Analysis of xx-top500-147-base.sdk
Contents
Original Sudoku
level: medium
position: .9.83....6.....5.9.............2..3.5..9...........1...23....8......17.....5..... initial
Autosolve
position: .9583.21.63821.5.92.1.598.3...12593.5129.3..83.9..8152123.9..8595.38172....5.2391 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F1: 4,7 => CTR => F1: 6 * DIS # H3: 4,7 => CTR => H3: 6 * DIS # B4: 4,7 => CTR => B4: 6,8 * DIS # B9: 4,7 => CTR => B9: 6,8 * DIS # F1: 4,7 => CTR => F1: 6 * DIS # F7: 6 => CTR => F7: 4,7 * DIS # H3: 4,7 => CTR => H3: 6 * DIS # H5: 6 => CTR => H5: 4,7 * DIS # E5: 4,6 => CTR => E5: 7 * DIS # B6: 4,6 => CTR => B6: 7 * PRF # D7: 4,6 => SOL * DIS # I4: 4,6 => CTR => I4: 7 * DIS # E5: 4,6 => CTR => E5: 7 * DIS # C9: 4,6 => CTR => C9: 7 * DIS # C4: 7 => CTR => C4: 4,6 * PRF # D7: 4,6 => SOL * DIS # C9: 4,6 => CTR => C9: 7 * DIS # E5: 4,6 => CTR => E5: 7 * PRF # D7: 4,6 => SOL * DIS # I4: 4,6 => CTR => I4: 7 * CNT 20 HDP CHAINS / 56 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F1: 4,7 => CTR => F1: 6 * DIS F1: 6 # B4: 4,7 => CTR => B4: 6,8 * PRF F1: 6 + B4: 6,8 # B6: 4,7 => SOL * STA F1: 6 + B4: 6,8 + B6: 4,7 * CNT 3 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .9.83....6.....5.9.............2..3.5..9...........1...23....8......17.....5..... | initial |
| .9583.21.63821.5.92.1.598.3...12593.5129.3..83.9..8152123.9..8595.38172....5.2391 | autosolve |
| 795836214638214579241759863486125937512973648379468152123697485954381726867542391 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) A1: 4,7 B3: 4,7 F2: 4,7 H2: 4,7 D6: 4,6 G5: 4,6 C8: 4,6 E9: 4,6 G7: 4,6 I8: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,B3: 4.. / A1 = 4 => 0 pairs (X) / B3 = 4 => 20 pairs (_) G7,I8: 4.. / G7 = 4 => 0 pairs (*) / I8 = 4 => 0 pairs (X) F2,H2: 4.. / F2 = 4 => 0 pairs (*) / H2 = 4 => 0 pairs (X) C8,I8: 4.. / C8 = 4 => 0 pairs (*) / I8 = 4 => 0 pairs (X) G5,G7: 4.. / G5 = 4 => 0 pairs (X) / G7 = 4 => 0 pairs (_) F1,D3: 6.. / F1 = 6 => 14 pairs (_) / D3 = 6 => 0 pairs (X) I1,H3: 6.. / I1 = 6 => 0 pairs (X) / H3 = 6 => 14 pairs (_) G7,I8: 6.. / G7 = 6 => 0 pairs (X) / I8 = 6 => 0 pairs (_) F1,I1: 6.. / F1 = 6 => 14 pairs (_) / I1 = 6 => 0 pairs (X) D3,H3: 6.. / D3 = 6 => 0 pairs (X) / H3 = 6 => 14 pairs (_) C8,I8: 6.. / C8 = 6 => 0 pairs (X) / I8 = 6 => 0 pairs (_) F1,F7: 6.. / F1 = 6 => 14 pairs (_) / F7 = 6 => 0 pairs (X) G5,G7: 6.. / G5 = 6 => 0 pairs (*) / G7 = 6 => 0 pairs (X) H3,H5: 6.. / H3 = 6 => 14 pairs (_) / H5 = 6 => 0 pairs (X) A1,B3: 7.. / A1 = 7 => 20 pairs (_) / B3 = 7 => 0 pairs (X) E5,E6: 7.. / E5 = 7 => 20 pairs (_) / E6 = 7 => 0 pairs (X) I4,H5: 7.. / I4 = 7 => 20 pairs (_) / H5 = 7 => 0 pairs (X) D7,F7: 7.. / D7 = 7 => 12 pairs (_) / F7 = 7 => 0 pairs (*) F2,H2: 7.. / F2 = 7 => 14 pairs (_) / H2 = 7 => 0 pairs (*) E5,H5: 7.. / E5 = 7 => 20 pairs (_) / H5 = 7 => 0 pairs (X) B6,E6: 7.. / B6 = 7 => 20 pairs (_) / E6 = 7 => 0 pairs (X) C4,C9: 7.. / C4 = 7 => 0 pairs (X) / C9 = 7 => 12 pairs (_) D3,D7: 7.. / D3 = 7 => 0 pairs (*) / D7 = 7 => 0 pairs (X) I1,I4: 