Analysis of zz-www.sudokuoftheday.co.uk-20060824-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006
level: medium
position: 7......5.....6...9......1.8.48.1..9..9..8...3.7.6.5.....9.2..4......1....3..4.861 initial
Autosolve
position: 7...3..5.....6...99.....1.8.48.13.9..9..8..13.7.695.8...9.26.4......19...3..4.861 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 1,4 => CTR => A2: 3,8 * DIS # C2: 1,4 => CTR => C2: 3,5 * DIS # D1: 1,4 => CTR => D1: 2,9 * DIS # D2: 5,7 => CTR => D2: 1,2,4 * DIS # A5: 2,5 => CTR => A5: 6 * DIS # C9: 2,5 => CTR => C9: 7 * DIS # A2: 1,3 => CTR => A2: 4,8 * PRF # A2: 4,8 => SOL * DIS # C2: 1,3 => CTR => C2: 4,5 * DIS # D2: 2,7 => CTR => D2: 1,4,5 * DIS # G1: 2,4 => CTR => G1: 6 * PRF # G1: 6 => SOL * PRF # G2: 2,4 => SOL * DIS # G2: 3 => CTR => G2: 2,4 * PRF # I1: 2,4 => SOL * DIS # I1: 6 => CTR => I1: 2,4 * DIS # B7: 1,8 => CTR => B7: 5 * PRF # B7: 5 => SOL * PRF # A2: 1,8 => SOL * PRF # A2: 4,8 => SOL * DIS # A2: 1,3 => CTR => A2: 4,8 * DIS # C9: 2,5 => CTR => C9: 7 * DIS # A5: 2,5 => CTR => A5: 6 * DIS # D9: 9 => CTR => D9: 5,7 * DIS # C8: 5,7 => CTR => C8: 4,6 * DIS # D9: 7,9 => CTR => D9: 5 * DIS # G7: 5,7 => CTR => G7: 3 * PRF # G7: 3 => SOL * DIS # I4: 5,7 => CTR => I4: 6 * PRF # I4: 6 => SOL * PRF # H2: 2,3 => SOL * CNT 31 HDP CHAINS / 53 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 1,4 => CTR => A2: 3,8 * DIS A2: 3,8 # C2: 1,4 => CTR => C2: 3,5 * DIS A2: 3,8 + C2: 3,5 # D1: 1,4 => CTR => D1: 2,9 * PRF A2: 3,8 + C2: 3,5 + D1: 2,9 # D3: 2,4 => SOL * STA A2: 3,8 + C2: 3,5 + D1: 2,9 + D3: 2,4 * CNT 4 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7......5.....6...9......1.8.48.1..9..9..8...3.7.6.5.....9.2..4......1....3..4.861 | initial |
| 7...3..5.....6...99.....1.8.48.13.9..9..8..13.7.695.8...9.26.4......19...3..4.861 | autosolve |
| 714938652825167439963452178548213796692784513371695284159826347486371925237549861 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) C1: 1,4 E3: 5,7 C5: 2,5 A6: 1,3 C6: 1,3 D4: 2,7 G6: 2,4 I6: 2,4 A7: 1,8 A8: 4,8 A9: 2,5 D7: 3,8 D8: 3,8 E8: 5,7 F9: 7,9 I7: 5,7 H8: 2,3 I8: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,D2: 1.. / D1 = 1 => 0 pairs (X) / D2 = 1 => 19 pairs (_) A6,C6: 1.. / A6 = 1 => 0 pairs (X) / C6 = 1 => 0 pairs (_) A7,B7: 1.. / A7 = 1 => 0 pairs (*) / B7 = 1 => 0 pairs (X) G6,I6: 2.. / G6 = 2 => 19 pairs (_) / I6 = 2 => 0 pairs (X) A9,C9: 2.. / A9 = 2 => 21 pairs (_) / C9 = 2 => 0 pairs (X) H8,I8: 2.. / H8 = 2 => 0 pairs (*) / I8 = 2 => 0 pairs (X) A4,D4: 2.. / A4 = 2 => 0 pairs (X) / D4 = 2 => 21 pairs (_) C5,C9: 2.. / C5 = 2 => 21 pairs (_) / C9 = 2 => 0 pairs (X) A6,C6: 3.. / A6 = 3 => 0 pairs (*) / C6 = 3 => 0 pairs (X) D7,D8: 3.. / D7 = 3 => 0 pairs (X) / D8 = 3 => 0 pairs (_) G7,H8: 3.. / G7 = 3 => 0 pairs (*) / H8 = 3 => 0 pairs (X) C3,H3: 3.. / C3 = 3 => 0 pairs (*) / H3 = 3 => 0 pairs (X) D7,G7: 3.. / D7 = 3 => 0 pairs (X) / G7 = 3 => 0 pairs (_) D8,H8: 3.. / D8 = 3 => 0 pairs (*) / H8 = 3 => 0 pairs (X) A2,A6: 3.. / A2 = 3 => 0 pairs (X) / A6 = 3 => 0 pairs (_) G2,G7: 3.. / G2 = 3 => 0 pairs (X) / G7 = 3 => 0 pairs (_) D5,F5: 4.. / D5 = 4 => 19 pairs (_) / F5 = 4 => 22 pairs (_) G6,I6: 4.. / G6 = 4 => 0 pairs (X) / I6 = 4 => 19 pairs (_) A8,C8: 4.. / A8 = 4 => 17 pairs (_) / C8 = 4 => 0 pairs (X) A2,A8: 4.. / A2 = 4 => 0 pairs (X) / A8 = 4 => 17 pairs (_) I1,I6: 4.. / I1 = 4 => 0 pairs (X) / I6 = 4 => 19 pairs (_) E8,D9: 5.. / E8 = 5 => 0 pairs (X) / D9 = 5 => 19 pairs (_) E3,E8: 5.. / E3 = 5 => 19 pairs (_) / E8 = 5 => 0 pairs (X) B3,C3: 6.. / B3 = 6 => 21 pairs (_) / C3 = 6 => 0 pairs (X) G1,I1: 6.. / G1 = 6 => 0 pairs (*) / I1 = 6 => 0 pairs (X) A4,A5: 6.. / A4 = 6 => 0 pairs (X) / A5 = 6 => 20 pairs (_) B8,C8: 6.. / B8 = 6 => 0 pairs (X) / C8 = 6 => 21 pairs (_) A5,G5: 6.. / A5 = 6 => 20 pairs (_) / G5 = 6 => 0 pairs (X) B3,B8: 6.. / B3 = 6 => 21 pairs (_) / B8 = 6 => 0 pairs (X) C3,C8: 6.. / C3 = 6 => 0 pairs (X) / C8 = 6 => 21 pairs (_) I1,I4: 6.. / I1 = 6 => 0 pairs (X) / I4 = 6 => 0 pairs (_) H2,H3: 7.. / H2 = 7 => 19 pairs (_) / H3 = 7 => 0 pairs (*) C8,C9: 7.. / C8 = 7 => 0 pairs (X) / C9 = 7 => 19 pairs (_) G7,I7: 7.. / G7 = 7 => 0 pairs (X) / I7 = 7 => 19 pairs (_) C8,E8: 7.. / C8 = 7 => 0 pairs (X) / E8 = 7 => 19 pairs (_) E3,E8: 7.. / E3 = 7 => 0 pairs (X) / E8 = 7 => 19 pairs (_) I4,I7: 7.. / I4 = 7 => 0 pairs (X) / I7 = 7 => 19 pairs (_) F1,F2: 8.. / F1 = 8 => 20 pairs (_) / F2 = 8 => 20 pairs (_) D7,D8: 8.. / D7 = 8 => 0 pairs (*) / D8 = 8 => 0 pairs (X) B1,F1: 8.. / B1 = 8 => 20 pairs (_) / F1 = 8 => 20 pairs (_) D1,F1: 9.. / D1 = 9 => 19 pairs (_) / F1 = 9 => 0 pairs (X) D9,F9: 9.. / D9 = 9 => 0 pairs (X) / F9 = 9 => 19 pairs (_) D1,D9: 9.. / D1 = 9 => 19 pairs (_) / D9 = 9 => 0 pairs (X) F1,F9: 9.. / F1 = 9 => 0 pairs (X) / F9 = 9 => 19 pairs (_) * DURATION: 0:00:57.238499 START: 02:02:11.669360 END: 