Analysis of xx-top500-399-base.sdk
Contents
Original Sudoku
level: medium
position: ....1.8...9.....3.2........4..5.3.6.7.1.....4..........5.2.......8...1.....6..... initial
Autosolve
position: 5...1.8..19.8...3.28.....1.4295837617319..5848651......5.2.1..8..8...1...126.8... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 4,7 => CTR => C1: 3,6 * DIS # C3: 4,7 => CTR => C3: 3,6 * DIS # D1: 4,7 => CTR => D1: 3 * DIS # F1: 4,7 => CTR => F1: 2,6,9 * DIS # E2: 4,7 => CTR => E2: 2,5,6 * DIS # E3: 4,7 => CTR => E3: 3,5,6,9 * PRF # E7: 4,7 => SOL * DIS # E8: 4,7 => CTR => E8: 3,5,9 * DIS # F1: 4,7 => CTR => F1: 2,6,9 * DIS # F8: 4,7 => CTR => F8: 5,9 * DIS # H1: 2,9 => CTR => H1: 4,7 * PRF # E7: 4,7 => SOL * DIS # C1: 4,7 => CTR => C1: 3,6 * DIS # C3: 4,7 => CTR => C3: 3,6 * DIS # E8: 4,7 => CTR => E8: 3,5,9 * DIS # F8: 4,7 => CTR => F8: 5,9 * DIS # H8: 4,7 => CTR => H8: 2,5,9 * DIS # E9: 3,9 => CTR => E9: 4,5,7 * PRF # G9: 3,9 => SOL * DIS # G9: 4 => CTR => G9: 3,9 * DIS # I9: 3,9 => CTR => I9: 7 * PRF # I9: 7 => SOL * CNT 22 HDP CHAINS / 57 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 4,7 => CTR => C1: 3,6 * DIS C1: 3,6 # C3: 4,7 => CTR => C3: 3,6 * DIS C1: 3,6 + C3: 3,6 # D1: 4,7 => CTR => D1: 3 * DIS C1: 3,6 + C3: 3,6 + D1: 3 # F1: 4,7 => CTR => F1: 2,9 * DIS C1: 3,6 + C3: 3,6 + D1: 3 + F1: 2,9 # H1: 2,9 => CTR => H1: 4,7 * DIS C1: 3,6 + C3: 3,6 + D1: 3 + F1: 2,9 + H1: 4,7 # E2: 4,7 => CTR => E2: 2,5,6 * DIS C1: 3,6 + C3: 3,6 + D1: 3 + F1: 2,9 + H1: 4,7 + E2: 2,5,6 # E3: 4,7 => CTR => E3: 5,6,9 * PRF C1: 3,6 + C3: 3,6 + D1: 3 + F1: 2,9 + H1: 4,7 + E2: 2,5,6 + E3: 5,6,9 # E7: 4,7 => SOL * STA C1: 3,6 + C3: 3,6 + D1: 3 + F1: 2,9 + H1: 4,7 + E2: 2,5,6 + E3: 5,6,9 + E7: 4,7 * CNT 8 HDP CHAINS / 15 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....1.8...9.....3.2........4..5.3.6.7.1.....4..........5.2.......8...1.....6..... | initial |
| 5...1.8..19.8...3.28.....1.4295837617319..5848651......5.2.1..8..8...1...126.8... | autosolve |
| 546312879197864235283795416429583761731926584865147923354271698678439152912658347 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) B1: 4,7 E5: 2,6 F5: 2,6 E6: 4,7 F6: 4,7 H6: 2,9 C7: 4,7 B8: 4,7 A9: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E5,F5: 2.. / E5 = 2 => 7 pairs (_) / F5 = 2 => 10 pairs (_) H8,I8: 2.. / H8 = 2 => 20 pairs (_) / I8 = 2 => 0 pairs (*) E2,E5: 2.. / E2 = 2 => 10 pairs (_) / E5 = 2 => 7 pairs (_) G2,G6: 2.. / G2 = 2 => 9 pairs (_) / G6 = 2 => 12 