Analysis of xx-top500-075-base.sdk
Contents
Original Sudoku
level: medium
position: .41.........3..5.....2.....2..5..3......4..6.8.........6..1..4.37....2........... initial
Autosolve
position: .41.......293.15.4.832.41..2945..3..1.7.4..6.8.61..4..96..1..4.37.4..2..41....... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E2: 8 => CTR => E2: 6,7 * DIS # G1: 7,8 => CTR => G1: 6,9 * DIS # E2: 6 => CTR => E2: 7,8 * DIS # H4: 7,8 => CTR => H4: 1 * DIS # H9: 7,8 => CTR => H9: 3,5,9 * DIS # I3: 7,9 => CTR => I3: 6 * DIS # H6: 7,9 => CTR => H6: 2,5 * PRF # H9: 7,9 => SOL * DIS # D1: 8,9 => CTR => D1: 6,7 * DIS # D9: 8,9 => CTR => D9: 6,7 * DIS # H6: 7,9 => CTR => H6: 2,5 * DIS # G9: 8,9 => CTR => G9: 6,7 * DIS # I6: 2,5 => CTR => I6: 7,9 * DIS # F7: 3 => CTR => F7: 2,5 * DIS # C9: 2 => CTR => C9: 5,8 * PRF # H8: 5,8 => SOL * DIS # I8: 5,8 => CTR => I8: 1,6,9 * DIS # D1: 7,8 => CTR => D1: 6,9 * DIS # G9: 7,8 => CTR => G9: 6,9 * DIS # H9: 7,8 => CTR => H9: 3,5,9 * DIS # G1: 7,8 => CTR => G1: 6,9 * DIS # I9: 3,5 => CTR => I9: 6,7,8,9 * DIS # F7: 2 => CTR => F7: 3,5 * CNT 23 HDP CHAINS / 68 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E2: 8 => CTR => E2: 6,7 * DIS E2: 6,7 # I3: 7,9 => CTR => I3: 6 * PRF E2: 6,7 + I3: 6 # H9: 7,9 => SOL * STA E2: 6,7 + I3: 6 + H9: 7,9 * CNT 3 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .41.........3..5.....2.....2..5..3......4..6.8.........6..1..4.37....2........... | initial |
| .41.......293.15.4.832.41..2945..3..1.7.4..6.8.61..4..96..1..4.37.4..2..41....... | autosolve |
| 741658932629371584583294176294586317137942865856137429962815743378469251415723698 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) A2: 6,7 H1: 2,3 I1: 2,3 H2: 7,8 H3: 7,9 B5: 3,5 B6: 3,5 D5: 8,9 F5: 2,3 E6: 2,3 F6: 7,9 G5: 8,9 I5: 2,5 C7: 2,5 C8: 5,8 D7: 7,8 E9: 2,3 G7: 7,8 I7: 3,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H4,I4: 1.. / H4 = 1 => 25 pairs (_) / I4 = 1 => 0 pairs (X) H8,I8: 1.. / H8 = 1 => 0 pairs (X) / I8 = 1 => 25 pairs (_) H4,H8: 1.. / H4 = 1 => 25 pairs (_) / H8 = 1 => 0 pairs (X) I4,I8: 1.. / I4 = 1 => 0 pairs (X) / I8 = 1 => 25 pairs (_) H1,I1: 2.. / H1 = 2 => 0 pairs (X) / I1 = 2 => 11 pairs (_) F5,E6: 2.. / F5 = 2 => 11 pairs (_) / E6 = 2 => 0 pairs (X) C7,C9: 2.. / C7 = 2 => 20 pairs (_) / C9 = 2 => 0 pairs (X) F5,I5: 2.. / F5 = 2 => 11 pairs (_) / I5 = 2 => 0 pairs (X) C7,F7: 2.. / C7 = 2 => 20 pairs (_) / F7 = 2 => 0 pairs (X) E6,E9: 