Analysis of xx-top500-304-base.sdk
Contents
Original Sudoku
level: medium
position: ....3.21.84................3.....5.1..64..........73.....85.....7.....4...1...... initial
Autosolve
position: 5.7.3421884.1.57......784..3.4.8.571756413982..85.73644..85.127.753.1849.8174.6.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A3: 6,9 => SOL * DIS # A3: 1 => CTR => A3: 6,9 * DIS # B3: 6,9 => CTR => B3: 1,3 * DIS # B7: 6,9 => CTR => B7: 3 * PRF # B7: 3 => SOL * DIS # D3: 6,9 => CTR => D3: 2 * DIS # D4: 2 => CTR => D4: 6,9 * DIS # H3: 3,9 => CTR => H3: 5 * PRF # H3: 5 => SOL * DIS # C2: 3,9 => CTR => C2: 2 * PRF # I3: 3,6 => SOL * DIS # I3: 5 => CTR => I3: 3,6 * PRF # B6: 2,9 => SOL * DIS # B6: 1 => CTR => B6: 2,9 * DIS # D4: 2,9 => CTR => D4: 6 * PRF # D4: 6 => SOL * DIS # B6: 1,9 => CTR => B6: 2 * PRF # B6: 2 => SOL * PRF # A3: 1,9 => SOL * DIS # A3: 6 => CTR => A3: 1,9 * PRF # D4: 2,6 => SOL * DIS # D4: 9 => CTR => D4: 2,6 * DIS # D4: 2,9 => CTR => D4: 6 * PRF # D4: 6 => SOL * PRF # B6: 2,9 => SOL * DIS # B6: 1 => CTR => B6: 2,9 * DIS # E2: 2,9 => CTR => E2: 6 * PRF # E2: 6 => SOL * PRF # B7: 3,9 => SOL * DIS # B7: 6 => CTR => B7: 3,9 * DIS # C2: 3,9 => CTR => C2: 2 * DIS # B7: 6,9 => CTR => B7: 3 * PRF # B7: 3 => SOL * PRF # E2: 2,6 => SOL * DIS # E2: 9 => CTR => E2: 2,6 * PRF # H3: 3,5 => SOL * DIS # H3: 9 => CTR => H3: 3,5 * DIS # I3: 3,5 => CTR => I3: 6 * PRF # I3: 6 => SOL * CNT 39 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A3: 6,9 => SOL * STA A3: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....3.21.84................3.....5.1..64..........73.....85.....7.....4...1...... | initial |
| 5.7.3421884.1.57......784..3.4.8.571756413982..85.73644..85.127.753.1849.8174.6.. | autosolve |
| 567934218842165793913278456394682571756413982128597364439856127675321849281749635 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) B1: 6,9 D1: 6,9 H2: 3,9 I2: 3,6 B4: 2,9 A6: 1,9 F4: 2,6 E6: 2,9 C7: 3,9 A8: 2,6 A9: 2,9 F7: 6,9 E8: 2,6 F9: 2,9 H9: 3,5 I9: 3,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A3,B3: 1.. / A3 = 1 => 0 pairs (X) / B3 = 1 => 0 pairs (_) A6,B6: 1.. / A6 = 1 => 0 pairs (*) / B6 = 1 => 0 pairs (X) A3,A6: 1.. / A3 = 1 => 0 pairs (X) / A6 = 1 => 0 pairs (_) B3,B6: 1.. / B3 = 1 => 0 pairs (*) / B6 = 1 => 0 pairs (X) C2,C3: 2.. / C2 = 2 => 21 pairs (_) / C3 = 2 => 0 pairs (X) E2,D3: 2.. / E2 = 2 => 0 pairs (X) / D3 = 2 => 21 pairs (_) B4,B6: 2.. / B4 = 2 => 0 pairs (X) / B6 = 2 => 0 pairs (_) A8,A9: 2.. / A8 = 2 => 0 pairs (X) / A9 = 2 => 0 pairs (_) E8,F9: 2.. / E8 = 2 => 0 pairs (*) / F9 = 2 => 0 pairs (X) C2,E2: 2.. / C2 = 2 => 21 pairs (_) / E2 = 2 => 0 pairs (X) C3,D3: 2.. / C3 = 2 => 0 pairs (X) / D3 = 2 => 21 pairs (_) B6,E6: 2.. / B6 = 2 => 