Analysis of xx-top95-065-base.sdk
Contents
Original Sudoku
level: medium
position: ...36....85.......9.4..8........68.........17..9..45...1.5...6.4....9..2.....3... initial
Autosolve
position: ...365...85...127.9.4..8........68.......2.17..9..45...1.5.7.6.4....9..2.9...3... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C8: 3,6 => CTR => C8: 5,7,8 * DIS # G3: 1 => CTR => G3: 3,6 * DIS # B5: 3,6 => CTR => B5: 4,8 * DIS # G5: 4,9 => CTR => G5: 3,6 * DIS # G3: 1 => CTR => G3: 3,6 * DIS # E5: 8,9 => CTR => E5: 3,5 * DIS # G5: 4,9 => CTR => G5: 3,6 * DIS # H4: 2,3 => CTR => H4: 4,9 * DIS # A6: 2,3 => CTR => A6: 1,6,7 * DIS # B6: 2,3 => CTR => B6: 6,7,8 * DIS # G5: 4,9 => CTR => G5: 3,6 * DIS # A6: 2,3 => CTR => A6: 1,6,7 * DIS # D8: 1,8 => CTR => D8: 6 * CNT 13 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C8: 3,6 => CTR => C8: 5,7,8 * DIS C8: 5,7,8 # G3: 1 => CTR => G3: 3,6 * DIS C8: 5,7,8 + G3: 3,6 # B5: 3,6 => CTR => B5: 4,8 * DIS C8: 5,7,8 + G3: 3,6 + B5: 4,8 # G5: 4,9 => CTR => G5: 3,6 * DIS C8: 5,7,8 + G3: 3,6 + B5: 4,8 + G5: 3,6 # E5: 8,9 => CTR => E5: 3,5 * PRF C8: 5,7,8 + G3: 3,6 + B5: 4,8 + G5: 3,6 + E5: 3,5 # A6: 3,6 => SOL * STA C8: 5,7,8 + G3: 3,6 + B5: 4,8 + G5: 3,6 + E5: 3,5 + A6: 3,6 * CNT 6 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...36....85.......9.4..8........68.........17..9..45...1.5...6.4....9..2.....3... | initial |
| ...365...85...127.9.4..8........68.......2.17..9..45...1.5.7.6.4....9..2.9...3... | autosolve |
| 127365489853491276964278351231756894548932617679184523312547968485619732796823145 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) B1: 2,7 C2: 3,6 B3: 3,6 D2: 4,9 E2: 4,9 D3: 2,7 E3: 2,7 G1: 4,9 I2: 3,6 H3: 3,5 I3: 1,5 D5: 8,9 I4: 4,9 H6: 2,3 I6: 3,6 A7: 2,3 E8: 1,8 I9: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,C1: 1.. / A1 = 1 => 20 pairs (_) / C1 = 1 => 19 pairs (_) G3,I3: 1.. / G3 = 1 => 0 pairs (X) / I3 = 1 => 20 pairs (_) C1,C4: 1.. / C1 = 1 => 19 pairs (_) / C4 = 1 => 20 pairs (_) I3,I9: 1.. / I3 = 1 => 20 pairs (_) / I9 = 1 => 0 pairs (X) D3,E3: 2.. / D3 = 2 => 16 pairs (_) / E3 = 2 => 19 pairs (_) H4,H6: 2.. / H4 = 2 => 0 pairs (X) / H6 = 2 => 17 pairs (_) D3,D9: 2.. / D3 = 2 => 16 pairs (_) / D9 = 2 => 19 pairs (_) C2,B3: 3.. / C2 = 3 => 0 pairs (*) / B3 = 3 => 0 pairs (X) C2,I2: 3.. / C2 = 3 => 0 pairs (*) / I2 = 3 => 0 pairs (X) I2,I6: 3.. / I2 = 3 => 0 pairs (X) / I6 = 3 => 