pairs (_) C1,C3: 3.. / C1 = 3 => 0 pairs (X) / C3 = 3 => 12 pairs (_) G6,I6: 3.. / G6 = 3 => 14 pairs (_) / I6 = 3 => 11 pairs (_) C1,D1: 3.. / C1 = 3 => 0 pairs (X) / D1 = 3 => 12 pairs (_) E6,F6: 4.. / E6 = 4 => 0 pairs (*) / F6 = 4 => 0 pairs (X) C7,B8: 4.. / C7 = 4 => 0 pairs (*) / B8 = 4 => 0 pairs (X) B1,B8: 4.. / B1 = 4 => 0 pairs (*) / B8 = 4 => 0 pairs (X) I2,I3: 5.. / I2 = 5 => 9 pairs (_) / I3 = 5 => 9 pairs (_) H8,H9: 5.. / H8 = 5 => 0 pairs (*) / H9 = 5 => 0 pairs (X) E9,H9: 5.. / E9 = 5 => 0 pairs (*) / H9 = 5 => 0 pairs (X) E5,F5: 6.. / E5 = 6 => 10 pairs (_) / F5 = 6 => 7 pairs (_) A7,A8: 6.. / A7 = 6 => 22 pairs (_) / A8 = 6 => 12 pairs (_) G7,I8: 6.. / G7 = 6 => 12 pairs (_) / I8 = 6 => 22 pairs (_) A7,G7: 6.. / A7 = 6 => 22 pairs (_) / G7 = 6 => 12 pairs (_) A8,I8: 6.. / A8 = 6 => 12 pairs (_) / I8 = 6 => 22 pairs (_) E6,F6: 7.. / E6 = 7 => 0 pairs (X) / F6 = 7 => 0 pairs (_) C7,B8: 7.. / C7 = 7 => 0 pairs (X) / B8 = 7 => 0 pairs (_) B1,B8: 7.. / B1 = 7 => 0 pairs (X) / B8 = 7 => 0 pairs (_) * DURATION: 0:00:33.587125 START: 16:26:50.451563 END: 16:27:24.038688 2017-05-04 * CP COUNT: (21) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B1,B8,C7,E5,E6,F5,F6,H6) * 5...1.8..19.8...3.28.....1.4295837617319..5848651......5.2.1..8..8...1...126.8... * PAIR B1: 4,7 BLK 1 C1: 4,7,3,6 # reduction candidate for 4,7 C1: 4,7 => CTR * 5..31.8..1968...3.283....1.4295837617319..5848651......5.2.1..8..8...1...126.8... C1: 3,6 # 10 pairs C2: 4,7,6 # reduction candidate for 4,7 C2: 4,7 # 12 pairs C3: 4,7,3,6 # reduction candidate for 4,7 C3: 4,7 => CTR * 5.3.1.8..1968...3.28.....1.4295837617319..5848651......5.2.16.86.8...1.2.126.8... C3: 3,6 # 10 pairs * PAIR B1: 4,7 ROW 1 D1: 4,7,3 # reduction candidate for 4,7 D1: 4,7 => CTR * 5.3.1.8..19.8...3.28.....1.4295837617319..5848651......5.2.16.86.8...1.2.126.8... D1: 3 # 12 pairs F1: 4,7,2,6,9 # reduction candidate for 4,7 F1: 4,7 => CTR * 5...1.8.919.8...3.28.....1.4295837617319..5848651..293.5.2.1..8..8...1.2.126.8..7 F1: 2,6,9 # 9 pairs H1: 4,7,2,9 # reduction candidate for 4,7 H1: 4,7 # 16 pairs * PAIR E5: 2,6 COL E E2: 2,6,4,5,7 # reduction candidate for 2,6 E2: 4,5,7 # 20 pairs E2: 2,6 # 10 pairs * PAIR F5: 2,6 COL F F1: 2,6,4,7,9 # reduction candidate for 2,6 F1: 2,6 # 11 pairs F2: 2,6,4,5,7 # reduction candidate for 2,6 F2: 2,6 # 13 pairs * PAIR E6: 4,7 COL E E2: 4,7,2,5,6 # reduction candidate for 4,7 E2: 4,7 => CTR * 5...1.8..19.8...3.28..6..1.4295837617319265848651......5.2.1..8..8...1...126.8... E2: 