Analysis of xx-top500-129-base.sdk
Contents
Original Sudoku
level: medium
position: ....38.6..24...................7.2...1.4.....8......3....6..4.1..9...5..3........ initial
Autosolve
position: 1..238.64.241..385.38....12..6371248.1348.65.84....13..8.6.34.146981.5.33.1...8.6 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B1: 5,7 => SOL * DIS # B1: 9 => CTR => B1: 5,7 * DIS # C7: 5,7 => CTR => C7: 2 * DIS # F2: 6,9 => CTR => F2: 7 * PRF # F2: 7 => SOL * DIS # E3: 6,9 => CTR => E3: 4,5 * DIS # F3: 6,9 => CTR => F3: 4,5,7 * PRF # A2: 6,9 => SOL * DIS # A2: 7 => CTR => A2: 6,9 * DIS # E6: 6,9 => CTR => E6: 2,5 * DIS # B1: 5 => CTR => B1: 7,9 * DIS # A3: 7,9 => CTR => A3: 6 * DIS # F3: 7,9 => CTR => F3: 4,5,6 * DIS # B1: 5,9 => CTR => B1: 7 * PRF # B1: 7 => SOL * PRF # A7: 2,7 => SOL * DIS # A7: 5 => CTR => A7: 2,7 * DIS # C7: 5 => CTR => C7: 2,7 * DIS # F6: 2,9 => CTR => F6: 5,6 * DIS # F9: 2,9 => CTR => F9: 4,5,7 * DIS # E6: 5,9 => CTR => E6: 2,6 * DIS # F6: 5,9 => CTR => F6: 2,6 * PRF # D3: 5,9 => SOL * DIS # D3: 7 => CTR => D3: 5,9 * DIS # D9: 5,9 => CTR => D9: 7 * PRF # D9: 7 => SOL * DIS # C7: 5,7 => CTR => C7: 2 * DIS # F9: 5,7 => CTR => F9: 2,4,9 * PRF # B1: 5,7 => SOL * DIS # B1: 9 => CTR => B1: 5,7 * DIS # D9: 5,9 => CTR => D9: 7 * PRF # D9: 7 => SOL * PRF # E9: 5,9 => SOL * DIS # F9: 5,9 => CTR => F9: 2,4,7 * DIS # E3: 5,9 => CTR => E3: 4,6 * DIS # E6: 5,9 => CTR => E6: 2,6 * DIS # F9: 2,7 => CTR => F9: 4,5,9 * DIS # H9: 7,9 => CTR => H9: 2 * PRF # H9: 2 => SOL * PRF # H9: 2,7 => SOL * DIS # H9: 9 => CTR => H9: 2,7 * CNT 41 HDP CHAINS / 64 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B1: 5,7 => SOL * STA B1: 5,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....38.6..24...................7.2...1.4.....8......3....6..4.1..9...5..3........ | initial |
| 1..238.64.241..385.38....12..6371248.1348.65.84....13..8.6.34.146981.5.33.1...8.6 | autosolve |
| 175238964924167385638945712596371248213489657847526139782653491469812573351794826 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) C1: 5,7 E2: 6,9 G1: 7,9 G3: 7,9 A4: 5,9 B4: 5,9 A5: 2,7 C6: 2,7 F5: 2,9 D6: 5,9 I5: 7,9 I6: 7,9 B9: 5,7 E7: 5,9 F8: 2,7 H7: 7,9 H8: 2,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A5,C6: 2.. / A5 = 2 => 21 pairs (_) / C6 = 2 => 0 pairs (X) A7,C7: 2.. / A7 = 2 => 0 pairs (X) / C7 = 2 => 21 pairs (_) H8,H9: 2.. / H8 = 2 => 0 pairs (X) / H9 = 2 => 0 pairs (_) A5,F5: 2.. / A5 = 2 => 21 pairs (_) / F5 = 2 => 0 pairs (X) F8,H8: 2.. / F8 = 2 => 0 pairs (*) / H8 = 2 => 0 