Analysis of xx-top500-243-base.sdk
Contents
Original Sudoku
level: medium
position: ...5....1...3.2...89...........9.75.12.........3......6...7.4.......3.2.......... initial
Autosolve
position: 23.5.9.717.13.259.895.173.24..291753129735...5738..2196129784359...5312.35.12.9.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E1: 8 => CTR => E1: 4,6 * DIS # E2: 4,6 => CTR => E2: 8 * DIS # E2: 4,6 => CTR => E2: 8 * DIS # I2: 6,8 => CTR => I2: 4 * PRF # I2: 4 => SOL * PRF # E1: 6,8 => SOL * DIS # E1: 4 => CTR => E1: 6,8 * DIS # I2: 8 => CTR => I2: 4,6 * DIS # H5: 8 => CTR => H5: 4,6 * DIS # E2: 4,6 => CTR => E2: 8 * DIS # H5: 6,8 => CTR => H5: 4 * PRF # H5: 4 => SOL * PRF # I5: 6,8 => SOL * DIS # I5: 4 => CTR => I5: 6,8 * PRF # C8: 4,8 => SOL * PRF # I9: 6,8 => SOL * DIS # H5: 6,8 => CTR => H5: 4 * PRF # H5: 4 => SOL * CNT 18 HDP CHAINS / 31 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E1: 8 => CTR => E1: 4,6 * PRF E1: 4,6 # C8: 4,8 => SOL * STA E1: 4,6 + C8: 4,8 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...5....1...3.2...89...........9.75.12.........3......6...7.4.......3.2.......... | initial |
| 23.5.9.717.13.259.895.173.24..291753129735...5738..2196129784359...5312.35.12.9.. | autosolve |
| 234569871761382594895417362486291753129735648573846219612978435948653127357124986 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) C1: 4,6 B2: 4,6 D3: 4,6 G1: 6,8 H3: 4,6 B4: 6,8 C4: 6,8 E6: 4,6 F6: 4,6 G5: 6,8 B8: 4,8 D8: 4,6 F9: 4,6 H9: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,B2: 4.. / C1 = 4 => 0 pairs (*) / B2 = 4 => 0 pairs (X) I2,H3: 4.. / I2 = 4 => 0 pairs (*) / H3 = 4 => 0 pairs (X) E6,F6: 4.. / E6 = 4 => 0 pairs (*) / F6 = 4 => 0 pairs (X) H5,I5: 4.. / H5 = 4 => 0 pairs (*) / I5 = 4 => 0 pairs (X) D8,F9: 4.. / D8 = 4 => 0 pairs (X) / F9 = 4 => 0 pairs (_) C1,E1: 4.. / C1 = 4 => 0 pairs (*) / E1 = 4 => 0 pairs (X) D3,H3: 4.. / D3 = 4 => 0 pairs (*) / H3 = 4 => 0 pairs (X) C9,F9: 4.. / C9 = 4 => 0 pairs (X) / F9 = 4 => 0 pairs (_) B2,B8: 4.. / B2 = 4 => 0 pairs (X) / B8 = 4 => 0 pairs (_) D3,D8: 4.. / D3 = 4 => 0 pairs (*) / D8 = 4 => 0 pairs (X) F6,F9: 4.. / F6 = 4 => 0 pairs (X) / F9 = 4 => 0 pairs (_) H3,H5: 4.. / H3 = 4 => 0 pairs (X) / H5 = 4 => 0 pairs (_) I2,I5: 4.. / I2 = 4 => 0 pairs (*) / I5 = 4 => 0 pairs (X) C1,B2: 6.. / C1 = 6 => 0 pairs (X) / B2 = 6 => 0 pairs (_) B4,C4: 6.. / B4 = 6 => 0 pairs (X) / C4 = 6 => 0 pairs (_) E6,F6: 6.. / E6 = 6 => 0 pairs (X) / F6 = 6 => 0 pairs (_) D8,F9: 6.. / D8 = 6 => 0 pairs (*) / F9 = 6 => 0 pairs (X) D3,H3: 6.. / D3 = 6 => 0 pairs (X) / H3 = 6 => 0 pairs (_) D8,I8: 6.. / D8 = 6 => 0 pairs (*) / I8 = 6 => 0 pairs (X) B2,B4: 6.. / B2 = 6 => 0 pairs (*) / B4 = 6 => 0 pairs (X) C1,C4: 6.. / C1 = 6 => 0 pairs (X) / C4 = 6 => 0 pairs (_) D3,D8: 6.. / D3 = 6 => 0 pairs (X) / D8 = 6 => 0 pairs (_) F6,F9: 6.. / F6 = 6 => 0 pairs (*) / F9 = 6 => 0 pairs (X) G1,G5: 6.. / G1 = 6 => 0 pairs (X) / G5 = 6 => 16 pairs (_) C8,C9: 7.. / C8 = 7 => 16 pairs (_) / C9 = 7 => 0 pairs (*) I8,I9: 7.. / I8 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) C8,I8: 7.. / C8 = 7 => 16 pairs (_) / I8 = 7 => 0 pairs (*) C9,I9: 7.. / C9 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) E1,E2: 8.. / E1 = 8 => 0 pairs (X) / E2 = 8 => 16 pairs (_) G1,I2: 8.. / G1 = 8 => 16 pairs (_) / I2 = 8 => 0 pairs (X) B4,C4: 8.. / B4 = 8 => 0 pairs (*) / C4 = 8 => 0 pairs (X) E1,G1: 8.. / E1 = 8 => 0 pairs (X) / G1 = 8 => 16 pairs (_) E2,I2: 8.. / E2 = 8 => 16 pairs (_) / I2 = 8 => 0 pairs (X) B4,B8: 8.. / B4 = 8 => 0 pairs (*) / B8 = 8 => 0 pairs (X) G1,G5: 8.. / G1 = 8 => 16 pairs (_) / G5 = 8 => 0 pairs (X) H5,H9: 8.. / H5 = 8 => 0 pairs (X) / H9 = 8 => 19 pairs (_) * DURATION: 0:00:58.727044 START: 11:06:22.480009 END: 11:07:21.207053 2017-05-04 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B4,B8,C1,C4,D3,D8,E6,F6,F9,G1,G5,H3,H9) * 23.5.9.717.13.259.895.173.24..291753129735...5738..2196129784359...5312.35.12.9.. * PAIR C1: 4,6 ROW 1 E1: 4,6,8 # reduction candidate for 4,6 E1: 8 => CTR * 2345896717613425988956173424862917531297358645738642196129784359...5312.35.12.9.. E1: 4,6 # 16 pairs * PAIR B2: 4,6 ROW 2 E2: 4,6,8 # reduction candidate for 4,6 E2: 4,6 => CTR * 23.58967176134259889561734248629175312973586457386421961297843594..5312.35.12.9.. E2: 8 # 16 pairs I2: 4,6,8 # reduction candidate for 4,6 I2: 4,6 # 16 pairs * PAIR D3: 4,6 BLK 2 E1: 4,6,8 # reduction candidate for 4,6 E1: 4,6 # 16 pairs E2: 4,6,8 # reduction candidate for 4,6 E2: 4,6 => CTR * 23.58967176134259889561734248629175312973586457386421961297843594..5312.35.12.9.. E2: 8 # 16 pairs * PAIR G1: 6,8 BLK 3 I2: 6,8,4 # reduction candidate for 6,8 I2: 6,8 => CTR * 2365498717.13.259.895.173424..291753129735..45738..2196129784359..453126354126987 I2: 4 => SOLVED * 234569871761382594895417362486291753129735648573846219612978435948653127357124986 * PAIR G1: 6,8 ROW 1 E1: 6,8,4 # reduction candidate for 6,8 E1: 6,8 => SOLVED * 234569871761382594895417362486291753129735648573846219612978435948653127357124986 E1: 4 => CTR * 23.5498717413825968956173.24..291753129735...5738..2196129784359...5312.35.12.9.. * PAIR H3: 4,6 BLK 3 I2: 4,6,8 # reduction candidate for 4,6 I2: 8 => CTR * 23.5.9.717.13.2598895.173424..2917531297358645738..2196129784359..453126354126987 I2: 4,6 # 16 pairs * PAIR H3: 4,6 COL H H5: 4,6,8 # reduction candidate for 4,6 H5: 8 => CTR * 23.5.9.717.13.259.895.173424..291753129735.845738..2196129784359..45312635.12.9.. H5: 4,6 # 19 pairs * PAIR E6: 4,6 COL E E1: 4,6,8 # reduction candidate for 4,6 E1: 4,6 # 16 pairs E2: 4,6,8 # reduction candidate for 4,6 E2: 4,6 => CTR * 23.58967176134259889561734248629175312973586457386421961297843594..5312.35.12.9.. E2: 8 # 16 pairs * PAIR G5: 6,8 BLK 6 H5: 6,8,4 # reduction candidate for 6,8 H5: 6,8 => CTR * 2365498717.13.259.895.173424..291753129735..45738..2196129784359..453126354126987 H5: 4 => SOLVED * 234569871761382594895417362486291753129735648573846219612978435948653127357124986 I5: 6,8,4 # reduction candidate for 6,8 I5: 6,8 => SOLVED * 234569871761382594895417362486291753129735648573846219612978435948653127357124986 I5: 4 => CTR * 2365498717.13.259.895.173424..291753129735..45738..2196129784359..453126354126987 * PAIR