0 pairs (_) D2,E2: 4.. / D2 = 4 => 16 pairs (_) / E2 = 4 => 0 pairs (X) B4,B5: 4.. / B4 = 4 => 0 pairs (X) / B5 = 4 => 18 pairs (_) B5,G5: 4.. / B5 = 4 => 18 pairs (_) / G5 = 4 => 0 pairs (X) D2,D9: 4.. / D2 = 4 => 16 pairs (_) / D9 = 4 => 0 pairs (X) H3,I3: 5.. / H3 = 5 => 20 pairs (_) / I3 = 5 => 0 pairs (X) E4,E5: 5.. / E4 = 5 => 18 pairs (_) / E5 = 5 => 19 pairs (_) C8,H8: 5.. / C8 = 5 => 19 pairs (_) / H8 = 5 => 0 pairs (X) I3,I9: 5.. / I3 = 5 => 0 pairs (X) / I9 = 5 => 20 pairs (_) C2,B3: 6.. / C2 = 6 => 0 pairs (X) / B3 = 6 => 0 pairs (_) I2,G3: 6.. / I2 = 6 => 0 pairs (*) / G3 = 6 => 0 pairs (X) G5,I6: 6.. / G5 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) D8,D9: 6.. / D8 = 6 => 18 pairs (_) / D9 = 6 => 0 pairs (X) C2,I2: 6.. / C2 = 6 => 0 pairs (X) / I2 = 6 => 0 pairs (_) B3,G3: 6.. / B3 = 6 => 0 pairs (*) / G3 = 6 => 0 pairs (X) G3,G5: 6.. / G3 = 6 => 0 pairs (X) / G5 = 6 => 0 pairs (_) I2,I6: 6.. / I2 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) D3,E3: 7.. / D3 = 7 => 19 pairs (_) / E3 = 7 => 16 pairs (_) G8,G9: 7.. / G8 = 7 => 19 pairs (_) / G9 = 7 => 19 pairs (_) H1,I1: 8.. / H1 = 8 => 17 pairs (_) / I1 = 8 => 20 pairs (_) I1,I7: 8.. / I1 = 8 => 20 pairs (_) / I7 = 8 => 17 pairs (_) D2,E2: 9.. / D2 = 9 => 0 pairs (X) / E2 = 9 => 16 pairs (_) G7,I7: 9.. / G7 = 9 => 23 pairs (_) / I7 = 9 => 19 pairs (_) H1,H4: 9.. / H1 = 9 => 20 pairs (_) / H4 = 9 => 21 pairs (_) * DURATION: 0:01:02.848511 START: 00:16:13.495085 END: 00:17:16.343596 2017-05-04 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B1,B3,C2,D2,D3,D5,E2,E3,E8,G1,H3,H6,I2,I3,I4,I6,I9) * ...365...85...127.9.4..8........68.......2.17..9..45...1.5.7.6.4....9..2.9...3... * PAIR B1: 2,7 BLK 1 A1: 2,7,1 # reduction candidate for 2,7 A1: 2,7 # 19 pairs C1: 2,7,1 # reduction candidate for 2,7 C1: 2,7 # 20 pairs * PAIR B1: 2,7 COL B B4: 2,7,3,4 # reduction candidate for 2,7 B4: 2,7 # 19 pairs B6: 2,7,3,6,8 # reduction candidate for 2,7 B6: 2,7 # 19 pairs * PAIR C2: 3,6 COL C C5: 3,6,5,8 # reduction candidate for 3,6 C5: 3,6 # 20 pairs C8: 3,6,5,7,8 # reduction candidate for 3,6 C8: 3,6 => CTR * ...365...853491276964278135...7.68...4.9.2617679..4523.1.5.7.6.4861.9.52.9.6.3..1 C8: 5,7,8 # 18 pairs * PAIR B3: 3,6 ROW 3 G3: 3,6,1 # reduction candidate for 3,6 G3: 1 => CTR * 721365...853..12769642781351327.68...4...2617679..4523.1.5.7.6.48..19352.9...37.1 G3: 3,6 # 20 pairs * PAIR B3: 3,6 COL B B5: 3,6,4,8 # reduction candidate for 3,6 B5: 3,6 => CTR * ...365...85...127.9.4..8....4...68.9.....2417..9..45.6.1.5.796.4....9..2.9...3... B5: 4,8 # 19 pairs B6: 3,6,2,7,8 # reduction candidate for 3,6 B6: 3,6 # 21 pairs B8: 3,6,7,8 # reduction candidate for 3,6 B8: 3,6 # 20 pairs * PAIR G1: 4,9 BLK 3 H1: 4,9,8 # reduction candidate for 4,9 H1: 4,9 # 20 pairs I1: 4,9,8 # reduction candidate for 4,9 I1: 4,9 # 17 pairs * PAIR G1: 4,9 COL G G5: 4,9,3,6 # reduction candidate for 4,9 G5: 4,9 => CTR * ...365...856..1273934..8651.....68.......2.17..9..45.6.1.5.7.6.4.5..9382.9...3..5 G5: 3,6 # 20 pairs G7: 4,9,3 # reduction candidate for 4,9 G7: 4,9 # 22 pairs * PAIR I2: 3,6 BLK 3 G3: 3,6,1 # reduction candidate for 3,6 G3: 1 => CTR * 721365...853..12769642781351327.68...4...2617679..4523.1.5.7.6.48..19352.9...37.1 G3: 3,6 # 20 pairs * PAIR H3: 3,5 COL H H8: 3,5,8 # reduction candidate for 3,5 H8: 8 # 26 pairs H8: 3,5 # 22 pairs * PAIR D5: 8,9 BLK 5 E5: 8,9,3,5 # reduction candidate for 8,9 E5: 8,9 => CTR * ...3659..856..1273934278651.4..568..56...2417..9.34526.1.5.7.6.4.56.9..269...3..5 E5: 3,5 # 19 pairs * PAIR I4: 4,9 BLK 6 H4: 4,9,2,3 # reduction candidate for 4,9 H4: 4,9 # 20 pairs G5: 4,9,3,6 # reduction candidate for 4,9 G5: 4,9 => CTR * ...365...856..1273934..8651.....68.......2.17..9..45.6.1.5.7.6.4.5..9382.9...3..5 G5: 3,6 # 20 pairs * PAIR I4: 4,9 COL I I1: 4,9,8 # reduction candidate for 4,9 I1: 4,9 # 17 pairs I7: 4,9,8 # reduction candidate for 4,9 I7: 4,9 # 20 pairs * PAIR H6: 2,3 BLK 6 H4: 2,3,4,9 # reduction candidate for 2,3 H4: 2,3 => CTR * ...365498856491273934..8651...9.68.464.8.2917.89..45.621.5473694....9.82.9...3.45 H4: 4,9 # 20 pairs * PAIR H6: 2,3 ROW 6 A6: 2,3,1,6,7 # reduction candidate for 2,3 A6: 2,3 => CTR * ...365...856491273934..8651.....68...4.9.23173.9..45262135.7.6.465..9732798..3..5 A6: 1,6,7 # 18 pairs B6: 2,3,6,7,8 # reduction candidate for 2,3 B6: 2,3 => CTR * ...365...85.491273934..8651.....68.....9.2.17.29..4536.1.5.7.6.4.5..9382.9...3... B6: 6,7,8 # 18 pairs * PAIR I6: 3,6 BLK 6 G5: 3,6,4,9 # reduction candidate for 3,6 G5: 4,9 => CTR * ...365...856..1273934..8651.....68.......2.17..9..45.6.1.5.7.6.4.5..9382.9...3..5 G5: 3,6 # 20 pairs * PAIR I6: 3,6 ROW 6 A6: 3,6,1,2,7 # reduction candidate for 3,6 A6: 3,6 # 20 pairs B6: 3,6,2,7,8 # reduction candidate for 3,6 B6: 3,6 # 21 pairs * PAIR A7: 2,3 BLK 