2,5,6 # 9 pairs E3: 4,7,3,5,6,9 # reduction candidate for 4,7 E3: 4,7 => CTR * 5...1.8..19.8...3.28.....1.4295837617319..5848651......5.2.1..8..8...1...126.8... E3: 3,5,6,9 # 9 pairs E7: 4,7,3,9 # reduction candidate for 4,7 E7: 4,7 => SOLVED * 546312879197864235283795416429583761731926584865147923354271698678439152912658347 E7: 3,9 # 10 pairs E8: 4,7,3,5,9 # reduction candidate for 4,7 E8: 4,7 => CTR * 5...1.8..19.8...3.28.....1.4295837617319..5848651......5.2.1..8..8...1...126.8... E8: 3,5,9 # 9 pairs E9: 4,7,3,5,9 # reduction candidate for 4,7 E9: 4,7 # 11 pairs * PAIR F6: 4,7 COL F F1: 4,7,2,6,9 # reduction candidate for 4,7 F1: 4,7 => CTR * 5...1.8.919.8...3.28.....1.4295837617319..5848651..293.5.2.1..8..8...1.2.126.8..7 F1: 2,6,9 # 9 pairs F2: 4,7,2,5,6 # reduction candidate for 4,7 F2: 4,7 # 12 pairs F3: 4,7,5,6,9 # reduction candidate for 4,7 F3: 4,7 # 12 pairs F8: 4,7,5,9 # reduction candidate for 4,7 F8: 4,7 => CTR * 5.3.1.8..19.8...3.28..3..1.4295837617319..5848651......5.291..8..835.1...126.8... F8: 5,9 # 10 pairs * PAIR H6: 2,9 BLK 6 G6: 2,9,3 # reduction candidate for 2,9 G6: 2,9 # 11 pairs I6: 2,9,3 # reduction candidate for 2,9 I6: 2,9 # 14 pairs * PAIR H6: 2,9 COL H H1: 2,9,4,7 # reduction candidate for 2,9 H1: 2,9 => CTR * 5...1.8..19.8...3.28.....1.4295837617319..5848651......5.2.1..8..8...1...126.8... H1: 4,7 # 16 pairs H8: 2,9,4,5,7 # reduction candidate for 2,9 H8: 2,9 # 20 pairs * PAIR C7: 4,7 ROW 7 E7: 4,7,3,9 # reduction candidate for 4,7 E7: 4,7 => SOLVED * 546312879197864235283795416429583761731926584865147923354271698678439152912658347 E7: 3,9 # 10 pairs H7: 4,7,9 # reduction candidate for 4,7 H7: 4,7 # 11 pairs * PAIR C7: 4,7 COL C C1: 4,7,3,6 # reduction candidate for 4,7 C1: 4,7 => CTR * 5..31.8..1968...3.283....1.4295837617319..5848651......5.2.1..8..8...1...126.8... C1: 3,6 # 10 pairs C2: 4,7,6 # reduction candidate for 4,7 C2: 4,7 # 12 pairs C3: 4,7,3,6 # reduction candidate for 4,7 C3: 4,7 => CTR * 5.3.1.8..1968...3.28.....1.4295837617319..5848651......5.2.16.86.8...1.2.126.8... C3: 3,6 # 10 pairs * PAIR B8: 4,7 ROW 8 D8: 4,7,3 # reduction candidate for 4,7 D8: 4,7 # 11 pairs E8: 4,7,3,5,9 # reduction candidate for 4,7 E8: 4,7 => CTR * 5...1.8..19.8...3.28.....1.4295837617319..5848651......5.2.1..8..8...1...126.8... E8: 3,5,9 # 9 pairs F8: 4,7,5,9 # reduction candidate for 4,7 F8: 4,7 => CTR * 5.3.1.8..19.8...3.28..3..1.4295837617319..5848651......5.291..8..835.1...126.8... F8: 