0 pairs (*) / E6 = 2 => 0 pairs (X) A8,E8: 2.. / A8 = 2 => 0 pairs (X) / E8 = 2 => 0 pairs (_) A9,F9: 2.. / A9 = 2 => 0 pairs (*) / F9 = 2 => 0 pairs (X) D3,D4: 2.. / D3 = 2 => 21 pairs (_) / D4 = 2 => 0 pairs (X) F4,F9: 2.. / F4 = 2 => 0 pairs (*) / F9 = 2 => 0 pairs (X) B7,C7: 3.. / B7 = 3 => 0 pairs (*) / C7 = 3 => 0 pairs (X) H9,I9: 3.. / H9 = 3 => 0 pairs (*) / I9 = 3 => 0 pairs (X) B3,B7: 3.. / B3 = 3 => 0 pairs (X) / B7 = 3 => 0 pairs (_) H3,I3: 5.. / H3 = 5 => 0 pairs (*) / I3 = 5 => 0 pairs (X) H9,I9: 5.. / H9 = 5 => 0 pairs (X) / I9 = 5 => 0 pairs (_) H3,H9: 5.. / H3 = 5 => 0 pairs (*) / H9 = 5 => 0 pairs (X) I3,I9: 5.. / I3 = 5 => 0 pairs (X) / I9 = 5 => 0 pairs (_) I2,I3: 6.. / I2 = 6 => 0 pairs (X) / I3 = 6 => 0 pairs (_) D4,F4: 6.. / D4 = 6 => 0 pairs (*) / F4 = 6 => 0 pairs (X) B7,A8: 6.. / B7 = 6 => 0 pairs (X) / A8 = 6 => 0 pairs (_) F7,E8: 6.. / F7 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) B1,D1: 6.. / B1 = 6 => 0 pairs (*) / D1 = 6 => 0 pairs (X) E2,I2: 6.. / E2 = 6 => 0 pairs (*) / I2 = 6 => 0 pairs (X) B7,F7: 6.. / B7 = 6 => 0 pairs (X) / F7 = 6 => 0 pairs (_) A8,E8: 6.. / A8 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) A3,A8: 6.. / A3 = 6 => 0 pairs (X) / A8 = 6 => 0 pairs (_) E2,E8: 6.. / E2 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) F4,F7: 6.. / F4 = 6 => 0 pairs (X) / F7 = 6 => 0 pairs (_) H2,H3: 9.. / H2 = 9 => 0 pairs (*) / H3 = 9 => 0 pairs (X) D4,E6: 9.. / D4 = 9 => 0 pairs (X) / E6 = 9 => 0 pairs (_) F7,F9: 9.. / F7 = 9 => 0 pairs (X) / F9 = 9 => 0 pairs (_) B1,D1: 9.. / B1 = 9 => 0 pairs (X) / D1 = 9 => 0 pairs (_) B4,D4: 9.. / B4 = 9 => 0 pairs (*) / D4 = 9 => 0 pairs (X) A9,F9: 9.. / A9 = 9 => 0 pairs (X) / F9 = 9 => 0 pairs (_) E2,E6: 9.. / E2 = 9 => 0 pairs (X) / E6 = 9 => 0 pairs (_) * DURATION: 0:01:08.545689 START: 13:21:42.007728 END: 13:22:50.553417 2017-05-04 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A8,A9,B1,B4,C7,D1,E6,E8,F4,F7,F9,H2,H9,I2,I9) * 5.7.3421884.1.57......784..3.4.8.571756413982..85.73644..85.127.753.1849.8174.6.. * PAIR B1: 6,9 BLK 1 A3: 6,9,1 # reduction candidate for 6,9 A3: 6,9 => SOLVED * 567934218842165793913278456394682571756413982128597364439856127675321849281749635 A3: 1 => CTR * 5.7.3421884.1.57..1...784..3.4.8.5717564139829185273644..85.127.753.1849.8174.6.. B3: 6,9,1,3 # reduction candidate for 6,9 B3: 6,9 => CTR * 5.7.3421884.1.57..1...784..3.4.8.57175641398291852736443.85.127.753.1849.8174.6.. B3: 1,3 # 17 pairs * PAIR B1: 6,9 COL B B7: 6,9,3 # reduction candidate for 6,9 B7: 6,9 => CTR * 5.7.3421884.1.57...3..784..3.4.8.571756413982.185273644.385.12727536184998174.6.. B7: 3 => SOLVED * 567934218842165793913278456394682571756413982128597364439856127675321849281749635 * PAIR D1: 6,9 BLK 2 E2: 6,9,2 # reduction candidate for 6,9 E2: 6,9 # 21 pairs D3: 6,9,2 # reduction candidate for 6,9 D3: 6,9 => CTR * 5.7.3421884.1257.6..2.784..3.4286571756413982.285973644638591272753618499817426.. D3: 2 # 21 pairs * PAIR D1: 6,9 COL D D4: 6,9,2 # reduction candidate for 6,9 D4: 2 => CTR * 5.7.3421884.1.57......784..39428657175641398212859736446.85.127.753.1849.8174.6.. D4: 6,9 # 21 pairs * PAIR H2: 3,9 BLK 3 H3: 3,9,5 # reduction candidate for 3,9 H3: 3,9 => CTR * 5.7.3421884.1.57.661..784.53.4.865717564139821.85.73644..85.127.75361849.81742653 H3: 5 => SOLVED * 567934218842165793913278456394682571756413982128597364439856127675321849281749635 * PAIR H2: 3,9 ROW 2 C2: 3,9,2 # reduction candidate for 3,9 C2: 3,9 => CTR * 5.7.3421884.1257.6..2.784..3.4286571756413982.285973644638591272753618499817426.. C2: 2 # 21 pairs * PAIR I2: 3,6 BLK 3 I3: 3,6,5 # reduction candidate for 3,6 I3: 3,6 => SOLVED * 567934218842165793913278456394682571756413982128597364439856127675321849281749635 I3: 5 => CTR * 5.7.3421884.1.57.661..784.53.4.865717564139821.85.73644..85.127.75361849.81742653 * PAIR B4: 2,9 BLK 4 B6: 2,9,1 # reduction candidate for 2,9 B6: 2,9 => SOLVED * 567934218842165793913278456394682571756413982128597364439856127675321849281749635 B6: 1 => CTR * 5.7.3421884.1.57......784..32498657175641398291852736446.85.127.753.1849.8174.6.. * PAIR B4: 2,9 ROW 4 D4: 2,9,6 # reduction candidate for 2,9 D4: 2,9 => CTR * 5976342188421.57......784..3.4.86571756413982..85.73644638591272753618499817426.. D4: 6 => SOLVED * 567934218842165793913278456394682571756413982128597364439856127675321849281749635 * PAIR A6: 1,9 BLK 4 B6: 1,9,2 # reduction candidate for 1,9 B6: 1,9 => CTR * 5976342188421.57......784..324986571756413982..85273644638591272753618499817426.. B6: 2 => SOLVED * 567934218842165793913278456394682571756413982128597364439856127675321849281749635 * PAIR A6: 1,9 COL A A3: 1,9,6 # reduction candidate for 1,9 A3: 1,9 => SOLVED * 567934218842165793913278456394682571756413982128597364439856127675321849281749635 A3: 6 => CTR * 5.7.3421884.1.57..61..784..3.4.8.5717564139821.85.73644..85.127.753.1849.8174.6.. * PAIR F4: 2,6 BLK 5 D4: 2,6,9 # reduction candidate for 2,6 D4: 2,6 => SOLVED * 567934218842165793913278456394682571756413982128597364439856127675321849281749635 D4: 9 => CTR * 5.7.3421884.1.57.....2784..3.4986571756413982..85273644638591272753618499817426.. * PAIR E6: 2,9 BLK 5 D4: 2,9,6 # reduction candidate for 2,9 D4: 2,9 => CTR * 5976342188421.57......784..3.4.86571756413982..85.73644638591272753618499817426.. D4: 6 => SOLVED * 567934218842165793913278456394682571756413982128597364439856127675321849281749635 * PAIR E6: 2,9 ROW 6 B6: 2,9,1 # reduction candidate