Analysis of zz-www.sudokuoftheday.co.uk-20060414-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006
level: medium
position: .4.9.5.......2.3....71....29..5.....43.....1...8.4.6...6.38..977.....2..3.9...8.. initial
Autosolve
position: 2439.5.......2.3....71....29..5.....43.....1...8.4.6...6.38..9778....2..3.9...8.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 1,5 => CTR => B2: 9 * PRF # C7: 1,5 => SOL * DIS # B2: 1 => CTR => B2: 5,9 * DIS # G3: 4 => CTR => G3: 5,9 * DIS # H1: 6,7 => CTR => H1: 8 * DIS # E4: 6,7 => CTR => E4: 1,3 * DIS # E9: 6,7 => CTR => E9: 1,5 * PRF # E4: 3,6 => SOL * DIS # F4: 2,7 => CTR => F4: 1,3,6,8 * DIS # F6: 2,7 => CTR => F6: 1,3,9 * DIS # H4: 4,7 => CTR => H4: 2,3,8 * PRF # C7: 1,5 => SOL * DIS # B9: 1,5 => CTR => B9: 2 * PRF # G7: 4 => SOL * DIS # H8: 4,6 => CTR => H8: 3,5 * CNT 15 HDP CHAINS / 55 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 1,5 => CTR => B2: 9 * DIS B2: 9 # H1: 6,7 => CTR => H1: 8 * DIS B2: 9 + H1: 8 # E4: 6,7 => CTR => E4: 1,3 * DIS B2: 9 + H1: 8 + E4: 1,3 # E9: 6,7 => CTR => E9: 1,5 * DIS B2: 9 + H1: 8 + E4: 1,3 + E9: 1,5 # D2: 6,7 => CTR => D2: 4,8 * DIS B2: 9 + H1: 8 + E4: 1,3 + E9: 1,5 + D2: 4,8 # F4: 2,7 => CTR => F4: 1,3,6,8 * PRF B2: 9 + H1: 8 + E4: 1,3 + E9: 1,5 + D2: 4,8 + F4: 1,3,6,8 # D5: 2,7 => SOL * STA B2: 9 + H1: 8 + E4: 1,3 + E9: 1,5 + D2: 4,8 + F4: 1,3,6,8 + D5: 2,7 * CNT 7 HDP CHAINS / 23 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .4.9.5.......2.3....71....29..5.....43.....1...8.4.6...6.38..977.....2..3.9...8.. | initial |
| 2439.5.......2.3....71....29..5.....43.....1...8.4.6...6.38..9778....2..3.9...8.. | autosolve |
| 243975186691824375857163942916538724432796518578241639165382497784619253329457861 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A2: 6,8 C2: 1,5 A3: 6,8 B3: 5,9 E1: 6,7 E3: 3,6 G1: 1,7 A6: 1,5 D6: 2,7 G4: 4,7 A7: 1,5 D8: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,C2: 1.. / B2 = 1 => 0 pairs (X) / C2 = 1 => 15 pairs (_) G1,I1: 1.. / G1 = 1 => 13 pairs (_) / I1 = 1 => 0 pairs (X) A6,A7: 1.. / A6 = 1 => 0 pairs (X) / A7 = 1 => 17 pairs (_) G1,G7: 1.. / G1 = 1 => 13 pairs (_) / G7 = 1 => 0 pairs (X) H4,H6: 2.. / H4 = 2 => 15 pairs (_) / H6 = 2 => 0 pairs (X) C7,B9: 2.. / C7 = 2 => 0 pairs (X) / B9 = 2 => 16 pairs (_) C7,F7: 2.. / C7 = 2 => 0 pairs (X) / F7 = 2 => 16 pairs (_) E3,F3: 3.. / E3 = 3 => 11 pairs (_) / F3 = 3 => 0 pairs (*) H8,I8: 3.. / H8 = 3 => 16 pairs (_) / I8 = 3 => 19 pairs (_) E3,E4: 3.. / E3 = 3 => 11 pairs (_) / E4 = 3 => 0 pairs (*) C7,C8: 4.. / C7 = 4 => 18 pairs (_) / C8 = 4 => 13 pairs (_) E8,E9: 5.. / E8 = 5 => 0 pairs (X) / E9 = 5 => 14 pairs (_) A6,A7: 5.. / A6 = 5 => 17 pairs (_) / A7 = 5 => 0 pairs (X) A2,A3: 6.. / A2 = 6 => 10 pairs (_) / A3 = 6 => 11 pairs (_) C4,C5: 6.. / C4 = 6 => 13 pairs (_) / C5 = 6 => 0 pairs (X) B4,B6: 7.. / B4 = 7 => 17 pairs (_) / B6 = 7 => 0 pairs (*) A2,A3: 8.. / A2 = 8 => 11 pairs (_) / A3 = 8 => 10 pairs (_) H1,I1: 8.. / H1 = 8 => 13 pairs (_) / I1 = 8 => 0 pairs (X) A3,F3: 8.. / A3 = 8 => 10 pairs (_) / F3 = 8 => 11 pairs (_) D2,D5: 8.. / D2 = 8 => 12 pairs (_) / D5 = 8 => 13 pairs (_) H1,H4: 8.. / H1 = 8 => 13 pairs (_) / H4 = 8 => 0 pairs (X) B2,B3: 9.. / B2 = 9 => 15 pairs (_) / B3 = 9 => 0 pairs (X) I2,G3: 9.. / I2 = 9 => 0 pairs (X) / G3 = 9 => 15 pairs (_) E8,F8: 9.. / E8 = 9 => 16 pairs (_) / F8 = 9 => 16 pairs (_) B2,I2: 9.. / B2 = 9 => 15 pairs (_) / I2 = 9 => 0 pairs (X) B3,G3: 9.. / B3 = 9 => 0 pairs (X) / G3 = 9 => 15 pairs (_) F6,I6: 9.. / F6 = 9 => 19 pairs (_) / I6 = 9 => 16 pairs (_) E5,E8: 9.. / E5 = 9 => 16 pairs (_) / E8 = 9 => 16 pairs (_) G3,G5: 9.. / G3 = 9 => 15 pairs (_) / G5 = 9 => 0 pairs (X) * DURATION: 0:00:28.899670 START: 22:23:02.686440 END: 22:23:31.586110 2019-04-30 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A6,A7,B3,C2,D6,D8,E1,E3,G1,G4) * 2439.5.......2.3....71....29..5.....43.....1...8.4.6...6.38..9778....2..3.9...8.. * PAIR A2: 6,8 ROW 2 D2: 6,8,4,7 # reduction candidate for 6,8 D2: 6,8 # 15 pairs F2: 6,8,4,7 # reduction candidate for 6,8 F2: 6,8 # 15 pairs * PAIR C2: 1,5 BLK 1 B2: 1,5,9 # reduction candidate for 1,5 B2: 1,5 => CTR * 2439.5.......2.3.9.9713..529.6513.28432...915..8249673.6.382597785.9.23.329.5.8.. B2: 9 # 15 pairs * PAIR C2: 1,5 COL C C7: 1,5,2,4 # reduction candidate for 1,5 C7: 1,5 => SOLVED * 243975186691824375857163942916538724432796518578241639165382497784619253329457861 C7: 2,4 # 13 pairs C8: 1,5,4 # reduction candidate for 1,5 C8: 1,5 # 18 pairs * PAIR A3: 6,8 ROW 3 F3: 6,8,3,4 # reduction candidate for 6,8 F3: 6,8 # 13 pairs F3: 3,4 # 12 pairs * PAIR B3: 5,9 BLK 1 B2: 5,9,1 # reduction candidate for 5,9 B2: 1 => CTR * 2439.5....15.2.3.9.971....29..5.....43....915..8.496.3.6.38..9778..9.2..3.9...8.. B2: 5,9 # 15 pairs * PAIR B3: 5,9 ROW 3 G3: 5,9,4 # reduction candidate for 5,9 G3: 4 => CTR * 2439.5.......2.3.9.971..4529..5..7..43....91..7824963556.38.19778....2..3.9...8.. G3: 5,9 # 14 pairs * PAIR E1: 6,7 BLK 2 D2: 6,7,4,8 # reduction candidate for 6,7 D2: 6,7 # 16 pairs F2: 6,7,4,8 # reduction candidate for 6,7 F2: 6,7 # 14 pairs * PAIR E1: 6,7 ROW 1 H1: 6,7,8 # reduction candidate for 6,7 H1: 6,7 => CTR * 243975168.91.2.375..71....297.5..48343....71...8743629.6.38.59778....23.329.578.1 H1: 8 # 13 pairs * PAIR E1: 6,7 COL E E4: 6,7,1,3 # reduction candidate for 6,7 E4: 6,7 => CTR * 2439.5178.91.2.35..5713.9.29..57.48343..9.7155.8.4.6.9164382597785.192..329.5.8.1 E4: 1,3 # 13 pairs E5: 6,7,9 # reduction candidate for 6,7 E5: 6,7 # 16 pairs E9: 6,7,1,5 # reduction candidate for 6,7 E9: 6,7 => CTR * 243965178.91.2.3...5713.9.29..51..8343..9..15518.43629165382497784659231329471856 E9: 1,5 # 13 pairs * PAIR E3: 3,6 BLK 2 F3: 3,6,4,8 # reduction candidate for 3,6 F3: 3,6 # 17 pairs F3: 4,8 # 12 pairs * PAIR E3: 3,6 COL E E4: 3,6,1,7 # reduction candidate for 3,6 E4: 3,6 => SOLVED * 243975186691824375857163942916538724432796518578241639165382497784619253329457861 E4: 1,7 # 12 pairs * PAIR A6: 1,5 BLK 4 B6: 1,5,2,7 # reduction candidate for 1,5 B6: 1,5 # 20 pairs B6: 2,7 # 17 pairs * PAIR D6: 2,7 BLK 5 F4: 2,7,1,3,6,8 # reduction candidate for 2,7 F4: 2,7 => CTR * 2439.51...91.2.35..571..9.29.65.7428432...715578241639.6.382.9778....2..329...8.. F4: 1,3,6,8 # 12 pairs D5: 2,7,6,8 # reduction candidate for 2,7 D5: 2,7 # 16 pairs F5: 2,7,6,8,9 # reduction candidate for 2,7 F5: 2,7 # 15 pairs F6: 2,7,1,3,9 # reduction candidate for 2,7 F6: 2,7 => CTR * 2439.5186.91.2.375.571..9429765..42.43.....1.518.4.63916.38..9778....2.3329...8.1 F6: 1,3,9 # 12 pairs * PAIR D6: 2,7 ROW 6 B6: 2,7,1,5 # reduction candidate for 2,7 B6: 2,7 # 17 pairs H6: 2,7,3,5 # reduction candidate for 2,7 H6: 2,7 # 22 pairs * PAIR D6: 2,7 COL D D9: 2,7,4,6 # reduction candidate for 2,7 D9: 4,6 # 16 pairs D9: 2,7 # 14 pairs * PAIR G4: 4,7 BLK 6 H4: 4,7,2,3,8 # reduction candidate for 4,7 H4: 4,7 => CTR * 2439.5.8.....2.3....71....297.5..4..43.....1...874.62..6.38..9778....23.3.9...8.. H4: 2,3,8 # 12 pairs * PAIR A7: 1,5 BLK 7 C7: 1,5,2,4 # reduction candidate for 1,5 C7: 1,5 => SOLVED * 243975186691824375857163942916538724432796518578241639165382497784619253329457861 C7: 2,4 # 13 pairs C8: 1,5,4 # reduction candidate for 1,5 C8: 1,5 # 18 pairs B9: 1,5,2 # reduction candidate for 1,5 B9: 1,5 => CTR * 