7 C7: 2,3,8 # reduction candidate for 2,3 C7: 2,3 # 24 pairs C7: 8 # 21 pairs * PAIR A7: 2,3 COL A A4: 2,3,1,5,7 # reduction candidate for 2,3 A4: 2,3 # 21 pairs A6: 2,3,1,6,7 # reduction candidate for 2,3 A6: 2,3 => CTR * ...365...856491273934..8651.....68...4.9.23173.9..45262135.7.6.465..9732798..3..5 A6: 1,6,7 # 18 pairs * PAIR E8: 1,8 BLK 8 D8: 1,8,6 # reduction candidate for 1,8 D8: 1,8 => CTR * ...365...856491273934278651....568..645982317.89.34526.1.5.7.6.46.819732.9.6.3... D8: 6 # 18 pairs D9: 1,8,2,4,6 # reduction candidate for 1,8 D9: 1,8 # 17 pairs E9: 1,8,2,4 # reduction candidate for 1,8 E9: 1,8 # 22 pairs * PAIR E8: 1,8 COL E E6: 1,8,3,7 # reduction candidate for 1,8 E6: 3,7 # 19 pairs E6: 1,8 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-065-base-pr-000.dot * REASONING * DIS # C8: 3,6 => CTR => C8: 5,7,8 * DIS # G3: 1 => CTR => G3: 3,6 * DIS # B5: 3,6 => CTR => B5: 4,8 * DIS # G5: 4,9 => CTR => G5: 3,6 * DIS # G3: 1 => CTR => G3: 3,6 * DIS # E5: 8,9 => CTR => E5: 3,5 * DIS # G5: 4,9 => CTR => G5: 3,6 * DIS # H4: 2,3 => CTR => H4: 4,9 * DIS # A6: 2,3 => CTR => A6: 1,6,7 * DIS # B6: 2,3 => CTR => B6: 6,7,8 * DIS # G5: 4,9 => CTR => G5: 3,6 * DIS # A6: 2,3 => CTR => A6: 1,6,7 * DIS # D8: 1,8 => CTR => D8: 6 * CNT 13 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B1,B3,C2,D2,D3,D5,E2,E3,E8,G1,H3,H6,I2,I3,I4,I6,I9) * ...365...85...127.9.4..8........68.......2.17..9..45...1.5.7.6.4....9..2.9...3... * PAIR B1: 2,7 BLK 1 A1: 2,7,1 # reduction candidate for 2,7 A1: 2,7 # 19 pairs C1: 2,7,1 # reduction candidate for 2,7 C1: 2,7 # 20 pairs * PAIR B1: 2,7 COL B B4: 2,7,3,4 # reduction candidate for 2,7 B4: 2,7 # 19 pairs B6: 2,7,3,6,8 # reduction candidate for 2,7 B6: 2,7 # 19 pairs * PAIR C2: 3,6 COL C C5: 3,6,5,8 # reduction candidate for 3,6 C5: 3,6 # 20 pairs C8: 3,6,5,7,8 # reduction candidate for 3,6 C8: 3,6 => CTR * ...365...853491276964278135...7.68...4.9.2617679..4523.1.5.7.6.4861.9.52.9.6.3..1 * RESTART * PAIR C2: 3,6 COL C C5: 3,6,5,8 # reduction candidate for 3,6 C5: 3,6 # 20 pairs C5: 5,8 # 19 pairs * PAIR RESTART * PAIR C2: 3,6 COL C C5: 3,6,5,8 # reduction candidate for 3,6 C5: 3,6 # 20 pairs C5: 5,8 # 19 pairs * PAIR B3: 3,6 ROW 3 G3: 3,6,1 # reduction candidate for 3,6 G3: 1 => CTR * 72136548985349127696427813513.7.68...4...2617679184523.1.5.7.6.48.619352596823741 * PAIR B3: 3,6 COL B B5: 3,6,4,8 # reduction candidate