pairs (X) A5,A7: 2.. / A5 = 2 => 21 pairs (_) / A7 = 2 => 0 pairs (X) C6,C7: 2.. / C6 = 2 => 0 pairs (X) / C7 = 2 => 21 pairs (_) E6,E9: 2.. / E6 = 2 => 0 pairs (*) / E9 = 2 => 0 pairs (X) E3,F3: 4.. / E3 = 4 => 17 pairs (_) / F3 = 4 => 0 pairs (X) E9,F9: 4.. / E9 = 4 => 0 pairs (X) / F9 = 4 => 17 pairs (_) E3,E9: 4.. / E3 = 4 => 17 pairs (_) / E9 = 4 => 0 pairs (X) F3,F9: 4.. / F3 = 4 => 0 pairs (X) / F9 = 4 => 17 pairs (_) B1,C1: 5.. / B1 = 5 => 0 pairs (X) / C1 = 5 => 18 pairs (_) A4,B4: 5.. / A4 = 5 => 0 pairs (*) / B4 = 5 => 0 pairs (X) A4,A7: 5.. / A4 = 5 => 0 pairs (*) / A7 = 5 => 0 pairs (X) C1,C7: 5.. / C1 = 5 => 18 pairs (_) / C7 = 5 => 0 pairs (X) A2,A3: 6.. / A2 = 6 => 0 pairs (X) / A3 = 6 => 18 pairs (_) E6,F6: 6.. / E6 = 6 => 0 pairs (X) / F6 = 6 => 20 pairs (_) G1,G3: 7.. / G1 = 7 => 0 pairs (X) / G3 = 7 => 0 pairs (_) A5,C6: 7.. / A5 = 7 => 0 pairs (X) / C6 = 7 => 21 pairs (_) I5,I6: 7.. / I5 = 7 => 21 pairs (_) / I6 = 7 => 0 pairs (X) A2,F2: 7.. / A2 = 7 => 0 pairs (X) / F2 = 7 => 0 pairs (_) A5,I5: 7.. / A5 = 7 => 0 pairs (X) / I5 = 7 => 21 pairs (_) C6,I6: 7.. / C6 = 7 => 21 pairs (_) / I6 = 7 => 0 pairs (X) F8,H8: 7.. / F8 = 7 => 0 pairs (X) / H8 = 7 => 0 pairs (_) B1,B9: 7.. / B1 = 7 => 0 pairs (*) / B9 = 7 => 0 pairs (X) D3,D9: 7.. / D3 = 7 => 0 pairs (X) / D9 = 7 => 0 pairs (_) G1,G3: 9.. / G1 = 9 => 0 pairs (*) / G3 = 9 => 0 pairs (X) A4,B4: 9.. / A4 = 9 => 0 pairs (X) / B4 = 9 => 0 pairs (_) I5,I6: 9.. / I5 = 9 => 0 pairs (X) / I6 = 9 => 21 pairs (_) H7,H9: 9.. / H7 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) B1,G1: 9.. / B1 = 9 => 0 pairs (X) / G1 = 9 => 0 pairs (_) F5,I5: 9.. / F5 = 9 => 21 pairs (_) / I5 = 9 => 0 pairs (X) E7,H7: 9.. / E7 = 9 => 0 pairs (X) / H7 = 9 => 0 pairs (_) B1,B4: 9.. / B1 = 9 => 0 pairs (X) / B4 = 9 => 0 pairs (_) * DURATION: 0:01:01.788919 START: 07:10:21.152849 END: 07:11:22.941768 2017-05-04 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,B4,B9,C1,C6,D6,E2,E7,F5,F8,G1,G3,H7,H8,I5,I6) * 1..238.64.241..385.38....12..6371248.1348.65.84....13..8.6.34.146981.5.33.1...8.6 * PAIR C1: 5,7 BLK 1 B1: 5,7,9 # reduction candidate for 5,7 B1: 5,7 => SOLVED * 175238964924167385638945712596371248213489657847526139782653491469812573351794826 B1: 9 => CTR * 1952387647241693856387..91295637124821348.65.84....13.5826934714698175233715..896 * PAIR C1: 5,7 COL C C7: 5,7,2 # reduction candidate for 5,7 C7: 5,7 => CTR * 1..238.64.241..385.38.4..12596371248713482659842...13728.6.34.14698175233.1.248.6 C7: 2 # 21 pairs * PAIR E2: 