2439.5186...42.37...71..94297.5..42.43.8.271..2874.6..1623845977846592313592..8.. B9: 2 # 16 pairs * PAIR A7: 1,5 ROW 7 G7: 1,5,4 # reduction candidate for 1,5 G7: 4 => SOLVED * 243975186691824375857163942916538724432796518578241639165382497784619253329457861 G7: 1,5 # 15 pairs * PAIR D8: 4,6 BLK 8 F8: 4,6,1,9 # reduction candidate for 4,6 F8: 4,6 # 26 pairs D9: 4,6,2,7 # reduction candidate for 4,6 D9: 4,6 # 16 pairs F9: 4,6,1,2,7 # reduction candidate for 4,6 F9: 4,6 # 17 pairs * PAIR D8: 4,6 ROW 8 H8: 4,6,3,5 # reduction candidate for 4,6 H8: 4,6 => CTR * 243975186..1.2.37...71...529..5.....43.....155.8.4.6.9164382597785...2.3329.5.8.1 H8: 3,5 # 13 pairs I8: 4,6,1,3,5 # reduction candidate for 4,6 I8: 4,6 # 25 pairs * PAIR D8: 4,6 COL D D2: 4,6,7,8 # reduction candidate for 4,6 D2: 4,6 # 15 pairs D2: 7,8 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060414-absurd-base-pr-000.dot * REASONING * DIS # B2: 1,5 => CTR => B2: 9 * PRF # C7: 1,5 => SOL * DIS # B2: 1 => CTR => B2: 5,9 * DIS # G3: 4 => CTR => G3: 5,9 * DIS # H1: 6,7 => CTR => H1: 8 * DIS # E4: 6,7 => CTR => E4: 1,3 * DIS # E9: 6,7 => CTR => E9: 1,5 * PRF # E4: 3,6 => SOL * DIS # F4: 2,7 => CTR => F4: 1,3,6,8 * DIS # F6: 2,7 => CTR => F6: 1,3,9 * DIS # H4: 4,7 => CTR => H4: 2,3,8 * PRF # C7: 1,5 => SOL * DIS # B9: 1,5 => CTR => B9: 2 * PRF # G7: 4 => SOL * DIS # H8: 4,6 => CTR => H8: 3,5 * CNT 15 HDP CHAINS / 55 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A6,A7,B3,C2,D6,D8,E1,E3,G1,G4) * 2439.5.......2.3....71....29..5.....43.....1...8.4.6...6.38..9778....2..3.9...8.. * PAIR A2: 6,8 ROW 2 D2: 6,8,4,7 # reduction candidate for 6,8 D2: 6,8 # 15 pairs F2: 6,8,4,7 # reduction candidate for 6,8 F2: 6,8 # 15 pairs * PAIR C2: 1,5 BLK 1 B2: 1,5,9 # reduction candidate for 1,5 B2: 1,5 => CTR * 2439.5.......2.3.9.9713..529.6513.28432...915..8249673.6.382597785.9.23.329.5.8.. * PAIR A3: 6,8 ROW 3 F3: 6,8,3,4 # reduction candidate for 6,8 F3: 6,8 # 16 pairs F3: 3,4 # 16 pairs * PAIR E1: 6,7 BLK 2 D2: 6,7,4,8 # reduction candidate for 6,7 D2: 6,7 # 19 pairs F2: 6,7,4,8 # reduction candidate for 6,7 F2: 6,7 # 17 pairs * PAIR E1: 6,7 ROW 1 H1: 6,7,8 # reduction candidate for 6,7 H1: 6,7 => CTR * 2439.51.8.91.2.3...571..9.297.5..48343....71..1874362916.38.597785...23.329.578.1 * PAIR E1: 6,7 COL E E4: 6,7,1,3 # reduction candidate for 6,7 E4: 6,7 => CTR * 2439.5186.91.2.3...5713.9.29..5....843..9..155.8.4.6.916.38.597785.192.3329.5.8.1 