,4,6 # reduction candidate for 3,4 C1: 3,4 # 21 pairs C1: 6 # 6 pairs * PAIR C2: 3,4 ROW 2 G2: 3,4,7 # reduction candidate for 3,4 G2: 3,4 # 17 pairs H2: 3,4,1,2,7 # reduction candidate for 3,4 H2: 3,4 => CTR * ....3..9.81.9267.5..5.4.61..216........3.2..1.5..1926.1395..42648216...9567294183 H2: 1,2,7 # 5 pairs * PAIR C2: 3,4 COL C C6: 3,4,8 # reduction candidate for 3,4 C6: 8 # 16 pairs C6: 3,4 # 6 pairs * PAIR A6: 3,7 BLK 4 A4: 3,7,9 # reduction candidate for 3,7 A4: 3,7 # 15 pairs A4: 9 # 7 pairs * PAIR A6: 3,7 ROW 6 I6: 3,7,4,8 # reduction candidate for 3,7 I6: 3,7 # 14 pairs I6: 4,8 # 7 pairs * PAIR A6: 3,7 COL A A1: 3,7,2,6 # reduction candidate for 3,7 A1: 3,7 # 13 pairs A3: 3,7,2,9 # reduction candidate for 3,7 A3: 3,7 # 9 pairs * PAIR C8: 2,7 ROW 8 F8: 2,7,3 # reduction candidate for 2,7 F8: 2,7 # 8 pairs H8: 2,7,3,5 # reduction candidate for 2,7 H8: 2,7 # 8 pairs * PAIR C9: 2,7 ROW 9 D9: 2,7,4 # reduction candidate for 2,7 D9: 2,7 # 12 pairs F9: 2,7,3,4 # reduction candidate for 2,7 F9: 2,7 # 14 pairs I9: 2,7,3,4 # reduction candidate for 2,7 I9: 2,7 # 14 pairs * PAIR G7: 4,7 BLK 9 H7: 4,7,2 # reduction candidate for 4,7 H7: 4,7 # 16 pairs I9: 4,7,2,3 # reduction candidate for 4,7 I9: 4,7 # 11 pairs * PAIR G7: 4,7 ROW 7 F7: 4,7,2,8 # reduction candidate for 4,7 F7: 4,7 # 8 pairs F7: 2,8 # 6 pairs * PAIR G7: 4,7 COL G G1: 4,7,3,8 # reduction candidate for 4,7 G1: 4,7 => CTR * 2.67354988.4.263.53.5.4.6...216........3....17538192641395....648.16.5.956.49.18. G1: 3,8 # 6 pairs G2: 4,7,3 # reduction candidate for 4,7 G2: 4,7 # 8 pairs G4: 4,7,3,5,8,9 # reduction candidate for 4,7 G4: 4,7 => CTR * 2.67358948.4.263.53.5.416..9216.....6483.29.17534192681395...2648216.5.9567294183 G4: 3,5,8,9 # 5 pairs G5: 4,7,5,8,9 # reduction candidate for 4,7 G5: 4,7 => CTR * ......89.8....63.53.5.4.6..7216..9.....3....1.5..1926.1395....648.16.5.956..9.18. G5: 5,8,9 # 5 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0087-base-pr-000.dot * REASONING * DIS # H2: 3,4 => CTR => H2: 1,2,7 * DIS # G1: 4,7 => CTR => G1: 3,8 * DIS # G4: 4,7 => CTR => G4: 3,5,8,9 * DIS # G5: 4,7 => CTR => G5: 5,8,9 * CNT 4 HDP CHAINS / 29 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,C2,C8,C9,G7) * .......9.8....6..5..5.4.6...216........3....1.5..1926.1395....648.16...956..9.18. * PAIR C2: 3,4 BLK 1 C1: 3,4,6 # reduction candidate for 3,4 C1: 3,4 # 21 pairs C1: 6 # 6 pairs * PAIR C2: 3,4 ROW 2 G2: 3,4,7 # reduction candidate for 3,4 G2: 3,4 # 17 pairs H2: 3,4,1,2,7 # reduction candidate for 3,4 H2: 3,4 => CTR * ....3..9.81.9267.5..5.4.61..216........3.2..1.5..1926.1395..42648216...9567294183 * RESTART * PAIR C2: 3,4 ROW 2 G2: 3,4,7 # reduction candidate for 3,4 G2: 3,4 # 17 pairs G2: 7 # 12 pairs * PAIR C2: 3,4 COL C C6: 3,4,8 # reduction candidate for 3,4 C6: 8 # 16 pairs C6: 3,4 # 6 pairs * PAIR RESTART * PAIR C2: 3,4 BLK 1 C1: 3,4,6 # reduction candidate for 3,4 C1: 3,4 # 21 pairs C1: 6 # 6 pairs * PAIR C2: 3,4 ROW 2 G2: 3,4,7 # reduction candidate for 3,4 G2: 3,4 # 17 pairs G2: 7 # 12 pairs * PAIR C2: 3,4 COL C C6: 3,4,8 # reduction candidate for 3,4 C6: 8 # 16 pairs C6: 3,4 # 6 pairs * PAIR A6: 3,7 BLK 4 A4: 3,7,9 # reduction candidate for 3,7 A4: 3,7 # 15 pairs A4: 9 # 7 pairs * PAIR A6: 3,7 ROW 6 I6: 3,7,4,8 # reduction candidate for 3,7 I6: 3,7 # 14 pairs I6: 4,8 # 7 pairs * PAIR A6: 3,7 COL A A1: 3,7,2,6 # reduction candidate for 3,7 A1: 3,7 # 13 pairs A3: 3,7,2,9 # reduction candidate for 3,7 A3: 3,7 # 9 pairs * PAIR C8: 2,7 ROW 8 F8: 2,7,3 # reduction candidate for 2,7 F8: 2,7 # 8 pairs H8: 2,7,3,5 # reduction candidate for 2,7 H8: 2,7 # 9 pairs * PAIR C9: 2,7 ROW 9 D9: 2,7,4 # reduction candidate for 2,7 D9: 2,7 # 13 pairs F9: 2,7,3,4 # reduction candidate for 2,7 F9: 2,7 # 14 pairs I9: 2,7,3,4 # reduction candidate for 2,7 I9: 2,7 # 14 pairs * PAIR G7: 4,7 BLK 9 H7: 4,7,2 # reduction candidate for 4,7 H7: 4,7 # 16 pairs I9: 4,7,2,3 # reduction candidate for 4,7 I9: 4,7 # 12 pairs * PAIR G7: 4,7 ROW 7 F7: 4,7,2,8 # reduction candidate for 4,7 F7: 4,7 # 9 pairs F7: 2,8 # 6 pairs * PAIR G7: 4,7 COL G G1: 4,7,3,8 # reduction candidate for 4,7 G1: 4,7 => CTR * 2.67354988.4.263.53.5.4.6...216........3....17538192641395...4648.16.5.956.49.18. G2: 4,7,3 # reduction candidate for 4,7 G2: 4,7 # 8 pairs G4: 4,7,3,5,8,9 # reduction candidate for 4,7 G4: 4,7 => CTR * 2.67358948.4.263.53.5.416..9216.....6483.29.17534192681395...2648216.5.9567294183 G5: 4,7,5,8,9 # reduction candidate for 4,7 G5: 4,7 => CTR * ......89.8....63.53.5.4.6..7216..9.....3....1.5..1926.1395....648.16.5.956..9.18. * RESTART * PAIR G7: 4,7 COL G G2: 4,7,3 # reduction candidate for 4,7 G2: 3 => CTR * .......948....63.53.5.4.6...216........3....17534192681395..4.648.16.759567294183 * PAIR RESTART * PAIR G7: 4,7 BLK 9 H7: 4,7,2 # reduction candidate for 4,7 H7: 4,7 # 18 pairs I9: 4,7,2,3 # reduction candidate for 4,7 I9: 4,7 # 14 pairs * PAIR G7: 4,7 ROW 7 F7: 4,7,2,8 # reduction candidate for 4,7 F7: 4,7 # 12 pairs F7: 2,8 # 9 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A6,C2,C8,C9,G1,G2,G7,G8) * .......9.8....6..5..5.4.6...216........3....1.5..1926.1395....648.16...956..9.18. * PAIR C2: 3,4 BLK 1 C1: 3,4,6 # reduction candidate for 3,4 C1: 3,4 # 21 pairs C1: 6 # 9 pairs * PAIR C2: 3,4 COL C C6: 3,4,8 # reduction candidate for 3,4 C6: 8 # 16 pairs C6: 3,4 # 10 pairs * PAIR G1: 3,8 BLK 3 I1: 3,8,2,4,7 # reduction candidate for 3,8 I1: 3,8 => CTR * ....3589.8.3..64.5..5.4.6...216........3....1.5..1926.1395..7.648.16...956..9.18. I3: 3,8,2,7 # reduction candidate for 3,8 I3: 3,8 # 9 pairs * RESTART * PAIR G1: 3,8 BLK 3 I3: 3,8,2,7 # reduction candidate for 3,8 I3: 2,7 # 19 pairs I3: 3,8 # 9 pairs * PAIR G1: 3,8 ROW 1 E1: 3,8,2,5,7 # reduction candidate for 3,8 E1: 2,5,7 => CTR * 2......948.4.367.5..5.4.632.216..34..4.3..951.5.41926.1395..4.648.1635.956..94183 * PAIR G1: 3,8 COL G G4: 3,8,5,9 # reduction candidate for 3,8 G4: 3,8 # 20 pairs G4: 5,9 # 19 pairs * PAIR RESTART * PAIR G1: 3,8 BLK 3 I3: 3,8,2,7 # reduction candidate for 3,8 I3: 2,7 => SOLVED * 216735894843926715795841632921657348674382951358419267139578426482163579567294183 * DURATION: 0:00:44.140640 START: 05:00:41.321603 END: 05:01:25.462243 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0087-base-pr-001.dot * REASONING * DIS # H2: 3,4 => CTR => H2: 1,2,7 * DIS H2: 1,2,7 # G1: 4,7 => CTR => G1: 3,8 * DIS H2: 1,2,7 + G1: 3,8 # G4: 4,7 => CTR => G4: 3,5,8,9 * DIS H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 # G5: 4,7 => CTR => G5: 5,8,9 * DIS H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 # G2: 3 => CTR => G2: 4,7 * DIS H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 # I1: 3,8 => CTR => I1: 2,4,7 * DIS H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 + I1: 2,4,7 # E1: 2,5,7 => CTR => E1: 3,8 * PRF H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 + I1: 2,4,7 + E1: 3,8 # I3: 2,7 => SOL * STA H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 + I1: 2,4,7 + E1: 3,8 + I3: 2,7 * CNT 8 HDP CHAINS / 53 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=87
Solution
position: 216735894843926715795841632921657348674382951358419267139578426482163579567294183 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:
* INC # C1: 3,4 => UNS * INC # C1: 6 => UNS * INC # G2: 3,4 => UNS * DIS # H2: 3,4 => CTR => H2: 1,2,7 * INC # H2: 1,2,7 => UNS * INC # C6: 3,4 => UNS * INC # C6: 8 => UNS * INC # A4: 3,7 => UNS * INC # A4: 9 => UNS * INC # I6: 3,7 => UNS * INC # I6: 4,8 => UNS * INC # A1: 3,7 => UNS * INC # A3: 3,7 => UNS * INC # F8: 2,7 => UNS * INC # H8: 2,7 => UNS * INC # D9: 2,7 => UNS * INC # F9: 2,7 => UNS * INC # I9: 2,7 => UNS * INC # H7: 4,7 => UNS * INC # I9: 4,7 => UNS * INC # F7: 4,7 => UNS * INC # F7: 2,8 => UNS * DIS # G1: 4,7 => CTR => G1: 3,8 * INC # G1: 3,8 => UNS * INC # G2: 4,7 => UNS * DIS # G4: 4,7 => CTR => G4: 3,5,8,9 * INC # G4: 3,5,8,9 => UNS * DIS # G5: 4,7 => CTR => G5: 5,8,9 * INC # G5: 5,8,9 => UNS * CNT 29 HDP CHAINS / 29 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 3,4 => UNS * INC # C1: 6 => UNS * INC # G2: 3,4 => UNS * DIS # H2: 3,4 => CTR => H2: 1,2,7 * INC H2: 1,2,7 # G2: 3,4 => UNS * INC H2: 1,2,7 # G2: 7 => UNS * INC H2: 1,2,7 # C6: 3,4 => UNS * INC H2: 1,2,7 # C6: 8 => UNS * INC H2: 1,2,7 # C1: 3,4 => UNS * INC