7.. / I1 = 7 => 0 pairs (X) / I4 = 7 => 20 pairs (_) A4,B4: 8.. / A4 = 8 => 12 pairs (_) / B4 = 8 => 11 pairs (_) A9,B9: 8.. / A9 = 8 => 11 pairs (_) / B9 = 8 => 12 pairs (_) A4,A9: 8.. / A4 = 8 => 12 pairs (_) / A9 = 8 => 11 pairs (_) B4,B9: 8.. / B4 = 8 => 11 pairs (_) / B9 = 8 => 12 pairs (_) * DURATION: 0:00:47.532143 START: 07:46:26.452977 END: 07:47:13.985120 2017-05-04 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B3,C8,D6,E9,F2,G5,G7,H2,I8) * .9583.21.63821.5.92.1.598.3...12593.5129.3..83.9..8152123.9..8595.38172....5.2391 * PAIR A1: 4,7 ROW 1 F1: 4,7,6 # reduction candidate for 4,7 F1: 4,7 => CTR * .9583.21663821.5.92.16598.3...125937512973.6837946815212379648595.38172....5.2391 F1: 6 # 14 pairs I1: 4,7,6 # reduction candidate for 4,7 I1: 4,7 # 14 pairs * PAIR A1: 4,7 COL A A4: 4,7,8 # reduction candidate for 4,7 A4: 4,7 # 11 pairs A9: 4,7,8 # reduction candidate for 4,7 A9: 4,7 # 12 pairs * PAIR B3: 4,7 ROW 3 D3: 4,7,6 # reduction candidate for 4,7 D3: 4,7 # 14 pairs H3: 4,7,6 # reduction candidate for 4,7 H3: 4,7 => CTR * .9583.21663821.5.92.16598.3...125937512973.6837946815212379648595.38172....5.2391 H3: 6 # 14 pairs * PAIR B3: 4,7 COL B B4: 4,7,6,8 # reduction candidate for 4,7 B4: 4,7 => CTR * 49583.21.63821457927165984384.12593.5129.3..8369478152123.9..8595.38172..8.542391 B4: 6,8 # 11 pairs B6: 4,7,6 # reduction candidate for 4,7 B6: 4,7 # 15 pairs B9: 4,7,6,8 # reduction candidate for 4,7 B9: 4,7 => CTR * .9583.21.63821.5.9241.598.34871259365129634.8369478152123.9..8595.38172.8..542391 B9: 6,8 # 11 pairs * PAIR F2: 4,7 BLK 2 F1: 4,7,6 # reduction candidate for 4,7 F1: 4,7 => CTR * .9583.21663821.5.92.16598.3...125937512973.6837946815212379648595.38172....5.2391 F1: 6 # 14 pairs D3: 4,7,6 # reduction candidate for 4,7 D3: 4,7 # 14 pairs * PAIR F2: 4,7 COL F F7: 4,7,6 # reduction candidate for 4,7 F7: 6 => CTR * .9583.21.63821.5.92.1.598.3...12593.5129.3..83.9..8152123796485954381726...542391 F7: 4,7 # 14 pairs * PAIR H2: 4,7 BLK 3 I1: 4,7,6 # reduction candidate for 4,7 I1: 4,7 # 14 pairs H3: 4,7,6 # reduction candidate for 4,7 H3: 4,7 => CTR * .9583.21663821.5.92.16598.3...125937512973.6837946815212379648595.38172....5.2391 H3: 6 # 14 pairs * PAIR H2: 4,7 COL H H5: 4,7,6 # reduction candidate for 4,7 H5: 6 => CTR * 79583.21.63821.5.92.1.598.3...125937512973468379..8152123.9.685956381724..7562391 H5: 4,7 # 14 pairs * PAIR D6: 4,6 BLK 5 E5: 4,6,7 # reduction candidate for 4,6 E5: 4,6 => CTR * .9583.217638217549271459863...12593.51294367834967815212379..8595.38172....5.2391 E5: 7 # 20 pairs E6: 4,6,7 # reduction candidate for 4,6 E6: 4,6 # 20 pairs * PAIR D6: 4,6 ROW 6 B6: 4,6,7 # reduction candidate for 4,6 B6: 4,6 => CTR * .9583.217638217549271459863...12593.51294367834967815212379..8595.38172....5.2391 B6: 7 # 20 pairs * PAIR D6: 4,6 COL D D3: 4,6,7 # reduction candidate for 4,6 D3: 4,6 # 12 pairs D7: 4,6,7 # reduction candidate for 4,6 D7: 4,6 => SOLVED * 795836214638214579241759863486125937512973648379468152123697485954381726867542391 D7: 7 # 12 pairs * PAIR G5: 4,6 BLK 