for 3,6 B5: 3,6 => CTR * ...365...85...127.9.4..8.51.4...68.9.....2417..9..45.6.1.5.796.4.5..9..2.9...3..5 B6: 3,6,2,7,8 # reduction candidate for 3,6 B6: 3,6 # 27 pairs B8: 3,6,7,8 # reduction candidate for 3,6 B8: 3,6 # 22 pairs * PAIR RESTART * PAIR B3: 3,6 COL B B6: 3,6,2,7,8 # reduction candidate for 3,6 B6: 3,6 # 27 pairs B8: 3,6,7,8 # reduction candidate for 3,6 B8: 3,6 # 22 pairs * PAIR G1: 4,9 BLK 3 H1: 4,9,8 # reduction candidate for 4,9 H1: 4,9 # 23 pairs I1: 4,9,8 # reduction candidate for 4,9 I1: 4,9 # 16 pairs * PAIR G1: 4,9 COL G G5: 4,9,3,6 # reduction candidate for 4,9 G5: 4,9 => CTR * ...365...85...127.9.4..8651.....68.......2.17..9..45.6.1.5.73694.5..9..2.9...3..5 * RESTART * PAIR RESTART * PAIR G1: 4,9 BLK 3 H1: 4,9,8 # reduction candidate for 4,9 H1: 4,9 # 24 pairs I1: 4,9,8 # reduction candidate for 4,9 I1: 4,9 # 16 pairs * PAIR D5: 8,9 BLK 5 E5: 8,9,3,5 # reduction candidate for 8,9 E5: 8,9 => CTR * ...365...856..1273934.78651....568..54...2317..9.34526.1.5.7.6.4.56.9.3269...3..5 * PAIR I4: 4,9 COL I I1: 4,9,8 # reduction candidate for 4,9 I1: 4,9 # 17 pairs I7: 4,9,8 # reduction candidate for 4,9 I7: 4,9 # 20 pairs * PAIR I6: 3,6 ROW 6 A6: 3,6,1,7 # reduction candidate for 3,6 A6: 3,6 => SOLVED * 127365489853491276964278351231756894548932617679184523312547968485619732796823145 * DURATION: 0:00:31.824340 START: 00:18:06.151455 END: 00:18:37.975795 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-065-base-pr-001.dot * REASONING * DIS # C8: 3,6 => CTR => C8: 5,7,8 * DIS C8: 5,7,8 # G3: 1 => CTR => G3: 3,6 * DIS C8: 5,7,8 + G3: 3,6 # B5: 3,6 => CTR => B5: 4,8 * DIS C8: 5,7,8 + G3: 3,6 + B5: 4,8 # G5: 4,9 => CTR => G5: 3,6 * DIS C8: 5,7,8 + G3: 3,6 + B5: 4,8 + G5: 3,6 # E5: 8,9 => CTR => E5: 3,5 * PRF C8: 5,7,8 + G3: 3,6 + B5: 4,8 + G5: 3,6 + E5: 3,5 # A6: 3,6 => SOL * STA C8: 5,7,8 + G3: 3,6 + B5: 4,8 + G5: 3,6 + E5: 3,5 + A6: 3,6 * CNT 6 HDP CHAINS / 26 HYP OPENED
Header Info
Top 95 Sudokus 065 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 127365489853491276964278351231756894548932617679184523312547968485619732796823145 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 # A1: 2,7 => UNS * INC # C1: 2,7 => UNS * INC # B4: 2,7 => UNS * INC # B6: 2,7 => UNS * INC # C5: 3,6 => UNS * DIS # C8: 3,6 => CTR => C8: 5,7,8 * INC # C8: 5,7,8 => UNS * INC # G3: 3,6 => UNS * DIS # G3: 1 => CTR => G3: 3,6 * DIS # B5: 3,6 => CTR => B5: 