2.. / E6 = 2 => 0 pairs (X) / E9 = 2 => 11 pairs (_) H1,H6: 2.. / H1 = 2 => 0 pairs (X) / H6 = 2 => 11 pairs (_) H1,I1: 3.. / H1 = 3 => 11 pairs (_) / I1 = 3 => 0 pairs (X) B5,B6: 3.. / B5 = 3 => 11 pairs (_) / B6 = 3 => 0 pairs (X) F5,E6: 3.. / F5 = 3 => 0 pairs (X) / E6 = 3 => 11 pairs (_) B5,F5: 3.. / B5 = 3 => 11 pairs (_) / F5 = 3 => 0 pairs (X) B6,E6: 3.. / B6 = 3 => 0 pairs (X) / E6 = 3 => 11 pairs (_) F7,I7: 3.. / F7 = 3 => 0 pairs (X) / I7 = 3 => 11 pairs (_) E6,E9: 3.. / E6 = 3 => 11 pairs (_) / E9 = 3 => 0 pairs (X) H1,H9: 3.. / H1 = 3 => 11 pairs (_) / H9 = 3 => 0 pairs (X) A1,A3: 5.. / A1 = 5 => 20 pairs (_) / A3 = 5 => 20 pairs (_) B5,B6: 5.. / B5 = 5 => 0 pairs (X) / B6 = 5 => 11 pairs (_) A3,E3: 5.. / A3 = 5 => 20 pairs (_) / E3 = 5 => 20 pairs (_) B5,I5: 5.. / B5 = 5 => 0 pairs (X) / I5 = 5 => 11 pairs (_) G1,I3: 6.. / G1 = 6 => 0 pairs (X) / I3 = 6 => 23 pairs (_) E4,F4: 6.. / E4 = 6 => 24 pairs (_) / F4 = 6 => 20 pairs (_) A2,E2: 6.. / A2 = 6 => 21 pairs (_) / E2 = 6 => 0 pairs (X) D1,D9: 6.. / D1 = 6 => 23 pairs (_) / D9 = 6 => 0 pairs (X) G1,G9: 6.. / G1 = 6 => 0 pairs (X) / G9 = 6 => 23 pairs (_) D7,G7: 7.. / D7 = 7 => 0 pairs (X) / G7 = 7 => 18 pairs (_) G1,H2: 8.. / G1 = 8 => 0 pairs (X) / H2 = 8 => 20 pairs (_) C8,C9: 8.. / C8 = 8 => 19 pairs (_) / C9 = 8 => 27 pairs (_) E2,H2: 8.. / E2 = 8 => 0 pairs (X) / H2 = 8 => 20 pairs (_) D5,G5: 8.. / D5 = 8 => 0 pairs (X) / G5 = 8 => 18 pairs (_) D7,G7: 8.. / D7 = 8 => 18 pairs (_) / G7 = 8 => 0 pairs (X) D5,F6: 9.. / D5 = 9 => 18 pairs (_) / F6 = 9 => 0 pairs (X) D5,G5: 9.. / D5 = 9 => 18 pairs (_) / G5 = 9 => 0 pairs (X) * DURATION: 0:01:04.315454 START: 05:16:38.206062 END: 05:17:42.521516 2017-05-04 * CP COUNT: (36) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B5,B6,C7,C8,D5,D7,E6,E9,F5,F6,G5,G7,H1,H2,H3,I1,I5,I7) * .41.......293.15.4.832.41..2945..3..1.7.4..6.8.61..4..96..1..4.37.4..2..41....... * PAIR A2: 6,7 BLK 1 A1: 6,7,5 # reduction candidate for 6,7 A1: 6,7 # 20 pairs A3: 6,7,5 # reduction candidate for 6,7 A3: 6,7 # 20 pairs * PAIR A2: 6,7 ROW 2 E2: 6,7,8 # reduction candidate for 6,7 E2: 8 => CTR * .416..8..629381574.832.41962945..3..1.784.96.8.61.94.796.71..4.37.4..2..41....6.. E2: 6,7 # 20 pairs * PAIR H2: 7,8 BLK 3 G1: 7,8,6,9 # reduction candidate for 7,8 G1: 7,8 => CTR * .4169....6293.15.4.832.41962945..3..1.784.96.8.61.94..96.71.84.37.4..2.941.9..6.. G1: 6,9 # 22 pairs * PAIR H2: 7,8 ROW 2 E2: 7,8,6 # reduction candidate for 7,8 E2: 6 => CTR * .41...6..7293615846832541..2945.63.11.7.4.86.8.61..4..96.81.74.37849521641.6.79.8 E2: 7,8 # 21 pairs * PAIR H2: 7,8 COL H H4: 7,8,1 # reduction candidate for 7,8 H4: 7,8 => CTR * .416..9...293.15.4.832.41..2945..3.11.794.86.8.61.74..96.81.74.37.4..21.41.7..... H4: 1 # 25 pairs H9: 7,8,3,5,9 # reduction candidate for 7,8 H9: 7,8 => CTR * .416...326293.15.4.832.41962945..31.13794286585613.42.962.15.433784..251415.23... H9: 3,5,9 # 19 pairs * PAIR H3: 7,9 BLK 3 G1: 7,9,6,8 # reduction candidate for 7,9 G1: 7,9 # 25 pairs I3: 7,9,6 # reduction candidate for 7,9 I3: 7,9 => CTR * .41...6...293.1584.832.41..2945.63.11.7.4.86.8.61..4..96.81.74.3784..21641.6.79.8 I3: 6 # 23 pairs * PAIR H3: 7,9 ROW 3 E3: 7,9,5,6 # reduction candidate for 7,9 E3: 5,6 # 20 pairs E3: 7,9 # 18 pairs * PAIR H3: 7,9 COL H H6: 7,9,2,5 # reduction candidate for 7,9 H6: 7,9 => CTR * .41....23.293.15.4.832.41..2945..3..1.7.4..6.8.61..4..96..13.4537.4..2..41..2..3. H6: 2,5 # 21 pairs H9: 7,9,3,5,8 # reduction candidate for 7,9 H9: 7,9 => SOLVED * 741658932629371584583294176294586317137942865856137429962815743378469251415723698 H9: 3,5,8 # 19 pairs * PAIR D5: 8,9 COL D D1: 8,9,6,7 # reduction candidate for 8,9 D1: 8,9 => CTR * .41...6...293.1584.832.41..2945.63..1.7.4..6.8.61..4..96.71.84.37.4..2.641.6..7.. D1: 6,7 # 20 pairs D9: 8,9,6,7 # reduction candidate for 8,9 D9: 8,9 => CTR * .416..7..6293715847832541962945..3.81.784.96.8.61.94..96.71.84.37.4..2.141.9..6.. D9: 6,7 # 20 pairs * PAIR F5: 2,3 COL F F7: 2,3,5 # reduction candidate for 2,3 F7: 2,3 # 20 pairs F9: 2,3,5,6,7,8,9 # reduction candidate for 2,3 F9: 2,3 # 11 pairs * PAIR F6: 7,9 ROW 6 H6: 7,9,2,5 # reduction candidate for 7,9 H6: 7,9 => CTR * .41....23.293.15.4.832.41..2945..3..1.7.4..6.8.61..4..96..13.4537.4..2..41..2..3. H6: 2,5 # 21 pairs I6: 7,9,2,5 # reduction candidate for 7,9 I6: 7,9 # 21 pairs * PAIR F6: 7,9 COL F F1: 7,9,5,6,8 # reduction candidate for 7,9 F1: 7,9 # 21 pairs F9: 7,9,2,3,5,6,8 # reduction candidate for 7,9 F9: 7,9 # 20 pairs * PAIR G5: 8,9 COL G G1: 8,9,6,7 # reduction candidate for 8,9 G1: 8,9 # 18 pairs G9: 8,9,6,7 # reduction candidate for 8,9 G9: 8,9 => CTR * .417..6..7293615846832541..2945763181.7.4..6.8.61..4..96..1.74.37.4..2..41.6.7... G9: 6,7 # 20 pairs * PAIR I5: 2,5 BLK 6 H6: 2,5,7,9 # reduction candidate for 2,5 H6: 2,5 # 21 pairs I6: 2,5,7,9 # reduction candidate for 2,5 I6: 2,5 => CTR * .41.......293.15.4.832.41..2945..3..1.7.4..6.8.61..4..96..1..4.37.4..2..41....... I6: 7,9 # 21 pairs * PAIR C7: 2,5 BLK 7 C9: 2,5,8 # reduction candidate for 2,5 C9: 8 # 27 pairs C9: 2,5 # 19 pairs * PAIR C7: 2,5 ROW 7 F7: 2,5,3 # reduction candidate for 2,5 F7: 3 => CTR * .41.......293.15.4.832.41..2945..3..1.7.4..6.8.61..4..962.13.4537.4..2..41..2.... F7: 2,5 # 11 pairs * PAIR C8: 5,8 BLK 7 C9: 5,8,2 # reduction candidate for 5,8 C9: 2 => CTR * .41....32.293.15.4.832.41..2945..3..1.7.4..6.8.61..4..96..1..4.3784..2..412.3.... C9: 5,8 # 20 pairs * PAIR C8: 5,8 ROW 8 E8: 5,8,6,9 # reduction candidate for 5,8 E8: 5,8 # 25 pairs F8: 5,8,6,9 # reduction candidate for 5,8 F8: 5,8 # 25 pairs H8: 5,8,1,9 # reduction candidate for 5,8 H8: 5,8 => SOLVED * 741658932629371584583294176294586317137942865856137429962815743378469251415723698 H8: 1,9 # 23 pairs I8: 5,8,1,6,9 # reduction candidate for 5,8 I8: 5,8 => CTR * .416.....6293.15.4.832.41.62945..3.11.794.86.8.61.74..96.81.74.37.4..21.41.7..6.. I8: 1,6,9 # 19 pairs * PAIR D7: 7,8 BLK 8 D9: 7,8,6,9 # reduction candidate for 7,8 D9: 7,8 # 18 pairs F9: 7,8,2,3,5,6,9 # reduction candidate for 7,8 F9: 7,8 # 26 pairs * PAIR D7: 7,8 COL D D1: 7,8,6,9 # reduction candidate for 7,8 D1: 7,8 => CTR * .41...6...293.1584.832.41..2945.63..1.794.86.8.61.74..96..1..4.37.4..2..41.6..... D1: 6,9 # 20 pairs * PAIR E9: 2,3 BLK 8 F7: 2,3,5 # reduction candidate for 2,3 F7: 2,3 # 20 pairs F9: 2,3,5,6,7,8,9 # reduction candidate for 2,3 F9: 2,3 # 11 pairs * PAIR G7: 7,8 BLK 9 G9: 7,8,6,9 # reduction candidate for 7,8 G9: 7,8 => CTR * .419..6...293.1584.832.41..2945.63.81.784.96.8.61.94..96.71.84.37.4..2..41.6..... G9: 6,9 # 20 pairs H9: 7,8,3,5,9 # reduction candidate for 7,8 H9: 7,8 => CTR * .416...326293.15.4.832.41962945..31.13794286585613.42.962.15.433784..251415.23... H9: 3,5,9 # 19 pairs I9: 7,8,3,5,6,9 # reduction candidate for 7,8 I9: 7,8 # 21 pairs * PAIR G7: 7,8 COL G G1: 7,8,6,9 # reduction candidate for 7,8 G1: 7,8 => CTR * .4169....6293.15.4.832.41962945..3..1.784.96.8.61.94..96.71.84.37.4..2.941.9..6.. G1: 6,9 # 22 pairs * PAIR I7: 3,5 BLK 9 H9: 3,5,7,8,9 # reduction candidate for 3,5 H9: 3,5 # 22 pairs I9: 3,5,6,7,8,9 # reduction candidate for 3,5 I9: 3,5 => CTR * .41.......293.15.4.832.41..2945..3..1.7.4..6.8.61..4..96..1..4.37.4..2..41....... I9: 6,7,8,9 # 19 pairs * PAIR I7: 3,5 ROW 7 F7: 3,5,2 # reduction candidate for 3,5 F7: 2 => CTR * .41....32.293.15.4.832.41..2945..3..1.7.43.658.61..4..96..12.4337.4..2..412.3.... F7: 3,5 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-075-base-pr-000.dot * REASONING * DIS # E2: 8 => CTR => E2: 6,7 * DIS # G1: 7,8 => CTR => G1: 6,9 * DIS # E2: 6 => CTR => E2: 7,8 * DIS # H4: 7,8 => CTR => H4: 1 * DIS # H9: 7,8 => CTR => H9: 3,5,9 * DIS # I3: 7,9 => CTR => I3: 6 * DIS # H6: 7,9 => CTR => H6: 2,5 * PRF # H9: 7,9 => SOL * DIS # D1: 8,9 => CTR => D1: 6,7 * DIS # D9: 8,9 => CTR => D9: 6,7 * DIS # H6: 7,9 => CTR => H6: 2,5 * DIS # G9: 8,9 => CTR => G9: 6,7 * DIS # I6: 2,5 => CTR => I6: 7,9 * DIS # F7: 3 => CTR => F7: 2,5 * DIS # C9: 2 => CTR => C9: 5,8 * PRF # H8: 5,8 => SOL * DIS # I8: 5,8 => CTR => I8: 1,6,9 * DIS # D1: 7,8 => CTR => D1: 6,9 * DIS # G9: 7,8 => CTR => G9: 6,9 * DIS # H9: 7,8 => CTR => H9: 3,5,9 * DIS # G1: 7,8 => CTR => G1: 6,9 * DIS # I9: 3,5 => CTR => I9: 6,7,8,9 * DIS # F7: 2 => CTR => F7: 3,5 * CNT 23 HDP CHAINS / 68 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B5,B6,C7,C8,D5,D7,E6,E9,F5,F6,G5,G7,H1,H2,H3,I1,I5,I7) * .41.......293.15.4.832.41..2945..3..1.7.4..6.8.61..4..96..1..4.37.4..2..41....... * PAIR A2: 6,7 BLK 1 A1: 6,7,5 # reduction candidate for 6,7 A1: 6,7 # 20 pairs A3: 6,7,5 # reduction candidate for 6,7 A3: 6,7 # 20 pairs * PAIR A2: 6,7 ROW 2 E2: 6,7,8 # reduction candidate for 6,7 E2: 8 => CTR * .416..8..629381574.832.41962945..3..1.784.96.8.61.94.796.71..4.37.4..2..41....6.. * PAIR RESTART * PAIR A2: 6,7 BLK 1 A1: 6,7,5 # reduction candidate for 6,7 A1: 6,7 # 21 pairs A3: 6,7,5 # reduction candidate for 6,7 A3: 6,7 # 22 pairs * PAIR H3: 7,9 BLK 3 G1: 7,9,6 # reduction candidate for 7,9 G1: 7,9 # 25 pairs I3: 7,9,6 # reduction candidate for 7,9 I3: 7,9 => CTR * .41...6...293.1584.832.41..2945.63.11.7.4.86.8.61..4..96.81.74.3784..21641.6.79.8 * RESTART * PAIR H3: 7,9 COL H H9: 7,9,3,5 # reduction candidate for 7,9 H9: 7,9 => SOLVED * 741658932629371584583294176294586317137942865856137429962815743378469251415723698 * DURATION: 0:00:10.203766 START: 05:18:46.251536 END: 05:18:56.455302 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-075-base-pr-001.dot * REASONING * DIS # E2: 8 => CTR => E2: 6,7 * DIS E2: 6,7 # I3: 7,9 => CTR => I3: 6 * PRF E2: 6,7 + I3: 6 # H9: 7,9 => SOL * STA E2: 6,7 + I3: 6 + H9: 7,9 * CNT 3 HDP CHAINS / 9 HYP OPENED
Header Info