6 I4: 4,6,7 # reduction candidate for 4,6 I4: 4,6 => CTR * .9583.217638217549271459863...12593.5129.3.783.967815212379468595.38172....5.2391 I4: 7 # 20 pairs H5: 4,6,7 # reduction candidate for 4,6 H5: 4,6 # 20 pairs * PAIR G5: 4,6 ROW 5 E5: 4,6,7 # reduction candidate for 4,6 E5: 4,6 => CTR * .9583.217638217549271459863...12593.51294367834967815212379..8595.38172....5.2391 E5: 7 # 20 pairs * PAIR C8: 4,6 BLK 7 B9: 4,6,7,8 # reduction candidate for 4,6 B9: 4,6 # 13 pairs C9: 4,6,7 # reduction candidate for 4,6 C9: 4,6 => CTR * .9583.217638217549271459863..712593.51294367834967815212379..8595.38172....5.2391 C9: 7 # 12 pairs * PAIR C8: 4,6 COL C C4: 4,6,7 # reduction candidate for 4,6 C4: 7 => CTR * .9583.217638217549271459863..712593.51294367834967815212379..8595.38172....5.2391 C4: 4,6 # 12 pairs * PAIR E9: 4,6 BLK 8 D7: 4,6,7 # reduction candidate for 4,6 D7: 4,6 => SOLVED * 795836214638214579241759863486125937512973648379468152123697485954381726867542391 D7: 7 # 12 pairs F7: 4,6,7 # reduction candidate for 4,6 F7: 4,6 # 12 pairs * PAIR E9: 4,6 ROW 9 B9: 4,6,7,8 # reduction candidate for 4,6 B9: 4,6 # 13 pairs C9: 4,6,7 # reduction candidate for 4,6 C9: 4,6 => CTR * .9583.217638217549271459863..712593.51294367834967815212379..8595.38172....5.2391 C9: 7 # 12 pairs * PAIR E9: 4,6 COL E E5: 4,6,7 # reduction candidate for 4,6 E5: 4,6 => CTR * .9583.217638217549271459863...12593.51294367834967815212379..8595.38172....5.2391 E5: 7 # 20 pairs E6: 4,6,7 # reduction candidate for 4,6 E6: 4,6 # 20 pairs * PAIR G7: 4,6 ROW 7 D7: 4,6,7 # reduction candidate for 4,6 D7: 4,6 => SOLVED * 795836214638214579241759863486125937512973648379468152123697485954381726867542391 D7: 7 # 12 pairs F7: 4,6,7 # reduction candidate for 4,6 F7: 4,6 # 12 pairs * PAIR I8: 4,6 COL I I1: 4,6,7 # reduction candidate for 4,6 I1: 4,6 # 20 pairs I4: 4,6,7 # reduction candidate for 4,6 I4: 4,6 => CTR * .9583.217638217549271459863...12593.5129.3.783.967815212379468595.38172....5.2391 I4: 7 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-147-base-pr-000.dot * REASONING * DIS # F1: 4,7 => CTR => F1: 6 * DIS # H3: 4,7 => CTR => H3: 6 * DIS # B4: 4,7 => CTR => B4: 6,8 * DIS # B9: 4,7 => CTR => B9: 6,8 * DIS # F1: 4,7 => CTR => F1: 6 * DIS # F7: 6 => CTR => F7: 4,7 * DIS # H3: 4,7 => CTR => H3: 6 * DIS # H5: 6 => CTR => H5: 4,7 * DIS # E5: 4,6 => CTR => E5: 7 * DIS # B6: 4,6 => CTR => B6: 7 * PRF # D7: 4,6 => SOL * DIS # I4: 4,6 => CTR => I4: 7 * DIS # E5: 4,6 => CTR => E5: 7 * DIS # C9: 4,6 => CTR => C9: 7 * DIS # C4: 7 => CTR => C4: 4,6 * PRF # D7: 4,6 => SOL * DIS # C9: 4,6 => CTR => C9: 7 * DIS # E5: 4,6 => CTR => E5: 7 * PRF # D7: 4,6 => SOL * DIS # I4: 4,6 => CTR => I4: 7 * CNT 20 HDP CHAINS / 56 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B3,C8,D6,E9,F2,G5,G7,H2,I8) * .9583.21.63821.5.92.1.598.3...12593.5129.3..83.9..8152123.9..8595.38172....5.2391 * PAIR A1: 4,7 ROW 1 F1: 4,7,6 # reduction candidate for 4,7 F1: 4,7 => CTR * .9583.21663821.5.92.16598.3...125937512973.6837946815212379648595.38172....5.2391 * RESTART * PAIR A1: 4,7 COL A A4: 4,7,8 # reduction candidate for 4,7 A4: 4,7 # 15 pairs A9: 4,7,8 # reduction candidate for 4,7 A9: 4,7 # 16 pairs * PAIR RESTART * PAIR A1: 4,7 COL A A4: 4,7,8 # reduction candidate for 4,7 A4: 4,7 # 15 pairs A9: 4,7,8 # reduction candidate for 4,7 A9: 4,7 # 16 pairs * PAIR B3: 4,7 COL B B4: 4,7,6,8 # reduction candidate for 4,7 B4: 4,7 => CTR * .9583621.63821.5.92.1.598638..12593.5129.3..8369478152123697485954381726786542391 B6: 4,7,6 # reduction candidate for 4,7 B6: 4,7 => SOLVED * 795836214638214579241759863486125937512973648379468152123697485954381726867542391 * DURATION: 0:00:07.885201 START: 07:48:06.017771 END: 07:48:13.902972 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-147-base-pr-001.dot * REASONING * DIS # F1: 4,7 => CTR => F1: 6 * DIS F1: 6 # B4: 4,7 => CTR => B4: 6,8 * PRF F1: 6 + B4: 6,8 # B6: 4,7 => SOL * STA F1: 6 + B4: 6,8 + B6: 4,7 * CNT 3 HDP CHAINS / 7 HYP OPENED
Header Info
Top 500 Minimum 17 147 solution: 795836214638214579241759863486125937512973648379468152123697485954381726867542391 info: 1815 FNBWX S8.f 24613 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 795836214638214579241759863486125937512973648379468152123697485954381726867542391 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 # F1: 4,7 => CTR => F1: 6 * INC # F1: 6 => UNS * INC # I1: 4,7 => UNS * INC # A4: 4,7 => UNS * INC # A9: 4,7 => UNS * INC # D3: 4,7 => UNS * DIS # H3: 4,7 => CTR => H3: 6 * INC # H3: 6 => UNS * DIS # B4: 4,7 => CTR => B4: 6,8 * INC # B4: 6,8 => UNS * INC # B6: 4,7 => UNS * DIS # B9: 4,7 => CTR => B9: 6,8 * INC # B9: 6,8 => UNS * DIS # F1: 4,7 => CTR => F1: 6 * INC # F1: 6 => UNS * INC # D3: 4,7 => UNS * INC # F7: 4,7 => UNS * DIS # F7: 6 => CTR => F7: 4,7 * INC # I1: 4,7 => UNS * DIS # H3: 4,7 => CTR => H3: 6 * INC # H3: 6 => UNS * INC # H5: 4,7 => UNS * DIS # H5: 6 => CTR => H5: 4,7 * DIS # E5: 4,6 => CTR => E5: 7 * INC # E5: 7 => UNS * INC # E6: 4,6 => UNS * DIS # B6: 4,6 => CTR => B6: 7 * INC # B6: 7 => UNS * INC # D3: 4,6 => UNS * PRF # D7: 4,6 => SOL * INC # D7: 7 => UNS * DIS # I4: 4,6 => CTR => I4: 7 * INC # I4: 7 => UNS * INC # H5: 4,6 => UNS * DIS # E5: 4,6 => CTR => E5: 7 * INC # E5: 7 => UNS * INC # B9: 4,6 => UNS * DIS # C9: 4,6 => CTR => C9: 7 * INC # C9: 7 => UNS * INC # C4: 4,6 => UNS * DIS # C4: 7 => CTR => C4: 4,6 * PRF # D7: 4,6 => SOL * INC # D7: 7 => UNS * INC # F7: 4,6 => UNS * INC # B9: 4,6 => UNS * DIS # C9: 4,6 => CTR => C9: 7 * INC # C9: 7 => UNS * DIS # E5: 4,6 => CTR => E5: 7 * INC # E5: 7 => UNS * INC # E6: 4,6 => UNS * PRF # D7: 4,6 => SOL * INC # D7: 7 => UNS * INC # F7: 4,6 => UNS * INC # I1: 4,6 => UNS * DIS # I4: 4,6 => CTR => I4: 7 * INC # I4: 7 => UNS * CNT 56 HDP CHAINS / 56 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # F1: 4,7 => CTR => F1: 6 * INC F1: 6 # A4: 4,7 => UNS * INC F1: 6 # A9: 4,7 => UNS * INC F1: 6 # A4: 4,7 => UNS * INC F1: 6 # A9: 4,7 => UNS * DIS F1: 6 # B4: 4,7 => CTR => B4: 6,8 * PRF F1: 6 + B4: 6,8 # B6: 4,7 => SOL * STA F1: 6 + B4: 6,8 + B6: 4,7 * CNT 7 HDP CHAINS / 7 HYP OPENED