for 2,9 B6: 2,9 => SOLVED * 567934218842165793913278456394682571756413982128597364439856127675321849281749635 B6: 1 => CTR * 5.7.3421884.1.57......784..32498657175641398291852736446.85.127.753.1849.8174.6.. * PAIR E6: 2,9 COL E E2: 2,9,6 # reduction candidate for 2,9 E2: 2,9 => CTR * 5.7.3421884.1.57.661..784..3.4.865717564139821.85.73644..85.127.75361849.817426.. E2: 6 => SOLVED * 567934218842165793913278456394682571756413982128597364439856127675321849281749635 * PAIR C7: 3,9 BLK 7 B7: 3,9,6 # reduction candidate for 3,9 B7: 3,9 => SOLVED * 567934218842165793913278456394682571756413982128597364439856127675321849281749635 B7: 6 => CTR * 5.7.3421884.1.57...3..784..3.4.8.571756413982.185273644638591272753.1849.8174.6.. * PAIR C7: 3,9 COL C C2: 3,9,2 # reduction candidate for 3,9 C2: 3,9 => CTR * 5.7.3421884.1257.6..2.784..3.4286571756413982.285973644638591272753618499817426.. C2: 2 # 21 pairs C3: 3,9,2 # reduction candidate for 3,9 C3: 3,9 # 21 pairs * PAIR F7: 6,9 ROW 7 B7: 6,9,3 # reduction candidate for 6,9 B7: 6,9 => CTR * 5.7.3421884.1.57...3..784..3.4.8.571756413982.185273644.385.12727536184998174.6.. B7: 3 => SOLVED * 567934218842165793913278456394682571756413982128597364439856127675321849281749635 * PAIR E8: 2,6 COL E E2: 2,6,9 # reduction candidate for 2,6 E2: 2,6 => SOLVED * 567934218842165793913278456394682571756413982128597364439856127675321849281749635 E2: 9 => CTR * 5.7.34218842195736...2784953.4986571756413982..852736446.85.127.753.1849.8174.6.. * PAIR H9: 3,5 COL H H3: 3,5,9 # reduction candidate for 3,5 H3: 3,5 => SOLVED * 567934218842165793913278456394682571756413982128597364439856127675321849281749635 H3: 9 => CTR * 5.7.3421884.1.5736613278495324.8.571756413982..85.73644..85.127.75361849.81742653 * PAIR I9: 3,5 COL I I3: 3,5,6 # reduction candidate for 3,5 I3: 3,5 => CTR * 5.7.3421884.1.57.661..784..3.4.865717564139821.85.73644..85.127.75361849.817426.. I3: 6 => SOLVED * 567934218842165793913278456394682571756413982128597364439856127675321849281749635 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-304-base-pr-000.dot * REASONING * PRF # A3: 6,9 => SOL * DIS # A3: 1 => CTR => A3: 6,9 * DIS # B3: 6,9 => CTR => B3: 1,3 * DIS # B7: 6,9 => CTR => B7: 3 * PRF # B7: 3 => SOL * DIS # D3: 6,9 => CTR => D3: 2 * DIS # D4: 2 => CTR => D4: 6,9 * DIS # H3: 3,9 => CTR => H3: 5 * PRF # H3: 5 => SOL * DIS # C2: 3,9 => CTR => C2: 2 * PRF # I3: 3,6 => SOL * DIS # I3: 5 => CTR => I3: 3,6 * PRF # B6: 2,9 => SOL * DIS # B6: 1 => CTR => B6: 2,9 * DIS # D4: 2,9 => CTR => D4: 6 * PRF # D4: 6 => SOL * DIS # B6: 1,9 => CTR => B6: 2 * PRF # B6: 2 => SOL * PRF # A3: 1,9 => SOL * DIS # A3: 6 => CTR => A3: 1,9 * PRF # D4: 2,6 => SOL * DIS # D4: 9 => CTR => D4: 2,6 * DIS # D4: 2,9 => CTR => D4: 6 * PRF # D4: 6 => SOL * PRF # B6: 2,9 => SOL * DIS # B6: 1 => CTR => B6: 2,9 * DIS # E2: 2,9 => CTR => E2: 6 * PRF # E2: 6 => SOL * PRF # B7: 3,9 => SOL * DIS # B7: 6 => CTR => B7: 3,9 * DIS # C2: 3,9 => CTR => C2: 2 * DIS # B7: 6,9 => CTR => B7: 3 * PRF # B7: 3 => SOL * PRF # E2: 2,6 => SOL * DIS # E2: 9 => CTR => E2: 2,6 * PRF # H3: 3,5 => SOL * DIS # H3: 9 => CTR => H3: 3,5 * DIS # I3: 3,5 => CTR => I3: 6 * PRF # I3: 6 => SOL * CNT 39 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A8,A9,B1,B4,C7,D1,E6,E8,F4,F7,F9,H2,H9,I2,I9) * 5.7.3421884.1.57......784..3.4.8.571756413982..85.73644..85.127.753.1849.8174.6.. * PAIR B1: 6,9 BLK 1 A3: 6,9,1 # reduction candidate for 6,9 A3: 6,9 => SOLVED * 567934218842165793913278456394682571756413982128597364439856127675321849281749635 * DURATION: 0:00:02.006549 START: 13:23:39.634693 END: 13:23:41.641242 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-304-base-pr-001.dot * REASONING * PRF # A3: 6,9 => SOL * STA A3: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 304 solution: 567934218842165793913278456394682571756413982128597364439856127675321849281749635 info: 2591 FNBWY S8.f 43060 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 567934218842165793913278456394682571756413982128597364439856127675321849281749635 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:
* PRF # A3: 6,9 => SOL * DIS # A3: 1 => CTR => A3: 6,9 * DIS # B3: 6,9 => CTR => B3: 1,3 * INC # B3: 1,3 => UNS * DIS # B7: 6,9 => CTR => B7: 3 * PRF # B7: 3 => SOL * INC # E2: 6,9 => UNS * DIS # D3: 6,9 => CTR => D3: 2 * INC # D3: 2 => UNS * INC # D4: 6,9 => UNS * DIS # D4: 2 => CTR => D4: 6,9 * DIS # H3: 3,9 => CTR => H3: 5 * PRF # H3: 5 => SOL * DIS # C2: 3,9 => CTR => C2: 2 * INC # C2: 2 => UNS * PRF # I3: 3,6 => SOL * DIS # I3: 5 => CTR => I3: 3,6 * PRF # B6: 2,9 => SOL * DIS # B6: 1 => CTR => B6: 2,9 * DIS # D4: 2,9 => CTR => D4: 6 * PRF # D4: 6 => SOL * DIS # B6: 1,9 => CTR => B6: 2 * PRF # B6: 2 => SOL * PRF # A3: 1,9 => SOL * DIS # A3: 6 => CTR => A3: 1,9 * PRF # D4: 2,6 => SOL * DIS # D4: 9 => CTR => D4: 2,6 * DIS # D4: 2,9 => CTR => D4: 6 * PRF # D4: 6 => SOL * PRF # B6: 2,9 => SOL * DIS # B6: 1 => CTR => B6: 2,9 * DIS # E2: 2,9 => CTR => E2: 6 * PRF # E2: 6 => SOL * PRF # B7: 3,9 => SOL * DIS # B7: 6 => CTR => B7: 3,9 * DIS # C2: 3,9 => CTR => C2: 2 * INC # C2: 2 => UNS * INC # C3: 3,9 => UNS * DIS # B7: 6,9 => CTR => B7: 3 * PRF # B7: 3 => SOL * PRF # E2: 2,6 => SOL * DIS # E2: 9 => CTR => E2: 2,6 * PRF # H3: 3,5 => SOL * DIS # H3: 9 => CTR => H3: 3,5 * DIS # I3: 3,5 => CTR => I3: 6 * PRF # I3: 6 => SOL * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A3: 6,9 => SOL * STA A3: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED