Analysis of xx-top500-165-base.sdk
Contents
Original Sudoku
level: medium
position: .2....1.....3.8......4.........1.5..4.......8.7.....3.1.....7..6.5........48..... initial
Autosolve
position: 82..9.1439413.8.5.35.4.18..268913574413...9.8579.84.31132.4978.6851374..7948.231. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # D1: 6,7 => SOL * DIS # D1: 5 => CTR => D1: 6,7 * DIS # E3: 6,7 => CTR => E3: 2 * DIS # D1: 5,6 => CTR => D1: 7 * PRF # D1: 7 => SOL * DIS # H3: 9 => CTR => H3: 2,6 * DIS # E2: 7 => CTR => E2: 2,6 * DIS # I3: 2,7 => CTR => I3: 9 * DIS # E2: 2,7 => CTR => E2: 6 * PRF # E2: 6 => SOL * PRF # D5: 5,6 => SOL * DIS # E5: 5,6 => CTR => E5: 7 * PRF # E5: 7 => SOL * DIS # D5: 2,6 => CTR => D5: 5,7 * PRF # D5: 5,7 => SOL * DIS # D5: 2,6 => CTR => D5: 5,7 * PRF # D5: 5,7 => SOL * DIS # H3: 9 => CTR => H3: 2,6 * DIS # D1: 5,6 => CTR => D1: 7 * PRF # D1: 7 => SOL * PRF # D5: 5,6 => SOL * DIS # E5: 5,6 => CTR => E5: 7 * PRF # E5: 7 => SOL * DIS # H3: 2,9 => CTR => H3: 6 * PRF # H3: 6 => SOL * DIS # I3: 7 => CTR => I3: 2,9 * CNT 26 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # D1: 6,7 => SOL * STA D1: 6,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2....1.....3.8......4.........1.5..4.......8.7.....3.1.....7..6.5........48..... | initial |
| 82..9.1439413.8.5.35.4.18..268913574413...9.8579.84.31132.4978.6851374..7948.231. | autosolve |
| 826795143941368257357421869268913574413576928579284631132649785685137492794852316 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) C1: 6,7 C3: 6,7 F1: 5,6 G2: 2,6 I2: 2,7 F5: 5,6 D6: 2,6 H5: 2,6 G6: 2,6 D7: 5,6 E9: 5,6 I7: 5,6 H8: 2,9 I8: 2,9 I9: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,E3: 2.. / E2 = 2 => 0 pairs (X) / E3 = 2 => 18 pairs (_) D5,D6: 2.. / D5 = 2 => 0 pairs (X) / D6 = 2 => 0 pairs (_) H5,G6: 2.. / H5 = 2 => 0 pairs (*) / G6 = 2 => 0 pairs (X) H8,I8: 2.. / H8 = 2 => 0 pairs (X) / I8 = 2 => 14 pairs (_) D5,H5: 2.. / D5 = 2 => 0 pairs (X) / H5 = 2 => 0 pairs (_) D6,G6: 2.. / D6 = 2 => 0 pairs (*) / G6 = 2 => 0 pairs (X) G2,G6: 2.. / G2 = 2 => 0 pairs (*) / G6 = 2 => 0 pairs (X) D1,F1: 5.. / D1 = 5 => 0 pairs (X) / F1 = 5 => 0 pairs (_) D7,E9: 5.. / D7 = 5 => 0 pairs (X) / E9 = 5 => 0 pairs (_) I7,I9: 5.. / I7 = 5 => 0 pairs (*) / I9 = 5 => 0 pairs (X) D7,I7: 5.. / D7 = 5 => 0 pairs (X) / I7 = 5 => 0 pairs (_) E9,I9: 5.. / E9 = 5 => 0 pairs (*) / I9 = 5 => 0 pairs (X) E5,E9: 5.. / E5 = 5 => 0 pairs (X) / E9 = 5 => 0 pairs (_) F1,F5: 5.. / F1 = 5 => 0 pairs (*) / F5 = 5 => 0 pairs (X) C1,C3: 6.. / C1 = 6 => 0 pairs (*) / C3 = 6 => 0 pairs (X) G2,H3: 6.. / G2 = 6 => 0 pairs (X) / H3 = 6 => 0 pairs (_) H5,G6: 