H2: 1,2,7 # C1: 6 => UNS * INC H2: 1,2,7 # G2: 3,4 => UNS * INC H2: 1,2,7 # G2: 7 => UNS * INC H2: 1,2,7 # C6: 3,4 => UNS * INC H2: 1,2,7 # C6: 8 => UNS * INC H2: 1,2,7 # A4: 3,7 => UNS * INC H2: 1,2,7 # A4: 9 => UNS * INC H2: 1,2,7 # I6: 3,7 => UNS * INC H2: 1,2,7 # I6: 4,8 => UNS * INC H2: 1,2,7 # A1: 3,7 => UNS * INC H2: 1,2,7 # A3: 3,7 => UNS * INC H2: 1,2,7 # F8: 2,7 => UNS * INC H2: 1,2,7 # H8: 2,7 => UNS * INC H2: 1,2,7 # D9: 2,7 => UNS * INC H2: 1,2,7 # F9: 2,7 => UNS * INC H2: 1,2,7 # I9: 2,7 => UNS * INC H2: 1,2,7 # H7: 4,7 => UNS * INC H2: 1,2,7 # I9: 4,7 => UNS * INC H2: 1,2,7 # F7: 4,7 => UNS * INC H2: 1,2,7 # F7: 2,8 => UNS * DIS H2: 1,2,7 # G1: 4,7 => CTR => G1: 3,8 * INC H2: 1,2,7 + G1: 3,8 # G2: 4,7 => UNS * DIS H2: 1,2,7 + G1: 3,8 # G4: 4,7 => CTR => G4: 3,5,8,9 * DIS H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 # G5: 4,7 => CTR => G5: 5,8,9 * INC H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 # G2: 4,7 => UNS * DIS H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 # G2: 3 => CTR => G2: 4,7 * INC H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 # H7: 4,7 => UNS * INC H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 # I9: 4,7 => UNS * INC H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 # F7: 4,7 => UNS * INC H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 # F7: 2,8 => UNS * INC H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 # C1: 3,4 => UNS * INC H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 # C1: 6 => UNS * INC H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 # C6: 3,4 => UNS * INC H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 # C6: 8 => UNS * DIS H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 # I1: 3,8 => CTR => I1: 2,4,7 * INC H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 + I1: 2,4,7 # I3: 3,8 => UNS * INC H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 + I1: 2,4,7 # I3: 3,8 => UNS * INC H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 + I1: 2,4,7 # I3: 2,7 => UNS * INC H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 + I1: 2,4,7 # E1: 3,8 => UNS * DIS H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 + I1: 2,4,7 # E1: 2,5,7 => CTR => E1: 3,8 * INC H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 + I1: 2,4,7 + E1: 3,8 # G4: 3,8 => UNS * INC H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 + I1: 2,4,7 + E1: 3,8 # G4: 5,9 => UNS * INC H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 + I1: 2,4,7 + E1: 3,8 # I3: 3,8 => UNS * PRF H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 + I1: 2,4,7 + E1: 3,8 # I3: 2,7 => SOL * STA H2: 1,2,7 + G1: 3,8 + G4: 3,5,8,9 + G5: 5,8,9 + G2: 4,7 + I1: 2,4,7 + E1: 3,8 + I3: 2,7 * CNT 53 HDP CHAINS / 53 HYP OPENED