6,9 BLK 2 F2: 6,9,7 # reduction candidate for 6,9 F2: 6,9 => CTR * 1..238.647241..385638....129563712482134896578475..1395826934714698175.33.1...8.6 F2: 7 => SOLVED * 175238964924167385638945712596371248213489657847526139782653491469812573351794826 E3: 6,9,4,5 # reduction candidate for 6,9 E3: 6,9 => CTR * 1..238.64.241..385.385.4.12..6371248.1348.65.84.92.13..8.6.34.146981.5.33.1.4.8.6 E3: 4,5 # 18 pairs F3: 6,9,4,5,7 # reduction candidate for 6,9 F3: 6,9 => CTR * 1..238.64.241..385.3854..12..6371248.1348.65.84.9.5137.8.6.34.146981.5.33.17.48.6 F3: 4,5,7 # 17 pairs * PAIR E2: 6,9 ROW 2 A2: 6,9,7 # reduction candidate for 6,9 A2: 6,9 => SOLVED * 175238964924167385638945712596371248213489657847526139782653491469812573351794826 A2: 7 => CTR * 1..238.647241..385638....129563712482134896578475..1395826934714698175.33.1...8.6 * PAIR E2: 6,9 COL E E6: 6,9,2,5 # reduction candidate for 6,9 E6: 6,9 => CTR * 175238964.241..385.3874..12..6371248.1348.65.84....13..8.653491469817523351924876 E6: 2,5 # 21 pairs * PAIR G1: 7,9 ROW 1 B1: 7,9,5 # reduction candidate for 7,9 B1: 5 => CTR * 157238964.241.7385.38...71259637124871348265.84....13..8.6.34.146981.5.33.1...8.6 B1: 7,9 # 18 pairs * PAIR G3: 7,9 ROW 3 A3: 7,9,6 # reduction candidate for 7,9 A3: 7,9 => CTR * 1..238.64624197385.385...12..6371248.1348.65.84.9..137.8.6534914698125.33.1...8.6 A3: 6 # 18 pairs D3: 7,9,5 # reduction candidate for 7,9 D3: 7,9 # 21 pairs F3: 7,9,4,5,6 # reduction candidate for 7,9 F3: 7,9 => CTR * 1..238.64.241..38563854..12..6371248.1348.65.84.9.5137.8.6.34.146981.5.33.17.48.6 F3: 4,5,6 # 17 pairs * PAIR B4: 5,9 COL B B1: 5,9,7 # reduction candidate for 5,9 B1: 5,9 => CTR * 1952387647241..3856387..9129563712482134896578475..13..8.6.3471469817523371...896 B1: 7 => SOLVED * 175238964924167385638945712596371248213489657847526139782653491469812573351794826 * PAIR A5: 2,7 COL A A7: 2,7,5 # reduction candidate for 2,7 A7: 2,7 => SOLVED * 175238964924167385638945712596371248213489657847526139782653491469812573351794826 A7: 5 => CTR * 1..238.64.241..385.38....12..63712482134896578475..1395826934714698175.33.1...8.6 * PAIR C6: 2,7 COL C C7: 2,7,5 # reduction candidate for 2,7 C7: 5 => CTR * 157238964.24169385.38....12..6371248.1348.65.842...137285693471469817523371524896 C7: 2,7 # 18 pairs * PAIR F5: 2,9 BLK 5 E6: 2,9,5,6 # reduction candidate for 2,9 E6: 2,9 # 23 pairs F6: 2,9,5,6 # reduction candidate for 2,9 F6: 2,9 => CTR * 175238.64.2419.385.38.45.12..6371248.1348.65.84.56.13..8.653491469817523351924876 F6: 5,6 # 