6.. / H5 = 6 => 0 pairs (X) / G6 = 6 => 0 pairs (_) D7,E9: 6.. / D7 = 6 => 0 pairs (*) / E9 = 6 => 0 pairs (X) I7,I9: 6.. / I7 = 6 => 0 pairs (X) / I9 = 6 => 0 pairs (_) E2,G2: 6.. / E2 = 6 => 0 pairs (*) / G2 = 6 => 0 pairs (X) D6,G6: 6.. / D6 = 6 => 0 pairs (X) / G6 = 6 => 0 pairs (_) D7,I7: 6.. / D7 = 6 => 0 pairs (*) / I7 = 6 => 0 pairs (X) E9,I9: 6.. / E9 = 6 => 0 pairs (X) / I9 = 6 => 0 pairs (_) F1,F5: 6.. / F1 = 6 => 0 pairs (X) / F5 = 6 => 0 pairs (_) G2,G6: 6.. / G2 = 6 => 0 pairs (X) / G6 = 6 => 0 pairs (_) H3,H5: 6.. / H3 = 6 => 0 pairs (*) / H5 = 6 => 0 pairs (X) C1,C3: 7.. / C1 = 7 => 0 pairs (X) / C3 = 7 => 0 pairs (_) I2,I3: 7.. / I2 = 7 => 16 pairs (_) / I3 = 7 => 0 pairs (X) D5,E5: 7.. / D5 = 7 => 0 pairs (X) / E5 = 7 => 0 pairs (_) C1,D1: 7.. / C1 = 7 => 0 pairs (X) / D1 = 7 => 0 pairs (_) E2,I2: 7.. / E2 = 7 => 0 pairs (X) / I2 = 7 => 16 pairs (_) D1,D5: 7.. / D1 = 7 => 0 pairs (*) / D5 = 7 => 0 pairs (X) H3,I3: 9.. / H3 = 9 => 0 pairs (X) / I3 = 9 => 14 pairs (_) H8,I8: 9.. / H8 = 9 => 14 pairs (_) / I8 = 9 => 0 pairs (X) H3,H8: 9.. / H3 = 9 => 0 pairs (X) / H8 = 9 => 14 pairs (_) I3,I8: 9.. / I3 = 9 => 14 pairs (_) / I8 = 9 => 0 pairs (X) * DURATION: 0:01:04.003834 START: 08:23:16.109585 END: 08:24:20.113419 2017-05-04 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C1,C3,D6,D7,E9,F1,F5,G2,G6,H5,H8,I2,I7,I8,I9) * 82..9.1439413.8.5.35.4.18..268913574413...9.8579.84.31132.4978.6851374..7948.231. * PAIR C1: 6,7 ROW 1 D1: 6,7,5 # reduction candidate for 6,7 D1: 6,7 => SOLVED * 826795143941368257357421869268913574413576928579284631132649785685137492794852316 D1: 5 => CTR * 8275961439413.865.3564.18..2689135744137.59.8579.84.31132.4978.6851374..7948.231. * PAIR C3: 6,7 ROW 3 E3: 6,7,2 # reduction candidate for 6,7 E3: 6,7 => CTR * 82..9.14394132865735.4.18..268913574413...9685796842311325497866851374..794862315 E3: 2 # 18 pairs * PAIR F1: 5,6 BLK 2 D1: 5,6,7 # reduction candidate for 5,6 D1: 5,6 => CTR * 827.9.1439413.8.5.3564.18..2689135744137..9.8579.84.31132.4978.6851374..7948.231. D1: 7 => SOLVED * 826795143941368257357421869268913574413576928579284631132649785685137492794852316 * PAIR G2: 2,6 BLK 3 H3: 2,6,9 # reduction candidate for 2,6 H3: 9 => CTR * 82..9.1439413.865.35.4.189.268913574413...968579684231132549786685137429794862315 H3: 2,6 # 14 pairs * PAIR G2: 2,6 ROW 2 E2: 2,6,7 # reduction candidate for 2,6 E2: 7 => CTR * 82..9.14394137865235.4218972689135744137..9.8579.84.31132.4978.6851374..7948.231. E2: 2,6 # 16 pairs * PAIR I2: 2,7 BLK 3 I3: 2,7,9 # reduction candidate for 2,7 I3: 2,7 => CTR * 82..9.1439413.8.5.35.4.189.268913574413...968579684231132549786685137429794862315 