02:03:08.907859 2019-05-01 * CP COUNT: (44) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A7,A8,A9,C1,C5,C6,D4,D7,D8,E3,E8,F9,G6,H8,I6,I7,I8) * 7...3..5.....6...99.....1.8.48.13.9..9..8..13.7.695.8...9.26.4......19...3..4.861 * PAIR C1: 1,4 BLK 1 A2: 1,4,3,8 # reduction candidate for 1,4 A2: 1,4 => CTR * 7.4.3..5.1...6.4.99.....1.8.48.13.9..9..8..13371695284819326.4.4..8.1932.3..4.861 A2: 3,8 # 18 pairs C2: 1,4,3,5 # reduction candidate for 1,4 C2: 1,4 => CTR * 7...3..5.....6...99.....1.8.48.13.9..9..8..13173695.8.819326.4.4..8.1932.3..4.861 C2: 3,5 # 19 pairs * PAIR C1: 1,4 ROW 1 D1: 1,4,2,9 # reduction candidate for 1,4 D1: 1,4 => CTR * 78..39256....684.99...7.1.8.48.13.9..9..8..13.7.695.8...9.26.4...7.519.2.3.947861 D1: 2,9 # 20 pairs * PAIR E3: 5,7 BLK 2 D2: 5,7,1,2,4 # reduction candidate for 5,7 D2: 5,7 => CTR * 784139.5.....684.99...7.1.8.48.13.9..9..8..13.7.695284..9.263474.7..19...3.947861 D2: 1,2,4 # 19 pairs D3: 5,7,2,4 # reduction candidate for 5,7 D3: 5,7 # 22 pairs * PAIR C5: 2,5 BLK 4 A4: 2,5,6 # reduction candidate for 2,5 A4: 2,5 # 20 pairs A5: 2,5,6 # reduction candidate for 2,5 A5: 2,5 => CTR * 7...3.456....6.3.99.3...1.8648213.9..9..8.613371695284..9.26.4......1932.3..4.861 A5: 6 # 20 pairs * PAIR C5: 2,5 COL C C9: 2,5,7 # reduction candidate for 2,5 C9: 2,5 => CTR * 7...3..5.....6...99.6.7.138.48.13.9..9..8..13.7.695.8...9.26.4...7.519.2.3..4.861 C9: 7 # 19 pairs * PAIR A6: 1,3 COL A A2: 1,3,4,8 # reduction candidate for 1,3 A2: 1,3 => CTR * 7...3..5.....6.3.99.3...1.8.48.13.9..9..8..13371695284819326.4.4.6871932.37549861 A2: 4,8 => SOLVED * 714938652825167439963452178548213796692784513371695284159826347486371925237549861 * PAIR C6: 1,3 COL C C2: 1,3,4,5 # reduction candidate for 1,3 C2: 1,3 => CTR * 7.493.652.5.162479926.5.138.48.13.96695284713.71695284..9.263474..3.1925.3.549861 C2: 4,5 # 19 pairs * PAIR D4: 2,7 BLK 5 D5: 2,7,4 # reduction candidate for 2,7 D5: 2,7 # 22 pairs F5: 2,7,4 # reduction candidate for 2,7 F5: 2,7 # 19 pairs * PAIR D4: 2,7 COL D D2: 2,7,1,4,5 # reduction candidate for 2,7 D2: 2,7 => CTR * 784139.5.....684.99..5741.8.48.13.9..9.482713.7.695284..9.263474.7..19...3.947861 D2: 1,4,5 # 18 pairs D3: 2,7,4,5 # reduction candidate for 2,7 D3: 2,7 # 23 pairs * PAIR G6: 2,4 COL G G1: 2,4,6 # reduction candidate for 2,4 G1: 2,4 => CTR * 7...3.456....6.3.99.3...1.8.48.13.9..9..8..13371695284..9.26.4......1932.3..4.861 G1: 6 => SOLVED * 