4,8 * INC # B5: 4,8 => UNS * INC # B6: 3,6 => UNS * INC # B8: 3,6 => UNS * INC # H1: 4,9 => UNS * INC # I1: 4,9 => UNS * DIS # G5: 4,9 => CTR => G5: 3,6 * INC # G5: 3,6 => UNS * INC # G7: 4,9 => UNS * INC # G3: 3,6 => UNS * DIS # G3: 1 => CTR => G3: 3,6 * INC # H8: 3,5 => UNS * INC # H8: 8 => UNS * DIS # E5: 8,9 => CTR => E5: 3,5 * INC # E5: 3,5 => UNS * INC # H4: 4,9 => UNS * DIS # G5: 4,9 => CTR => G5: 3,6 * INC # G5: 3,6 => UNS * INC # I1: 4,9 => UNS * INC # I7: 4,9 => UNS * DIS # H4: 2,3 => CTR => H4: 4,9 * INC # H4: 4,9 => UNS * DIS # A6: 2,3 => CTR => A6: 1,6,7 * INC # A6: 1,6,7 => UNS * DIS # B6: 2,3 => CTR => B6: 6,7,8 * INC # B6: 6,7,8 => UNS * INC # G5: 3,6 => UNS * DIS # G5: 4,9 => CTR => G5: 3,6 * INC # A6: 3,6 => UNS * INC # B6: 3,6 => UNS * INC # C7: 2,3 => UNS * INC # C7: 8 => UNS * INC # A4: 2,3 => UNS * DIS # A6: 2,3 => CTR => A6: 1,6,7 * INC # A6: 1,6,7 => UNS * DIS # D8: 1,8 => CTR => D8: 6 * INC # D8: 6 => UNS * INC # D9: 1,8 => UNS * INC # E9: 1,8 => UNS * INC # E6: 1,8 => UNS * INC # E6: 3,7 => UNS * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 2,7 => UNS * INC # C1: 2,7 => UNS * INC # B4: 2,7 => UNS * INC # B6: 2,7 => UNS * INC # C5: 3,6 => UNS * DIS # C8: 3,6 => CTR => C8: 5,7,8 * INC C8: 5,7,8 # C5: 3,6 => UNS * INC C8: 5,7,8 # C5: 5,8 => UNS * INC C8: 5,7,8 # C5: 3,6 => UNS * INC C8: 5,7,8 # C5: 5,8 => UNS * INC C8: 5,7,8 # G3: 3,6 => UNS * DIS C8: 5,7,8 # G3: 1 => CTR => G3: 3,6 * DIS C8: 5,7,8 + G3: 3,6 # B5: 3,6 => CTR => B5: 4,8 * INC C8: 5,7,8 + G3: 3,6 + B5: 4,8 # B6: 3,6 => UNS * INC C8: 5,7,8 + G3: 3,6 + B5: 4,8 # B8: 3,6 => UNS * INC C8: 5,7,8 + G3: 3,6 + B5: 4,8 # B6: 3,6 => UNS * INC C8: 5,7,8 + G3: 3,6 + B5: 4,8 # B8: 3,6 => UNS * INC C8: 5,7,8 + G3: 3,6 + B5: 4,8 # H1: 4,9 => UNS * INC C8: 5,7,8 + G3: 3,6 + B5: 4,8 # I1: 4,9 => UNS * DIS C8: 5,7,8 + G3: 3,6 + B5: 4,8 # G5: 4,9 => CTR => G5: 3,6 * INC C8: 5,7,8 + G3: 3,6 + B5: 4,8 + G5: 3,6 # H1: 4,9 => UNS * INC C8: 5,7,8 + G3: 3,6 + B5: 4,8 + G5: 3,6 # I1: 4,9 => UNS * DIS C8: 5,7,8 + G3: 3,6 + B5: 4,8 + G5: 3,6 # E5: 8,9 => CTR => E5: 3,5 * INC C8: 5,7,8 + G3: 3,6 + B5: 4,8 + G5: 3,6 + E5: 3,5 # I1: 4,9 => UNS * INC C8: 5,7,8 + G3: 3,6 + B5: 4,8 + G5: 3,6 + E5: 3,5 # I7: 4,9 => UNS * PRF C8: 5,7,8 + G3: 3,6 + B5: 4,8 + G5: 3,6 + E5: 3,5 # A6: 3,6 => SOL * STA C8: 5,7,8 + G3: 3,6 + B5: 4,8 + G5: 3,6 + E5: 3,5 + A6: 3,6 * CNT 26 HDP CHAINS / 26 HYP OPENED