18 pairs * PAIR F5: 2,9 COL F F9: 2,9,4,5,7 # reduction candidate for 2,9 F9: 2,9 => CTR * 1..238.64.241..385.38..4.12..6371248.1348.65.84...513..8.6.34.146981.5.33.1.4.8.6 F9: 4,5,7 # 17 pairs * PAIR D6: 5,9 BLK 5 E6: 5,9,2,6 # reduction candidate for 5,9 E6: 5,9 => CTR * 1..238.647241..385.38.45.12..6371248.13482659842..613728.6.34.14698175233.1.248.6 E6: 2,6 # 18 pairs F6: 5,9,2,6 # reduction candidate for 5,9 F6: 5,9 => CTR * 17523896462419.385.38.4..12..6371248.13482659842.6913728.653491469817523351924876 F6: 2,6 # 20 pairs * PAIR D6: 5,9 COL D D3: 5,9,7 # reduction candidate for 5,9 D3: 5,9 => SOLVED * 175238964924167385638945712596371248213489657847526139782653491469812573351794826 D3: 7 => CTR * 1952387647241..3856387..9129563712482134896578475..1395826934.146981.5.33.1...8.6 D9: 5,9,7 # reduction candidate for 5,9 D9: 5,9 => CTR * 1952387647241..3856387..9129563712482134896578475..1395826934.146981.5.33.1...8.6 D9: 7 => SOLVED * 175238964924167385638945712596371248213489657847526139782653491469812573351794826 * PAIR B9: 5,7 BLK 7 A7: 5,7,2 # reduction candidate for 5,7 A7: 5,7 # 21 pairs C7: 5,7,2 # reduction candidate for 5,7 C7: 5,7 => CTR * 1..238.64.241..385.38.4..12596371248713482659842...13728.6.34.14698175233.1.248.6 C7: 2 # 21 pairs * PAIR B9: 5,7 ROW 9 D9: 5,7,9 # reduction candidate for 5,7 D9: 5,7 # 19 pairs F9: 5,7,2,4,9 # reduction candidate for 5,7 F9: 5,7 => CTR * 1..238.64.241..385.38..4.12..6371248.1348.65.84..2613..826.34914698125733.194.826 F9: 2,4,9 # 17 pairs * PAIR B9: 5,7 COL B B1: 5,7,9 # reduction candidate for 5,7 B1: 5,7 => SOLVED * 175238964924167385638945712596371248213489657847526139782653491469812573351794826 B1: 9 => CTR * 1952387647241693856387..91295637124821348.65.84....13.5826934714698175233715..896 * PAIR E7: 5,9 BLK 8 D9: 5,9,7 # reduction candidate for 5,9 D9: 5,9 => CTR * 1952387647241..3856387..9129563712482134896578475..1395826934.146981.5.33.1...8.6 D9: 7 => SOLVED * 175238964924167385638945712596371248213489657847526139782653491469812573351794826 E9: 5,9,2,4 # reduction candidate for 5,9 E9: 5,9 => SOLVED * 175238964924167385638945712596371248213489657847526139782653491469812573351794826 E9: 2,4 # 18 pairs F9: 5,9,2,4,7 # reduction candidate for 5,9 F9: 5,9 => CTR * 1..238.64.241..385.38..4.12..6371248.1348.65.84..2613..826.34914698125733.174.826 F9: 2,4,7 # 17 pairs * PAIR E7: 5,9 COL E E3: 5,9,4,6 # reduction candidate for 5,9 E3: 5,9 => CTR * 1.5238.64.2416.385638.54.12.563712482134896578475261395826934.146981.5.33.1.45826 