E5: 6,7,9 # reduction candidate for 6,7 E5: 6,7 # 20 pairs E9: 6,7,1,5 # reduction candidate for 6,7 E9: 6,7 => CTR * 2439.5186.91.2.375.571..9429..51....43..9..18..8.4.6.9.6.38..977846592313.9...8.. * RESTART * PAIR E1: 6,7 COL E E5: 6,7,9 # reduction candidate for 6,7 E5: 9 # 20 pairs E5: 6,7 # 20 pairs * PAIR RESTART * PAIR E1: 6,7 BLK 2 D2: 6,7,4,8 # reduction candidate for 6,7 D2: 6,7 => CTR * 2439.5.8..91.2.3...5713.9.297.5134284328...1.51824.673164382597785...23.329.5.8.. F2: 6,7,4,8 # reduction candidate for 6,7 F2: 6,7 # 23 pairs * RESTART * PAIR E1: 6,7 BLK 2 F2: 6,7,4,8 # reduction candidate for 6,7 F2: 6,7 # 23 pairs F2: 4,8 # 22 pairs * PAIR E1: 6,7 COL E E5: 6,7,9 # reduction candidate for 6,7 E5: 6,7 # 21 pairs E5: 9 # 20 pairs * PAIR E3: 3,6 BLK 2 F3: 3,6,4,8 # reduction candidate for 3,6 F3: 4,8 # 23 pairs F3: 3,6 # 22 pairs * PAIR D6: 2,7 BLK 5 F4: 2,7,1,3,6,8 # reduction candidate for 2,7 F4: 2,7 => CTR * 243975186.91.2.375.571..9429.65..4.8432....1...8.4.6...6.38..9778....2..3.9...8.. D5: 2,7,6,8 # reduction candidate for 2,7 D5: 2,7 => SOLVED * 243975186691824375857163942916538724432796518578241639165382497784619253329457861 * DURATION: 0:00:16.055009 START: 22:24:00.744009 END: 22:24:16.799018 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060414-absurd-base-pr-001.dot * REASONING * DIS # B2: 1,5 => CTR => B2: 9 * DIS B2: 9 # H1: 6,7 => CTR => H1: 8 * DIS B2: 9 + H1: 8 # E4: 6,7 => CTR => E4: 1,3 * DIS B2: 9 + H1: 8 + E4: 1,3 # E9: 6,7 => CTR => E9: 1,5 * DIS B2: 9 + H1: 8 + E4: 1,3 + E9: 1,5 # D2: 6,7 => CTR => D2: 4,8 * DIS B2: 9 + H1: 8 + E4: 1,3 + E9: 1,5 + D2: 4,8 # F4: 2,7 => CTR => F4: 1,3,6,8 * PRF B2: 9 + H1: 8 + E4: 1,3 + E9: 1,5 + D2: 4,8 + F4: 1,3,6,8 # D5: 2,7 => SOL * STA B2: 9 + H1: 8 + E4: 1,3 + E9: 1,5 + D2: 4,8 + F4: 1,3,6,8 + D5: 2,7 * CNT 7 HDP CHAINS / 23 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060414, absurd
Solution
position: 243975186691824375857163942916538724432796518578241639165382497784619253329457861 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 # D2: 6,8 => UNS * INC # F2: 6,8 => UNS * DIS # B2: 1,5 => CTR => B2: 9 * INC # B2: 9 => UNS * PRF # C7: 1,5 => SOL * INC # C7: 2,4 => UNS * INC # C8: 1,5 => UNS * INC # F3: 6,8 => UNS * INC # F3: 3,4 => UNS * INC # B2: 5,9 => UNS * DIS # B2: 1 => CTR => B2: 5,9 * INC # G3: 5,9 => UNS * DIS # G3: 4 => CTR => G3: 5,9 * INC # D2: 6,7 => UNS * INC # F2: 6,7 => UNS * DIS # H1: 6,7 => CTR => H1: 8 * INC # H1: 8 => UNS * DIS # E4: 6,7 => CTR => E4: 1,3 * INC # E4: 1,3 => UNS * INC # E5: 6,7 => UNS * DIS # E9: 6,7 => CTR => E9: 1,5 * INC # E9: 1,5 => UNS * INC # F3: 3,6 => UNS * INC # F3: 4,8 => UNS * PRF # E4: 3,6 => SOL * INC # E4: 1,7 => UNS * INC # B6: 1,5 => UNS * INC # B6: 2,7 => UNS * DIS # F4: 2,7 => CTR => F4: 1,3,6,8 * INC # F4: 1,3,6,8 => UNS * INC # D5: 2,7 => UNS * INC # F5: 2,7 => UNS * DIS # F6: 2,7 => CTR => F6: 1,3,9 * INC # F6: 1,3,9 => UNS * INC # B6: 2,7 => UNS * INC # H6: 2,7 => UNS * INC # D9: 2,7 => UNS * INC # D9: 4,6 => UNS * DIS # H4: 4,7 => CTR => H4: 2,3,8 * INC # H4: 2,3,8 => UNS * PRF # C7: 1,5 => SOL * INC # C7: 2,4 => UNS * INC # C8: 1,5 => UNS * DIS # B9: 1,5 => CTR => B9: 2 * INC # B9: 2 => UNS * INC # G7: 1,5 => UNS * PRF # G7: 4 => SOL * INC # F8: 4,6 => UNS * INC # D9: 4,6 => UNS * INC # F9: 4,6 => UNS * DIS # H8: 4,6 => CTR => H8: 3,5 * INC # H8: 3,5 => UNS * INC # I8: 4,6 => UNS * INC # D2: 4,6 => UNS * INC # D2: 7,8 => UNS * CNT 55 HDP CHAINS / 55 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D2: 6,8 => UNS * INC # F2: 6,8 => UNS * DIS # B2: 1,5 => CTR => B2: 9 * INC B2: 9 # F3: 6,8 => UNS * INC B2: 9 # F3: 3,4 => UNS * INC B2: 9 # D2: 6,7 => UNS * INC B2: 9 # F2: 6,7 => UNS * DIS B2: 9 # H1: 6,7 => CTR => H1: 8 * DIS B2: 9 + H1: 8 # E4: 6,7 => CTR => E4: 1,3 * INC B2: 9 + H1: 8 + E4: 1,3 # E5: 6,7 => UNS * DIS B2: 9 + H1: 8 + E4: 1,3 # E9: 6,7 => CTR => E9: 1,5 * INC B2: 9 + H1: 8 + E4: 1,3 + E9: 1,5 # E5: 6,7 => UNS * INC B2: 9 + H1: 8 + E4: 1,3 + E9: 1,5 # E5: 9 => UNS * DIS B2: 9 + H1: 8 + E4: 1,3 + E9: 1,5 # D2: 6,7 => CTR => D2: 4,8 * INC B2: 9 + H1: 8 + E4: 1,3 + E9: 1,5 + D2: 4,8 # F2: 6,7 => UNS * INC B2: 9 + H1: 8 + E4: 1,3 + E9: 1,5 + D2: 4,8 # F2: 6,7 => UNS * INC B2: 9 + H1: 8 + E4: 1,3 + E9: 1,5 + D2: 4,8 # F2: 4,8 => UNS * INC B2: 9 + H1: 8 + E4: 1,3 + E9: 1,5 + D2: 4,8 # E5: 6,7 => UNS * INC B2: 9 + H1: 8 + E4: 1,3 + E9: 1,5 + D2: 4,8 # E5: 9 => UNS * INC B2: 9 + H1: 8 + E4: 1,3 + E9: 1,5 + D2: 4,8 # F3: 3,6 => UNS * INC B2: 9 + H1: 8 + E4: 1,3 + E9: 1,5 + D2: 4,8 # F3: 4,8 => UNS * DIS B2: 9 + H1: 8 + E4: 1,3 + E9: 1,5 + D2: 4,8 # F4: 2,7 => CTR => F4: 1,3,6,8 * PRF B2: 9 + H1: 8 + E4: 1,3 + E9: 1,5 + D2: 4,8 + F4: 1,3,6,8 # D5: 2,7 => SOL * STA B2: 9 + H1: 8 + E4: 1,3 + E9: 1,5 + D2: 4,8 + F4: 1,3,6,8 + D5: 2,7 * CNT 23 HDP CHAINS / 23 HYP OPENED