714938652825167439963452178548213796692784513371695284159826347486371925237549861 G2: 2,4,3 # reduction candidate for 2,4 G2: 2,4 => SOLVED * 714938652825167439963452178548213796692784513371695284159826347486371925237549861 G2: 3 => CTR * 7.493..56..5164379963.5.128.48.13.9..9..8..13371695.8...9326.4...6871932.37549861 * PAIR I6: 2,4 COL I I1: 2,4,6 # reduction candidate for 2,4 I1: 2,4 => SOLVED * 714938652825167439963452178548213796692784513371695284159826347486371925237549861 I1: 6 => CTR * 7...3.456....6.3.99.3...1.8.48.13.9..9..8..13371695284..9.26.4......1932.3..4.861 * PAIR A7: 1,8 BLK 7 B7: 1,8,5 # reduction candidate for 1,8 B7: 1,8 => CTR * 7...3..56....6.3.99.3...1.8.48.13.9..9..8..13371695284..9326.4...6871932.37549861 B7: 5 => SOLVED * 714938652825167439963452178548213796692784513371695284159826347486371925237549861 * PAIR A7: 1,8 COL A A2: 1,8,3,4 # reduction candidate for 1,8 A2: 1,8 => SOLVED * 714938652825167439963452178548213796692784513371695284159826347486371925237549861 A2: 3,4 # 21 pairs * PAIR A8: 4,8 COL A A2: 4,8,1,3 # reduction candidate for 4,8 A2: 4,8 => SOLVED * 714938652825167439963452178548213796692784513371695284159826347486371925237549861 A2: 1,3 => CTR * 7...3..5.....6.3.99.3...1.8.48.13.9..9..8..13371695284819326.4.4.6871932.37549861 * PAIR A9: 2,5 BLK 7 C9: 2,5,7 # reduction candidate for 2,5 C9: 2,5 => CTR * 7...3..5.....6...99.6.7.138.48.13.9..9..8..13.7.695.8...9.26.4...7.519.2.3..4.861 C9: 7 # 19 pairs * PAIR A9: 2,5 COL A A4: 2,5,6 # reduction candidate for 2,5 A4: 2,5 # 20 pairs A5: 2,5,6 # reduction candidate for 2,5 A5: 2,5 => CTR * 7...3.456....6.3.99.3...1.8648213.9..9..8.613371695284..9.26.4......1932.3..4.861 A5: 6 # 20 pairs * PAIR E8: 5,7 BLK 8 D9: 5,7,9 # reduction candidate for 5,7 D9: 9 => CTR * 7...39.5.....68..99...7.1.8.48.13.9..9..8..13.7.695284..9.26.4...7.51932.3.947861 D9: 5,7 # 19 pairs * PAIR E8: 5,7 ROW 8 C8: 5,7,4,6 # reduction candidate for 5,7 C8: 5,7 => CTR * 7...3..5.....6...99.6...138.48.13.9..9..8..13.7.695.8...9.2634746...19...3..4.861 C8: 4,6 # 21 pairs * PAIR F9: 7,9 BLK 8 D9: 7,9,5 # reduction candidate for 7,9 D9: 7,9 => CTR * 7...3..5.....6...99...7.1.8.48.13.9..9..8..13.7.695284..9.26.4...7.51932.3..4.861 D9: 5 # 19 pairs * PAIR I7: 5,7 BLK 9 G7: 5,7,3 # reduction candidate for 5,7 G7: 5,7 => CTR * 7.493..56..5164379963.5.128.48.13.9..9..8..13371695.8...9326.4...6871932.37549861 G7: 3 => SOLVED * 