Analysis of xx-top500-066-base.sdk
Contents
Original Sudoku
level: medium
position: 1.....3...3...4......2....8....1.64..2.7.....5.8......6...3............1.......2. initial
Autosolve
position: 184.6.3.223.184.6..6.2.3418..38126454267..1835183462..6.2.318.484.62..313.14.8.26 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 7,9 => CTR => C2: 5 * PRF # C2: 5 => SOL * PRF # C3: 7,9 => SOL * DIS # C3: 5 => CTR => C3: 7,9 * DIS # E3: 7,9 => CTR => E3: 5 * PRF # E3: 5 => SOL * DIS # F1: 5,9 => CTR => F1: 7 * DIS # H1: 7 => CTR => H1: 5,9 * DIS # H1: 7,9 => CTR => H1: 5 * PRF # H1: 5 => SOL * PRF # G2: 7,9 => SOL * DIS # G2: 5 => CTR => G2: 7,9 * DIS # C2: 7,9 => CTR => C2: 5 * PRF # C2: 5 => SOL * DIS # B9: 7,9 => CTR => B9: 5 * DIS # E9: 5,9 => CTR => E9: 7 * DIS # F1: 5,9 => CTR => F1: 7 * DIS # H1: 7,9 => CTR => H1: 5 * PRF # H1: 5 => SOL * PRF # H7: 7,9 => SOL * DIS # H7: 5 => CTR => H7: 7,9 * DIS # B9: 7,9 => CTR => B9: 5 * PRF # F8: 7,9 => SOL * DIS # F8: 5 => CTR => F8: 7,9 * DIS # G8: 7,9 => CTR => G8: 5 * PRF # G8: 5 => SOL * DIS # C2: 7,9 => CTR => C2: 5 * PRF # C2: 5 => SOL * PRF # C3: 7,9 => SOL * DIS # C3: 5 => CTR => C3: 7,9 * DIS # E9: 5,9 => CTR => E9: 7 * PRF # B7: 5,9 => SOL * CNT 32 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 7,9 => CTR => C2: 5 * PRF C2: 5 => SOL * STA C2: 5 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.....3...3...4......2....8....1.64..2.7.....5.8......6...3............1.......2. | initial |
| 184.6.3.223.184.6..6.2.3418..38126454267..1835183462..6.2.318.484.62..313.14.8.26 | autosolve |
| 184967352235184769769253418973812645426795183518346297692531874847629531351478926 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) A3: 7,9 D1: 5,9 I2: 7,9 A4: 7,9 B4: 7,9 E5: 5,9 F5: 5,9 H6: 7,9 I6: 7,9 C8: 7,9 D7: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,C3: 5.. / C2 = 5 => 0 pairs (*) / C3 = 5 => 0 pairs (X) H1,G2: 5.. / H1 = 5 => 0 pairs (*) / G2 = 5 => 0 pairs (X) E5,F5: 5.. / E5 = 5 => 0 pairs (X) / F5 = 5 => 0 pairs (_) B7,B9: 5.. / B7 = 5 => 0 pairs (X) / B9 = 5 => 14 pairs (_) C2,G2: 5.. / C2 = 5 => 0 pairs (*) / G2 = 5 => 0 pairs (X) C3,E3: 5.. / C3 = 5 => 0 pairs (X) / E3 = 5 => 0 pairs (_) F8,G8: 5.. / F8 = 5 => 0 pairs (X) / G8 = 5 => 0 pairs (_) D1,D7: 5.. / D1 = 5 => 0 pairs (X) / D7 = 5 => 0 pairs (_) H1,H7: 5.. / H1 = 5 => 0 pairs (*) / H7 = 5 => 0 pairs (X) F1,E3: 7.. / F1 = 7 => 17 pairs (_) / E3 = 7 => 0 pairs (X) A4,B4: 7.. / A4 = 7 => 15 pairs (_) / B4 = 7 => 0 pairs (*) H6,I6: 7.. / H6 = 7 => 0 pairs (X) / I6 = 7 => 13 pairs (_) F8,E9: 7.. / F8 = 7 => 0 pairs (X) / E9 = 7 => 17 pairs (_) F1,H1: 7.. / F1 = 7 => 17 pairs (_) / H1 = 7 => 0 pairs (X) B7,H7: 7.. / B7 = 7 => 17 pairs (_) / H7 = 7 => 0 pairs (*) A3,A4: 7.. / A3 = 7 => 0 pairs (*) / A4 = 7 => 0 pairs (X) E3,E9: 7.. / E3 = 7 => 0 pairs (X) / E9 = 7 => 17 pairs (_) F1,F8: 7.. / F1 = 7 => 17 pairs (_) / F8 = 7 => 0 pairs (X) I2,I6: 7.. / I2 = 7 => 0 pairs (X) / I6 = 7 => 13 pairs (_) A4,B4: 9.. / A4 = 9 => 0 pairs (*) / B4 = 9 => 0 pairs (X) E5,F5: 9.. / E5 = 9 => 0 pairs (*) / F5 = 9 => 0 pairs (X) H6,I6: 9.. / H6 = 9 => 13 pairs (_) / I6 = 9 => 0 pairs (X) A3,A4: 9.. / A3 = 9 => 15 pairs (_) / A4 = 9 => 0 pairs (*) D1,D7: 9.. / D1 = 9 => 0 pairs (*) / D7 = 9 => 0 pairs (X) I2,I6: 9.. / I2 = 9 => 13 pairs (_) / I6 = 9 => 0 pairs (X) * DURATION: 0:00:55.623518 START: 04:54:29.852667 END: 04:55:25.476185 2017-05-04 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B4,C8,D1,D7,E5,F5,H6,I2,I6) * 184.6.3.223.184.6..6.2.3418..38126454267..1835183462..6.2.318.484.62..313.14.8.26 * PAIR A3: 7,9 BLK 1 C2: 7,9,5 # reduction candidate for 7,9 C2: 7,9 => CTR * 1845673922391845677652934189738126454267..1835183462..6.2.3185484.625.31351478926 C2: 5 => SOLVED * 184967352235184769769253418973812645426795183518346297692531874847629531351478926 C3: 7,9,5 # reduction candidate for 7,9 C3: 7,9 => SOLVED * 184967352235184769769253418973812645426795183518346297692531874847629531351478926 C3: 5 => CTR * 1845673922391845677652934189738126454267..1835183462..6.2.3185484.625.31351478926 * PAIR A3: 7,9 ROW 3 E3: 7,9,5 # reduction candidate for 7,9 E3: 7,9 => CTR * 1845673922391845677652934189738126454267..1835183462..6.2.3185484.625.31351478926 E3: 5 => SOLVED * 184967352235184769769253418973812645426795183518346297692531874847629531351478926 * PAIR D1: 5,9 BLK 2 F1: 5,9,7 # reduction candidate for 5,9 F1: 5,9 => CTR * 184.6.3722371845699652734187938126454267..1835183462976729318.484.62..313.14.8.26 F1: 7 # 17 pairs E3: 5,9,7 # reduction candidate for 5,9 E3: 5,9 # 17 pairs * PAIR D1: 5,9 ROW 1 H1: 5,9,7 # reduction candidate for 5,9 H1: 7 => CTR * 184.6.3722371845699652734187938126454267..1835183462976729318.484.62..313.14.8.26 H1: 5,9 # 17 pairs * PAIR I2: 7,9 BLK 3 H1: 7,9,5 # reduction candidate for 7,9 H1: 7,9 => CTR * 1845673922391845677652934189738126454267..1835183462..6.2.3185484.625.31351478926 H1: 5 => SOLVED * 184967352235184769769253418973812645426795183518346297692531874847629531351478926 G2: 7,9,5 # reduction candidate for 7,9 G2: 7,9 => SOLVED * 184967352235184769769253418973812645426795183518346297692531874847629531351478926 G2: 5 => CTR * 1845673922391845677652934189738126454267..1835183462..6.2.3185484.625.31351478926 * PAIR I2: 7,9 ROW 2 C2: 7,9,5 # reduction candidate for 7,9 C2: 7,9 => CTR * 1845673922391845677652934189738126454267..1835183462..6.2.3185484.625.31351478926 C2: 5 => SOLVED * 184967352235184769769253418973812645426795183518346297692531874847629531351478926 * PAIR B4: 7,9 COL B B7: 7,9,5 # reduction candidate for 7,9 B7: 7,9 # 14 pairs B9: 7,9,5 # reduction candidate for 7,9 B9: 7,9 => CTR * 18456739223.184.6..6.2.3418..38126454267..1835183462..65293187484.62..313.14.8.26 B9: 5 # 14 pairs * PAIR E5: 5,9 COL E E3: 5,9,7 # reduction candidate for 5,9 E3: 5,9 # 17 pairs E9: 5,9,7 # reduction candidate for 5,9 E9: 5,9 => CTR * 184.6.3.223.184.6..6.2734187938126454267..1835183462..6.2.318.48496275313.14.8.26 E9: 7 # 17 pairs * PAIR F5: 5,9 COL F F1: 5,9,7 # reduction candidate for 5,9 F1: 5,9 => CTR * 184.6.3722371845699652734187938126454267..1835183462976729318.484.62..313.14.8.26 F1: 7 # 17 pairs F8: 5,9,7 # reduction candidate for 5,9 F8: 5,9 # 17 pairs * PAIR H6: 7,9 COL H H1: 7,9,5 # reduction candidate for 7,9 H1: 7,9 => CTR * 1845673922391845677652934189738126454267..1835183462..6.2.3185484.625.31351478926 H1: 5 => SOLVED * 184967352235184769769253418973812645426795183518346297692531874847629531351478926 H7: 7,9,5 # reduction candidate for 7,9 H7: 7,9 => SOLVED * 184967352235184769769253418973812645426795183518346297692531874847629531351478926 H7: 5 => CTR * 18456739223.184.6..6.2.3418..38126454267..1835183462..672931854849625731351478926 * PAIR C8: 7,9 BLK 7 B7: 7,9,5 # reduction candidate for 7,9 B7: 7,9 # 14 pairs B9: 7,9,5 # reduction candidate for 7,9 B9: 7,9 => CTR * 18456739223.184.6..6.2.3418..38126454267..1835183462..65293187484.62..313.14.8.26 B9: 5 # 14 pairs * PAIR C8: 7,9 ROW 8 F8: 7,9,5 # reduction candidate for 7,9 F8: 7,9 => SOLVED * 184967352235184769769253418973812645426795183518346297692531874847629531351478926 F8: 5 => CTR * 18456739223918456776529341897381264542675918351834627.6.2.318.484.625.313.1478.26 G8: 7,9,5 # reduction candidate for 7,9 G8: 7,9 => CTR * 18456739223918456776529341897381264542675918351834627.6.2.318.484.625.313.1478.26 G8: 5 => SOLVED * 184967352235184769769253418973812645426795183518346297692531874847629531351478926 * PAIR C8: 7,9 COL C C2: 7,9,5 # reduction candidate for 7,9 C2: 7,9 => CTR * 1845673922391845677652934189738126454267..1835183462..6.2.3185484.625.31351478926 C2: 5 => SOLVED * 184967352235184769769253418973812645426795183518346297692531874847629531351478926 C3: 7,9,5 # reduction candidate for 7,9 C3: 7,9 => SOLVED * 184967352235184769769253418973812645426795183518346297692531874847629531351478926 C3: 5 => CTR * 1845673922391845677652934189738126454267..1835183462..6.2.3185484.625.31351478926 * PAIR D7: 5,9 BLK 8 F8: 5,9,7 # reduction candidate for 5,9 F8: 5,9 # 17 pairs E9: 5,9,7 # reduction candidate for 5,9 E9: 5,9 => CTR * 184.6.3.223.184.6..6.2734187938126454267..1835183462..6.2.318.48496275313.14.8.26 E9: 7 # 17 pairs * PAIR D7: 5,9 ROW 7 B7: 5,9,7 # reduction candidate for 5,9 B7: 5,9 => SOLVED * 184967352235184769769253418973812645426795183518346297692531874847629531351478926 B7: 7 # 17 pairs H7: 5,9,7 # reduction candidate for 5,9 H7: 5,9 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-066-base-pr-000.dot * REASONING * DIS # C2: 7,9 => CTR => C2: 5 * PRF # C2: 5 => SOL * PRF # C3: 7,9 => SOL * DIS # C3: 5 => CTR => C3: 7,9 * DIS # E3: 7,9 => CTR => E3: 5 * PRF # E3: 5 => SOL * DIS # F1: 5,9 => CTR => F1: 7 * DIS # H1: 7 => CTR => H1: 5,9 * DIS # H1: 7,9 => CTR => H1: 5 * PRF # H1: 5 => SOL * PRF # G2: 7,9 => SOL * DIS # G2: 5 => CTR => G2: 7,9 * DIS # C2: 7,9 => CTR => C2: 5 * PRF # C2: 5 => SOL * DIS # B9: 7,9 => CTR => B9: 5 * DIS # E9: 5,9 => CTR => E9: 7 * DIS # F1: 5,9 => CTR => F1: 7 * DIS # H1: 7,9 => CTR => H1: 5 * PRF # H1: 5 => SOL * PRF # H7: 7,9 => SOL * DIS # H7: 5 => CTR => H7: 7,9 * DIS # B9: 7,9 => CTR => B9: 5 * PRF # F8: 7,9 => SOL * DIS # F8: 5 => CTR => F8: 7,9 * DIS # G8: 7,9 => CTR => G8: 5 * PRF # G8: 5 => SOL * DIS # C2: 7,9 => CTR => C2: 5 * PRF # C2: 5 => SOL * PRF # C3: 7,9 => SOL * DIS # C3: 5 => CTR => C3: 7,9 * DIS # E9: 5,9 => CTR => E9: 7 * PRF # B7: 5,9 => SOL * CNT 32 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B4,C8,D1,D7,E5,F5,H6,I2,I6) * 184.6.3.223.184.6..6.2.3418..38126454267..1835183462..6.2.318.484.62..313.14.8.26 * PAIR A3: 7,9 BLK 1 C2: 7,9,5 # reduction candidate for 7,9 C2: 7,9 => CTR * 1845673922391845677652934189738126454267..1835183462..6.2.3185484.625.31351478926 C2: 5 => SOLVED * 184967352235184769769253418973812645426795183518346297692531874847629531351478926 * DURATION: 0:00:02.080023 START: 04:56:29.782353 END: 04:56:31.862376 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-066-base-pr-001.dot * REASONING * DIS # C2: 7,9 => CTR => C2: 5 * PRF C2: 5 => SOL * STA C2: 5 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 066 solution: 184967352235184769769253418973812645426795183518346297692531874847629531351478926 info: 1443 FNBHWXY S8.f 39943 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 184967352235184769769253418973812645426795183518346297692531874847629531351478926 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 # C2: 7,9 => CTR => C2: 5 * PRF # C2: 5 => SOL * PRF # C3: 7,9 => SOL * DIS # C3: 5 => CTR => C3: 7,9 * DIS # E3: 7,9 => CTR => E3: 5 * PRF # E3: 5 => SOL * DIS # F1: 5,9 => CTR => F1: 7 * INC # F1: 7 => UNS * INC # E3: 5,9 => UNS * INC # H1: 5,9 => UNS * DIS # H1: 7 => CTR => H1: 5,9 * DIS # H1: 7,9 => CTR => H1: 5 * PRF # H1: 5 => SOL * PRF # G2: 7,9 => SOL * DIS # G2: 5 => CTR => G2: 7,9 * DIS # C2: 7,9 => CTR => C2: 5 * PRF # C2: 5 => SOL * INC # B7: 7,9 => UNS * DIS # B9: 7,9 => CTR => B9: 5 * INC # B9: 5 => UNS * INC # E3: 5,9 => UNS * DIS # E9: 5,9 => CTR => E9: 7 * INC # E9: 7 => UNS * DIS # F1: 5,9 => CTR => F1: 7 * INC # F1: 7 => UNS * INC # F8: 5,9 => UNS * DIS # H1: 7,9 => CTR => H1: 5 * PRF # H1: 5 => SOL * PRF # H7: 7,9 => SOL * DIS # H7: 5 => CTR => H7: 7,9 * INC # B7: 7,9 => UNS * DIS # B9: 7,9 => CTR => B9: 5 * INC # B9: 5 => UNS * PRF # F8: 7,9 => SOL * DIS # F8: 5 => CTR => F8: 7,9 * DIS # G8: 7,9 => CTR => G8: 5 * PRF # G8: 5 => SOL * DIS # C2: 7,9 => CTR => C2: 5 * PRF # C2: 5 => SOL * PRF # C3: 7,9 => SOL * DIS # C3: 5 => CTR => C3: 7,9 * INC # F8: 5,9 => UNS * DIS # E9: 5,9 => CTR => E9: 7 * INC # E9: 7 => UNS * PRF # B7: 5,9 => SOL * INC # B7: 7 => UNS * INC # H7: 5,9 => UNS * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C2: 7,9 => CTR => C2: 5 * PRF C2: 5 => SOL * STA C2: 5 * CNT 2 HDP CHAINS / 1 HYP OPENED