I3: 9 # 14 pairs * PAIR I2: 2,7 ROW 2 E2: 2,7,6 # reduction candidate for 2,7 E2: 2,7 => CTR * 82..9.1439413.865.35.4.18..268913574413...9685796842311325497866851374..794862315 E2: 6 => SOLVED * 826795143941368257357421869268913574413576928579284631132649785685137492794852316 * PAIR F5: 5,6 BLK 5 D5: 5,6,2,7 # reduction candidate for 5,6 D5: 5,6 => SOLVED * 826795143941368257357421869268913574413576928579284631132649785685137492794852316 D5: 2,7 # 16 pairs E5: 5,6,7 # reduction candidate for 5,6 E5: 5,6 => CTR * 827.9.1439413682573564.18..2689135744137..928579284631132.4978.6851374927948.231. E5: 7 => SOLVED * 826795143941368257357421869268913574413576928579284631132649785685137492794852316 * PAIR D6: 2,6 BLK 5 D5: 2,6,5,7 # reduction candidate for 2,6 D5: 2,6 => CTR * 82.7951439413.8.573574.18..268913574413...9.8579.84.31132.4978.6851374..7948.231. D5: 5,7 => SOLVED * 826795143941368257357421869268913574413576928579284631132649785685137492794852316 * PAIR H5: 2,6 ROW 5 D5: 2,6,5,7 # reduction candidate for 2,6 D5: 2,6 => CTR * 82.7951439413.8.573574.18..268913574413...9.8579.84.31132.4978.6851374..7948.231. D5: 5,7 => SOLVED * 826795143941368257357421869268913574413576928579284631132649785685137492794852316 * PAIR H5: 2,6 COL H H3: 2,6,9 # reduction candidate for 2,6 H3: 9 => CTR * 82..9.1439413.865.35.4.189.268913574413...968579684231132549786685137429794862315 H3: 2,6 # 14 pairs * PAIR D7: 5,6 COL D D1: 5,6,7 # reduction candidate for 5,6 D1: 5,6 => CTR * 827.9.1439413.8.5.3564.18..2689135744137..9.8579.84.31132.4978.6851374..7948.231. D1: 7 => SOLVED * 826795143941368257357421869268913574413576928579284631132649785685137492794852316 D5: 5,6,2,7 # reduction candidate for 5,6 D5: 5,6 => SOLVED * 826795143941368257357421869268913574413576928579284631132649785685137492794852316 D5: 2,7 # 16 pairs * PAIR E9: 5,6 COL E E5: 5,6,7 # reduction candidate for 5,6 E5: 5,6 => CTR * 827.9.1439413682573564.18..2689135744137..928579284631132.4978.6851374927948.231. E5: 7 => SOLVED * 826795143941368257357421869268913574413576928579284631132649785685137492794852316 * PAIR H8: 2,9 COL H H3: 2,9,6 # reduction candidate for 2,9 H3: 2,9 => CTR * 82..9.1439413.865.35.4.18..268913574413...9685796842311325497866851374..794862315 H3: 6 => SOLVED * 826795143941368257357421869268913574413576928579284631132649785685137492794852316 * PAIR I8: 2,9 COL I I3: 2,9,7 # reduction candidate for 2,9 I3: 7 => CTR * 82..9.1439413.8.5.35.4.1897268913574413...968579684231132549786685137429794862315 I3: 2,9 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-165-base-pr-000.dot * REASONING * PRF # D1: 6,7 => SOL * DIS # D1: 5 => CTR => D1: 6,7 * DIS # E3: 6,7 => CTR => E3: 2 * DIS # D1: 5,6 => CTR => D1: 7 * PRF # D1: 7 => SOL * DIS # H3: 9 => CTR => H3: 2,6 * DIS # E2: 7 => CTR => E2: 2,6 * DIS # I3: 2,7 => CTR => I3: 9 * DIS # E2: 2,7 => CTR => E2: 6 * PRF # E2: 6 => SOL * PRF # D5: 5,6 => SOL * DIS # E5: 5,6 => CTR => E5: 7 * PRF # E5: 7 => SOL * DIS # D5: 2,6 => CTR => D5: 5,7 * PRF # D5: 5,7 => SOL * DIS # D5: 2,6 => CTR => D5: 5,7 * PRF # D5: 5,7 => SOL * DIS # H3: 9 => CTR => H3: 2,6 * DIS # D1: 5,6 => CTR => D1: 7 * PRF # D1: 7 => SOL * PRF # D5: 5,6 => SOL * DIS # E5: 5,6 => CTR => E5: 7 * PRF # E5: 7 => SOL * DIS # H3: 2,9 => CTR => H3: 6 * PRF # H3: 6 => SOL * DIS # I3: 7 => CTR => I3: 2,9 * CNT 26 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C1,C3,D6,D7,E9,F1,F5,G2,G6,H5,H8,I2,I7,I8,I9) * 82..9.1439413.8.5.35.4.18..268913574413...9.8579.84.31132.4978.6851374..7948.231. * PAIR C1: 6,7 ROW 1 D1: 6,7,5 # reduction candidate for 6,7 D1: 6,7 => SOLVED * 826795143941368257357421869268913574413576928579284631132649785685137492794852316 * DURATION: 0:00:01.978389 START: 08:24:57.127952 END: 08:24:59.106341 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-165-base-pr-001.dot * REASONING * PRF # D1: 6,7 => SOL * STA D1: 6,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 165 solution: 826795143941368257357421869268913574413576928579284631132649785685137492794852316 info: 1823 FNBWY S8.f 45375 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 826795143941368257357421869268913574413576928579284631132649785685137492794852316 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 # D1: 6,7 => SOL * DIS # D1: 5 => CTR => D1: 6,7 * DIS # E3: 6,7 => CTR => E3: 2 * INC # E3: 2 => UNS * DIS # D1: 5,6 => CTR => D1: 7 * PRF # D1: 7 => SOL * INC # H3: 2,6 => UNS * DIS # H3: 9 => CTR => H3: 2,6 * INC # E2: 2,6 => UNS * DIS # E2: 7 => CTR => E2: 2,6 * DIS # I3: 2,7 => CTR => I3: 9 * INC # I3: 9 => UNS * DIS # E2: 2,7 => CTR => E2: 6 * PRF # E2: 6 => SOL * PRF # D5: 5,6 => SOL * INC # D5: 2,7 => UNS * DIS # E5: 5,6 => CTR => E5: 7 * PRF # E5: 7 => SOL * DIS # D5: 2,6 => CTR => D5: 5,7 * PRF # D5: 5,7 => SOL * DIS # D5: 2,6 => CTR => D5: 5,7 * PRF # D5: 5,7 => SOL * INC # H3: 2,6 => UNS * DIS # H3: 9 => CTR => H3: 2,6 * DIS # D1: 5,6 => CTR => D1: 7 * PRF # D1: 7 => SOL * PRF # D5: 5,6 => SOL * INC # D5: 2,7 => UNS * DIS # E5: 5,6 => CTR => E5: 7 * PRF # E5: 7 => SOL * DIS # H3: 2,9 => CTR => H3: 6 * PRF # H3: 6 => SOL * INC # I3: 2,9 => UNS * DIS # I3: 7 => CTR => I3: 2,9 * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # D1: 6,7 => SOL * STA D1: 6,7 * CNT 1 HDP CHAINS / 1 HYP OPENED