Top 500 Minimum 17 075 solution: 741658932629371584583294176294586317137942865856137429962815743378469251415723698 info: 1493 FNTHWY S8.f 19306 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 741658932629371584583294176294586317137942865856137429962815743378469251415723698 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: 6,7 => UNS * INC # A3: 6,7 => UNS * INC # E2: 6,7 => UNS * DIS # E2: 8 => CTR => E2: 6,7 * DIS # G1: 7,8 => CTR => G1: 6,9 * INC # G1: 6,9 => UNS * INC # E2: 7,8 => UNS * DIS # E2: 6 => CTR => E2: 7,8 * DIS # H4: 7,8 => CTR => H4: 1 * INC # H4: 1 => UNS * DIS # H9: 7,8 => CTR => H9: 3,5,9 * INC # H9: 3,5,9 => UNS * INC # G1: 7,9 => UNS * DIS # I3: 7,9 => CTR => I3: 6 * INC # I3: 6 => UNS * INC # E3: 7,9 => UNS * INC # E3: 5,6 => UNS * DIS # H6: 7,9 => CTR => H6: 2,5 * INC # H6: 2,5 => UNS * PRF # H9: 7,9 => SOL * INC # H9: 3,5,8 => UNS * DIS # D1: 8,9 => CTR => D1: 6,7 * INC # D1: 6,7 => UNS * DIS # D9: 8,9 => CTR => D9: 6,7 * INC # D9: 6,7 => UNS * INC # F7: 2,3 => UNS * INC # F9: 2,3 => UNS * DIS # H6: 7,9 => CTR => H6: 2,5 * INC # H6: 2,5 => UNS * INC # I6: 7,9 => UNS * INC # F1: 7,9 => UNS * INC # F9: 7,9 => UNS * INC # G1: 8,9 => UNS * DIS # G9: 8,9 => CTR => G9: 6,7 * INC # G9: 6,7 => UNS * INC # H6: 2,5 => UNS * DIS # I6: 2,5 => CTR => I6: 7,9 * INC # I6: 7,9 => UNS * INC # C9: 2,5 => UNS * INC # C9: 8 => UNS * INC # F7: 2,5 => UNS * DIS # F7: 3 => CTR => F7: 2,5 * INC # C9: 5,8 => UNS * DIS # C9: 2 => CTR => C9: 5,8 * INC # E8: 5,8 => UNS * INC # F8: 5,8 => UNS * PRF # H8: 5,8 => SOL * INC # H8: 1,9 => UNS * DIS # I8: 5,8 => CTR => I8: 1,6,9 * INC # I8: 1,6,9 => UNS * INC # D9: 7,8 => UNS * INC # F9: 7,8 => UNS * DIS # D1: 7,8 => CTR => D1: 6,9 * INC # D1: 6,9 => UNS * INC # F7: 2,3 => UNS * INC # F9: 2,3 => UNS * DIS # G9: 7,8 => CTR => G9: 6,9 * INC # G9: 6,9 => UNS * DIS # H9: 7,8 => CTR => H9: 3,5,9 * INC # H9: 3,5,9 => UNS * INC # I9: 7,8 => UNS * DIS # G1: 7,8 => CTR => G1: 6,9 * INC # G1: 6,9 => UNS * INC # H9: 3,5 => UNS * DIS # I9: 3,5 => CTR => I9: 6,7,8,9 * INC # I9: 6,7,8,9 => UNS * INC # F7: 3,5 => UNS * DIS # F7: 2 => CTR => F7: 3,5 * CNT 68 HDP CHAINS / 68 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 6,7 => UNS * INC # A3: 6,7 => UNS * INC # E2: 6,7 => UNS * DIS # E2: 8 => CTR => E2: 6,7 * INC E2: 6,7 # A1: 6,7 => UNS * INC E2: 6,7 # A3: 6,7 => UNS * INC E2: 6,7 # G1: 7,9 => UNS * DIS E2: 6,7 # I3: 7,9 => CTR => I3: 6 * PRF E2: 6,7 + I3: 6 # H9: 7,9 => SOL * STA E2: 6,7 + I3: 6 + H9: 7,9 * CNT 9 HDP CHAINS / 9 HYP OPENED