714938652825167439963452178548213796692784513371695284159826347486371925237549861 * PAIR I7: 5,7 COL I I4: 5,7,6 # reduction candidate for 5,7 I4: 5,7 => CTR * 7...3.456....6.3.99.3...1.8.48.13.9..9..8..13371695284..9.26.4......1932.3..4.861 I4: 6 => SOLVED * 714938652825167439963452178548213796692784513371695284159826347486371925237549861 * PAIR H8: 2,3 COL H H2: 2,3,7 # reduction candidate for 2,3 H2: 2,3 => SOLVED * 714938652825167439963452178548213796692784513371695284159826347486371925237549861 H2: 7 # 19 pairs H3: 2,3,7 # reduction candidate for 2,3 H3: 2,3 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060824-absurd-base-pr-000.dot * REASONING * DIS # A2: 1,4 => CTR => A2: 3,8 * DIS # C2: 1,4 => CTR => C2: 3,5 * DIS # D1: 1,4 => CTR => D1: 2,9 * DIS # D2: 5,7 => CTR => D2: 1,2,4 * DIS # A5: 2,5 => CTR => A5: 6 * DIS # C9: 2,5 => CTR => C9: 7 * DIS # A2: 1,3 => CTR => A2: 4,8 * PRF # A2: 4,8 => SOL * DIS # C2: 1,3 => CTR => C2: 4,5 * DIS # D2: 2,7 => CTR => D2: 1,4,5 * DIS # G1: 2,4 => CTR => G1: 6 * PRF # G1: 6 => SOL * PRF # G2: 2,4 => SOL * DIS # G2: 3 => CTR => G2: 2,4 * PRF # I1: 2,4 => SOL * DIS # I1: 6 => CTR => I1: 2,4 * DIS # B7: 1,8 => CTR => B7: 5 * PRF # B7: 5 => SOL * PRF # A2: 1,8 => SOL * PRF # A2: 4,8 => SOL * DIS # A2: 1,3 => CTR => A2: 4,8 * DIS # C9: 2,5 => CTR => C9: 7 * DIS # A5: 2,5 => CTR => A5: 6 * DIS # D9: 9 => CTR => D9: 5,7 * DIS # C8: 5,7 => CTR => C8: 4,6 * DIS # D9: 7,9 => CTR => D9: 5 * DIS # G7: 5,7 => CTR => G7: 3 * PRF # G7: 3 => SOL * DIS # I4: 5,7 => CTR => I4: 6 * PRF # I4: 6 => SOL * PRF # H2: 2,3 => SOL * CNT 31 HDP CHAINS / 53 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A7,A8,A9,C1,C5,C6,D4,D7,D8,E3,E8,F9,G6,H8,I6,I7,I8) * 7...3..5.....6...99.....1.8.48.13.9..9..8..13.7.695.8...9.26.4......19...3..4.861 * PAIR C1: 1,4 BLK 1 A2: 1,4,3,8 # reduction candidate for 1,4 A2: 1,4 => CTR * 7.4.3..5.1...6.4.99.....1.8.48.13.9..9..8..13371695284819326.4.4..8.1932.3..4.861 C2: 1,4,3,5 # reduction candidate for 1,4 C2: 1,4 => CTR * 7...3..5.....6...99.....1.8.48.13.9..9..8..13173695.8.819326.4.4..8.1932.3..4.861 * RESTART * PAIR C1: 1,4 ROW 1 D1: 1,4,2,9 # reduction candidate for 1,4 D1: 1,4 => CTR * 78143925.....68..99.....1.8.48.13.9..9..8..13.7.695.8.819326.4.4..8.1932.3.947861 * PAIR RESTART * PAIR E3: 5,7 BLK 2 D3: 5,7,2,4 # reduction candidate for 5,7 D3: 2,4 => SOLVED * 714938652825167439963452178548213796692784513371695284159826347486371925237549861 * DURATION: 0:00:05.521228 START: 02:03:49.382831 END: 02:03:54.904059 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060824-absurd-base-pr-001.dot * REASONING * DIS # A2: 1,4 => CTR => A2: 3,8 * DIS A2: 3,8 # C2: 1,4 => CTR => C2: 3,5 * DIS A2: 3,8 + C2: 3,5 # D1: 1,4 => CTR => D1: 2,9 * PRF A2: 3,8 + C2: 3,5 + D1: 2,9 # D3: 2,4 => SOL * STA A2: 3,8 + C2: 3,5 + D1: 2,9 + D3: 2,4 * CNT 4 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060824, absurd
Solution
position: 714938652825167439963452178548213796692784513371695284159826347486371925237549861 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 # A2: 1,4 => CTR => A2: 3,8 * INC # A2: 3,8 => UNS * DIS # C2: 1,4 => CTR => C2: 3,5 * INC # C2: 3,5 => UNS * DIS # D1: 1,4 => CTR => D1: 2,9 * INC # D1: 2,9 => UNS * DIS # D2: 5,7 => CTR => D2: 1,2,4 * INC # D2: 1,2,4 => UNS * INC # D3: 5,7 => UNS * INC # A4: 2,5 => UNS * DIS # A5: 2,5 => CTR => A5: 6 * INC # A5: 6 => UNS * DIS # C9: 2,5 => CTR => C9: 7 * INC # C9: 7 => UNS * DIS # A2: 1,3 => CTR => A2: 4,8 * PRF # A2: 4,8 => SOL * DIS # C2: 1,3 => CTR => C2: 4,5 * INC # C2: 4,5 => UNS * INC # D5: 2,7 => UNS * INC # F5: 2,7 => UNS * DIS # D2: 2,7 => CTR => D2: 1,4,5 * INC # D2: 1,4,5 => UNS * INC # D3: 2,7 => UNS * DIS # G1: 2,4 => CTR => G1: 6 * PRF # G1: 6 => SOL * PRF # G2: 2,4 => SOL * DIS # G2: 3 => CTR => G2: 2,4 * PRF # I1: 2,4 => SOL * DIS # I1: 6 => CTR => I1: 2,4 * DIS # B7: 1,8 => CTR => B7: 5 * PRF # B7: 5 => SOL * PRF # A2: 1,8 => SOL * INC # A2: 3,4 => UNS * PRF # A2: 4,8 => SOL * DIS # A2: 1,3 => CTR => A2: 4,8 * DIS # C9: 2,5 => CTR => C9: 7 * INC # C9: 7 => UNS * INC # A4: 2,5 => UNS * DIS # A5: 2,5 => CTR => A5: 6 * INC # A5: 6 => UNS * INC # D9: 5,7 => UNS * DIS # D9: 9 => CTR => D9: 5,7 * DIS # C8: 5,7 => CTR => C8: 4,6 * INC # C8: 4,6 => UNS * DIS # D9: 7,9 => CTR => D9: 5 * INC # D9: 5 => UNS * DIS # G7: 5,7 => CTR => G7: 3 * PRF # G7: 3 => SOL * DIS # I4: 5,7 => CTR => I4: 6 * PRF # I4: 6 => SOL * PRF # H2: 2,3 => SOL * INC # H2: 7 => UNS * INC # H3: 2,3 => UNS * CNT 53 HDP CHAINS / 53 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A2: 1,4 => CTR => A2: 3,8 * DIS A2: 3,8 # C2: 1,4 => CTR => C2: 3,5 * DIS A2: 3,8 + C2: 3,5 # D1: 1,4 => CTR => D1: 2,9 * INC A2: 3,8 + C2: 3,5 + D1: 2,9 # D3: 5,7 => UNS * PRF A2: 3,8 + C2: 3,5 + D1: 2,9 # D3: 2,4 => SOL * STA A2: 3,8 + C2: 3,5 + D1: 2,9 + D3: 2,4 * CNT 5 HDP CHAINS / 5 HYP OPENED