E3: 4,6 # 18 pairs E6: 5,9,2,6 # reduction candidate for 5,9 E6: 5,9 => CTR * 1..238.647241..385.38.45.12..6371248.13482659842..613728.6.34.14698175233.1.248.6 E6: 2,6 # 18 pairs * PAIR F8: 2,7 BLK 8 F9: 2,7,4,5,9 # reduction candidate for 2,7 F9: 2,7 => CTR * 1..238.64.241..385.38..4.12..6371248.1348.65.84...513..8.6.34.146981.5.33.1.4.8.6 F9: 4,5,9 # 17 pairs * PAIR H7: 7,9 BLK 9 H9: 7,9,2 # reduction candidate for 7,9 H9: 7,9 => CTR * 1..238.647241..3856387..9129563712482134896578475..1395826934.14698175233.1...8.6 H9: 2 => SOLVED * 175238964924167385638945712596371248213489657847526139782653491469812573351794826 * PAIR H8: 2,7 BLK 9 H9: 2,7,9 # reduction candidate for 2,7 H9: 2,7 => SOLVED * 175238964924167385638945712596371248213489657847526139782653491469812573351794826 H9: 9 => CTR * 1..238.647241693856387..91295637124821348.65.84....13..8.6934714698175233715..896 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-129-base-pr-000.dot * REASONING * PRF # B1: 5,7 => SOL * DIS # B1: 9 => CTR => B1: 5,7 * DIS # C7: 5,7 => CTR => C7: 2 * DIS # F2: 6,9 => CTR => F2: 7 * PRF # F2: 7 => SOL * DIS # E3: 6,9 => CTR => E3: 4,5 * DIS # F3: 6,9 => CTR => F3: 4,5,7 * PRF # A2: 6,9 => SOL * DIS # A2: 7 => CTR => A2: 6,9 * DIS # E6: 6,9 => CTR => E6: 2,5 * DIS # B1: 5 => CTR => B1: 7,9 * DIS # A3: 7,9 => CTR => A3: 6 * DIS # F3: 7,9 => CTR => F3: 4,5,6 * DIS # B1: 5,9 => CTR => B1: 7 * PRF # B1: 7 => SOL * PRF # A7: 2,7 => SOL * DIS # A7: 5 => CTR => A7: 2,7 * DIS # C7: 5 => CTR => C7: 2,7 * DIS # F6: 2,9 => CTR => F6: 5,6 * DIS # F9: 2,9 => CTR => F9: 4,5,7 * DIS # E6: 5,9 => CTR => E6: 2,6 * DIS # F6: 5,9 => CTR => F6: 2,6 * PRF # D3: 5,9 => SOL * DIS # D3: 7 => CTR => D3: 5,9 * DIS # D9: 5,9 => CTR => D9: 7 * PRF # D9: 7 => SOL * DIS # C7: 5,7 => CTR => C7: 2 * DIS # F9: 5,7 => CTR => F9: 2,4,9 * PRF # B1: 5,7 => SOL * DIS # B1: 9 => CTR => B1: 5,7 * DIS # D9: 5,9 => CTR => D9: 7 * PRF # D9: 7 => SOL * PRF # E9: 5,9 => SOL * DIS # F9: 5,9 => CTR => F9: 2,4,7 * DIS # E3: 5,9 => CTR => E3: 4,6 * DIS # E6: 5,9 => CTR => E6: 2,6 * DIS # F9: 2,7 => CTR => F9: 4,5,9 * DIS # H9: 7,9 => CTR => H9: 2 * PRF # H9: 2 => SOL * PRF # H9: 2,7 => SOL * DIS # H9: 9 => CTR => H9: 2,7 * CNT 41 HDP CHAINS / 64 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,B4,B9,C1,C6,D6,E2,E7,F5,F8,G1,G3,H7,H8,I5,I6) * 1..238.64.241..385.38....12..6371248.1348.65.84....13..8.6.34.146981.5.33.1...8.6 * PAIR C1: 5,7 BLK 1 B1: 5,7,9 # reduction candidate for 5,7 B1: 5,7 => SOLVED * 175238964924167385638945712596371248213489657847526139782653491469812573351794826 * DURATION: 0:00:02.095369 START: 07:12:26.219939 END: 07:12:28.315308 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-129-base-pr-001.dot * REASONING * PRF # B1: 5,7 => SOL * STA B1: 5,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 129 solution: 175238964924167385638945712596371248213489657847526139782653491469812573351794826 info: 1811 FNBWY S8.f 4126 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 175238964924167385638945712596371248213489657847526139782653491469812573351794826 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 # B1: 5,7 => SOL * DIS # B1: 9 => CTR => B1: 5,7 * DIS # C7: 5,7 => CTR => C7: 2 * INC # C7: 2 => UNS * DIS # F2: 6,9 => CTR => F2: 7 * PRF # F2: 7 => SOL * DIS # E3: 6,9 => CTR => E3: 4,5 * INC # E3: 4,5 => UNS * DIS # F3: 6,9 => CTR => F3: 4,5,7 * INC # F3: 4,5,7 => UNS * PRF # A2: 6,9 => SOL * DIS # A2: 7 => CTR => A2: 6,9 * DIS # E6: 6,9 => CTR => E6: 2,5 * INC # E6: 2,5 => UNS * INC # B1: 7,9 => UNS * DIS # B1: 5 => CTR => B1: 7,9 * DIS # A3: 7,9 => CTR => A3: 6 * INC # A3: 6 => UNS * INC # D3: 7,9 => UNS * DIS # F3: 7,9 => CTR => F3: 4,5,6 * INC # F3: 4,5,6 => UNS * DIS # B1: 5,9 => CTR => B1: 7 * PRF # B1: 7 => SOL * PRF # A7: 2,7 => SOL * DIS # A7: 5 => CTR => A7: 2,7 * INC # C7: 2,7 => UNS * DIS # C7: 5 => CTR => C7: 2,7 * INC # E6: 2,9 => UNS * DIS # F6: 2,9 => CTR => F6: 5,6 * INC # F6: 5,6 => UNS * DIS # F9: 2,9 => CTR => F9: 4,5,7 * INC # F9: 4,5,7 => UNS * DIS # E6: 5,9 => CTR => E6: 2,6 * INC # E6: 2,6 => UNS * DIS # F6: 5,9 => CTR => F6: 2,6 * INC # F6: 2,6 => UNS * PRF # D3: 5,9 => SOL * DIS # D3: 7 => CTR => D3: 5,9 * DIS # D9: 5,9 => CTR => D9: 7 * PRF # D9: 7 => SOL * INC # A7: 5,7 => UNS * DIS # C7: 5,7 => CTR => C7: 2 * INC # C7: 2 => UNS * INC # D9: 5,7 => UNS * DIS # F9: 5,7 => CTR => F9: 2,4,9 * INC # F9: 2,4,9 => UNS * PRF # B1: 5,7 => SOL * DIS # B1: 9 => CTR => B1: 5,7 * DIS # D9: 5,9 => CTR => D9: 7 * PRF # D9: 7 => SOL * PRF # E9: 5,9 => SOL * INC # E9: 2,4 => UNS * DIS # F9: 5,9 => CTR => F9: 2,4,7 * INC # F9: 2,4,7 => UNS * DIS # E3: 5,9 => CTR => E3: 4,6 * INC # E3: 4,6 => UNS * DIS # E6: 5,9 => CTR => E6: 2,6 * INC # E6: 2,6 => UNS * DIS # F9: 2,7 => CTR => F9: 4,5,9 * INC # F9: 4,5,9 => UNS * DIS # H9: 7,9 => CTR => H9: 2 * PRF # H9: 2 => SOL * PRF # H9: 2,7 => SOL * DIS # H9: 9 => CTR => H9: 2,7 * CNT 64 HDP CHAINS / 64 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # B1: 5,7 => SOL * STA B1: 5,7 * CNT 1 HDP CHAINS / 1 HYP OPENED