5,9 # 10 pairs H8: 4,7,2,5,9 # reduction candidate for 4,7 H8: 4,7 => CTR * 5...128.919.8..23.28....41.4295837617319265848651..92335.2.16986.8...142912648357 H8: 2,5,9 # 9 pairs * PAIR A9: 3,9 BLK 7 A7: 3,9,6 # reduction candidate for 3,9 A7: 3,9 # 12 pairs A8: 3,9,6 # reduction candidate for 3,9 A8: 3,9 # 22 pairs * PAIR A9: 3,9 ROW 9 E9: 3,9,4,5,7 # reduction candidate for 3,9 E9: 3,9 => CTR * 5...1.87.19.8...3.28.....1.4295837617319..5848651......5.2.1..8.78...1...126.8457 E9: 4,5,7 # 9 pairs G9: 3,9,4 # reduction candidate for 3,9 G9: 3,9 => SOLVED * 546312879197864235283795416429583761731926584865147923354271698678439152912658347 G9: 4 => CTR * 57631.84.1948...3.2834...1.4295837617319..584865174329357241698648739152.126.8473 I9: 3,9,7 # reduction candidate for 3,9 I9: 3,9 => CTR * 57631284919.8...3.2834...1.4295837617319..5848651.4....57241.98.48739152912658473 I9: 7 => SOLVED * 546312879197864235283795416429583761731926584865147923354271698678439152912658347 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-399-base-pr-000.dot * REASONING * DIS # C1: 4,7 => CTR => C1: 3,6 * DIS # C3: 4,7 => CTR => C3: 3,6 * DIS # D1: 4,7 => CTR => D1: 3 * DIS # F1: 4,7 => CTR => F1: 2,6,9 * DIS # E2: 4,7 => CTR => E2: 2,5,6 * DIS # E3: 4,7 => CTR => E3: 3,5,6,9 * PRF # E7: 4,7 => SOL * DIS # E8: 4,7 => CTR => E8: 3,5,9 * DIS # F1: 4,7 => CTR => F1: 2,6,9 * DIS # F8: 4,7 => CTR => F8: 5,9 * DIS # H1: 2,9 => CTR => H1: 4,7 * PRF # E7: 4,7 => SOL * DIS # C1: 4,7 => CTR => C1: 3,6 * DIS # C3: 4,7 => CTR => C3: 3,6 * DIS # E8: 4,7 => CTR => E8: 3,5,9 * DIS # F8: 4,7 => CTR => F8: 5,9 * DIS # H8: 4,7 => CTR => H8: 2,5,9 * DIS # E9: 3,9 => CTR => E9: 4,5,7 * PRF # G9: 3,9 => SOL * DIS # G9: 4 => CTR => G9: 3,9 * DIS # I9: 3,9 => CTR => I9: 7 * PRF # I9: 7 => SOL * CNT 22 HDP CHAINS / 57 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B1,B8,C7,E5,E6,F5,F6,H6) * 5...1.8..19.8...3.28.....1.4295837617319..5848651......5.2.1..8..8...1...126.8... * PAIR B1: 4,7 BLK 1 C1: 4,7,3,6 # reduction candidate for 4,7 C1: 4,7 => CTR * 5..31.8..1968...3.283....1.4295837617319..5848651......5.2.1..8..8...1...126.8... C2: 4,7,6 # reduction candidate for 4,7 C2: 4,7 # 12 pairs C3: 4,7,3,6 # reduction candidate for 4,7 C3: 4,7 => CTR * 5.3.1.8..1968...3.28.....1.4295837617319..5848651......5.2.16.86.8...1.2.126.8... * RESTART * PAIR B1: 4,7 ROW 1 D1: 4,7,3 # reduction candidate for 4,7 D1: 4,7 => CTR * 5.3.1.8..19.8...3.286....1.4295837617319..5848651......5.2.16.86.8...1.2.126.8... F1: 4,7,2,9 # reduction candidate for 4,7 F1: 4,7 => CTR * 5.631.8.919.8...3.283....1.4295837617319..5848651..293.5.2.1..8..8...1.2.126.8..7 H1: 4,7,2,9 # reduction candidate for 4,7 H1: 4,7 # 16 pairs * RESTART * PAIR B1: 4,7 ROW 1 H1: 4,7,2,9 # reduction candidate for 4,7 H1: 2,9 => CTR * 54631.8.71978...3.283....1.4295837617319..5848651......542.1..8.784..1...126.8.4. * PAIR RESTART * PAIR E5: 2,6 COL E E2: 2,6,4,5,7 # reduction candidate for 2,6 E2: 4,5,7 # 20 pairs E2: 2,6 # 17 pairs * PAIR F5: 2,6 COL F F2: 2,6,4,5,7 # reduction candidate for 2,6 F2: 2,6 # 23 pairs F2: 4,5,7 # 16 pairs * PAIR E6: 4,7 COL E E2: 4,7,2,5,6 # reduction candidate for 4,7 E2: 4,7 => CTR * 5.631.8..19.8...3.283.6..1.4295837617319265848651......5.2.1..8..8...1...126.8... E3: 4,7,5,6,9 # reduction candidate for 4,7 E3: 4,7 => CTR * 5.631.8..19.85..3.283....154295837617319..5848651......5.2.1..8..8..51...126.8.5. E7: 4,7,3,9 # reduction candidate for 4,7 E7: 4,7 => SOLVED * 546312879197864235283795416429583761731926584865147923354271698678439152912658347 * DURATION: 0:00:16.145312 START: 16:28:09.429564 END: 16:28:25.574876 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-399-base-pr-001.dot * REASONING * DIS # C1: 4,7 => CTR => C1: 3,6 * DIS C1: 3,6 # C3: 4,7 => CTR => C3: 3,6 * DIS C1: 3,6 + C3: 3,6 # D1: 4,7 => CTR => D1: 3 * DIS C1: 3,6 + C3: 3,6 + D1: 3 # F1: 4,7 => CTR => F1: 2,9 * DIS C1: 3,6 + C3: 3,6 + D1: 3 + F1: 2,9 # H1: 2,9 => CTR => H1: 4,7 * DIS C1: 3,6 + C3: 3,6 + D1: 3 + F1: 2,9 + H1: 4,7 # E2: 4,7 => CTR => E2: 2,5,6 * DIS C1: 3,6 + C3: 3,6 + D1: 3 + F1: 2,9 + H1: 4,7 + E2: 2,5,6 # E3: 4,7 => CTR => E3: 5,6,9 * PRF C1: 3,6 + C3: 3,6 + D1: 3 + F1: 2,9 + H1: 4,7 + E2: 2,5,6 + E3: 5,6,9 # E7: 4,7 => SOL * STA C1: 3,6 + C3: 3,6 + D1: 3 + F1: 2,9 + H1: 4,7 + E2: 2,5,6 + E3: 5,6,9 + E7: 4,7 * CNT 8 HDP CHAINS / 15 HYP OPENED
Header Info
Top 500 Minimum 17 399 solution: 546312879197864235283795416429583761731926584865147923354271698678439152912658347 info: 90173 FNBX S8.f 2974 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 546312879197864235283795416429583761731926584865147923354271698678439152912658347 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 # C1: 4,7 => CTR => C1: 3,6 * INC # C1: 3,6 => UNS * INC # C2: 4,7 => UNS * DIS # C3: 4,7 => CTR => C3: 3,6 * INC # C3: 3,6 => UNS * DIS # D1: 4,7 => CTR => D1: 3 * INC # D1: 3 => UNS * DIS # F1: 4,7 => CTR => F1: 2,6,9 * INC # F1: 2,6,9 => UNS * INC # H1: 4,7 => UNS * INC # E2: 2,6 => UNS * INC # E2: 4,5,7 => UNS * INC # F1: 2,6 => UNS * INC # F2: 2,6 => UNS * DIS # E2: 4,7 => CTR => E2: 2,5,6 * INC # E2: 2,5,6 => UNS * DIS # E3: 4,7 => CTR => E3: 3,5,6,9 * INC # E3: 3,5,6,9 => UNS * PRF # E7: 4,7 => SOL * INC # E7: 3,9 => UNS * DIS # E8: 4,7 => CTR => E8: 3,5,9 * INC # E8: 3,5,9 => UNS * INC # E9: 4,7 => UNS * DIS # F1: 4,7 => CTR => F1: 2,6,9 * INC # F1: 2,6,9 => UNS * INC # F2: 4,7 => UNS * INC # F3: 4,7 => UNS * DIS # F8: 4,7 => CTR => F8: 5,9 * INC # F8: 5,9 => UNS * INC # G6: 2,9 => UNS * INC # I6: 2,9 => UNS * DIS # H1: 2,9 => CTR => H1: 4,7 * INC # H1: 4,7 => UNS * INC # H8: 2,9 => UNS * PRF # E7: 4,7 => SOL * INC # E7: 3,9 => UNS * INC # H7: 4,7 => UNS * DIS # C1: 4,7 => CTR => C1: 3,6 * INC # C1: 3,6 => UNS * INC # C2: 4,7 => UNS * DIS # C3: 4,7 => CTR => C3: 3,6 * INC # C3: 3,6 => UNS * INC # D8: 4,7 => UNS * DIS # E8: 4,7 => CTR => E8: 3,5,9 * INC # E8: 3,5,9 => UNS * DIS # F8: 4,7 => CTR => F8: 5,9 * INC # F8: 5,9 => UNS * DIS # H8: 4,7 => CTR => H8: 2,5,9 * INC # H8: 2,5,9 => UNS * INC # A7: 3,9 => UNS * INC # A8: 3,9 => UNS * DIS # E9: 3,9 => CTR => E9: 4,5,7 * INC # E9: 4,5,7 => UNS * PRF # G9: 3,9 => SOL * DIS # G9: 4 => CTR => G9: 3,9 * DIS # I9: 3,9 => CTR => I9: 7 * PRF # I9: 7 => SOL * CNT 57 HDP CHAINS / 57 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C1: 4,7 => CTR => C1: 3,6 * INC C1: 3,6 # C2: 4,7 => UNS * DIS C1: 3,6 # C3: 4,7 => CTR => C3: 3,6 * DIS C1: 3,6 + C3: 3,6 # D1: 4,7 => CTR => D1: 3 * DIS C1: 3,6 + C3: 3,6 + D1: 3 # F1: 4,7 => CTR => F1: 2,9 * INC C1: 3,6 + C3: 3,6 + D1: 3 + F1: 2,9 # H1: 4,7 => UNS * INC C1: 3,6 + C3: 3,6 + D1: 3 + F1: 2,9 # H1: 4,7 => UNS * DIS C1: 3,6 + C3: 3,6 + D1: 3 + F1: 2,9 # H1: 2,9 => CTR => H1: 4,7 * INC C1: 3,6 + C3: 3,6 + D1: 3 + F1: 2,9 + H1: 4,7 # E2: 2,6 => UNS * INC C1: 3,6 + C3: 3,6 + D1: 3 + F1: 2,9 + H1: 4,7 # E2: 4,5,7 => UNS * INC C1: 3,6 + C3: 3,6 + D1: 3 + F1: 2,9 + H1: 4,7 # F2: 2,6 => UNS * INC C1: 3,6 + C3: 3,6 + D1: 3 + F1: 2,9 + H1: 4,7 # F2: 4,5,7 => UNS * DIS C1: 3,6 + C3: 3,6 + D1: 3 + F1: 2,9 + H1: 4,7 # E2: 4,7 => CTR => E2: 2,5,6 * DIS C1: 3,6 + C3: 3,6 + D1: 3 + F1: 2,9 + H1: 4,7 + E2: 2,5,6 # E3: 4,7 => CTR => E3: 5,6,9 * PRF C1: 3,6 + C3: 3,6 + D1: 3 + F1: 2,9 + H1: 4,7 + E2: 2,5,6 + E3: 5,6,9 # E7: 4,7 => SOL * STA C1: 3,6 + C3: 3,6 + D1: 3 + F1: 2,9 + H1: 4,7 + E2: 2,5,6 + E3: 5,6,9 + E7: 4,7 * CNT 15 HDP CHAINS / 15 HYP OPENED