B8: 4,8 BLK 7 C8: 4,8,7 # reduction candidate for 4,8 C8: 4,8 => SOLVED * 234569871761382594895417362486291753129735648573846219612978435948653127357124986 C8: 7 # 16 pairs C9: 4,8,7 # reduction candidate for 4,8 C9: 4,8 # 16 pairs * PAIR H9: 6,8 BLK 9 I8: 6,8,7 # reduction candidate for 6,8 I8: 6,8 # 16 pairs I9: 6,8,7 # reduction candidate for 6,8 I9: 6,8 => SOLVED * 234569871761382594895417362486291753129735648573846219612978435948653127357124986 I9: 7 # 16 pairs * PAIR H9: 6,8 COL H H5: 6,8,4 # reduction candidate for 6,8 H5: 6,8 => CTR * 2365498717.13.259.895.173424..291753129735..45738..2196129784359..453126354126987 H5: 4 => SOLVED * 234569871761382594895417362486291753129735648573846219612978435948653127357124986 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-243-base-pr-000.dot * REASONING * DIS # E1: 8 => CTR => E1: 4,6 * DIS # E2: 4,6 => CTR => E2: 8 * DIS # E2: 4,6 => CTR => E2: 8 * DIS # I2: 6,8 => CTR => I2: 4 * PRF # I2: 4 => SOL * PRF # E1: 6,8 => SOL * DIS # E1: 4 => CTR => E1: 6,8 * DIS # I2: 8 => CTR => I2: 4,6 * DIS # H5: 8 => CTR => H5: 4,6 * DIS # E2: 4,6 => CTR => E2: 8 * DIS # H5: 6,8 => CTR => H5: 4 * PRF # H5: 4 => SOL * PRF # I5: 6,8 => SOL * DIS # I5: 4 => CTR => I5: 6,8 * PRF # C8: 4,8 => SOL * PRF # I9: 6,8 => SOL * DIS # H5: 6,8 => CTR => H5: 4 * PRF # H5: 4 => SOL * CNT 18 HDP CHAINS / 31 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B4,B8,C1,C4,D3,D8,E6,F6,F9,G1,G5,H3,H9) * 23.5.9.717.13.259.895.173.24..291753129735...5738..2196129784359...5312.35.12.9.. * PAIR C1: 4,6 ROW 1 E1: 4,6,8 # reduction candidate for 4,6 E1: 8 => CTR * 2345896717613425988956173424862917531297358645738642196129784359...5312.35.12.9.. * PAIR RESTART * PAIR B8: 4,8 BLK 7 C8: 4,8,7 # reduction candidate for 4,8 C8: 4,8 => SOLVED * 234569871761382594895417362486291753129735648573846219612978435948653127357124986 * DURATION: 0:00:04.298193 START: 11:07:53.044815 END: 11:07:57.343008 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-243-base-pr-001.dot * REASONING * DIS # E1: 8 => CTR => E1: 4,6 * PRF E1: 4,6 # C8: 4,8 => SOL * STA E1: 4,6 + C8: 4,8 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 243 solution: 234569871761382594895417362486291753129735648573846219612978435948653127357124986 info: 2069 FNWXY S8.f 44349 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 234569871761382594895417362486291753129735648573846219612978435948653127357124986 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:
* INC # E1: 4,6 => UNS * DIS # E1: 8 => CTR => E1: 4,6 * DIS # E2: 4,6 => CTR => E2: 8 * INC # E2: 8 => UNS * INC # I2: 4,6 => UNS * INC # E1: 4,6 => UNS * DIS # E2: 4,6 => CTR => E2: 8 * INC # E2: 8 => UNS * DIS # I2: 6,8 => CTR => I2: 4 * PRF # I2: 4 => SOL * PRF # E1: 6,8 => SOL * DIS # E1: 4 => CTR => E1: 6,8 * INC # I2: 4,6 => UNS * DIS # I2: 8 => CTR => I2: 4,6 * INC # H5: 4,6 => UNS * DIS # H5: 8 => CTR => H5: 4,6 * INC # E1: 4,6 => UNS * DIS # E2: 4,6 => CTR => E2: 8 * INC # E2: 8 => UNS * DIS # H5: 6,8 => CTR => H5: 4 * PRF # H5: 4 => SOL * PRF # I5: 6,8 => SOL * DIS # I5: 4 => CTR => I5: 6,8 * PRF # C8: 4,8 => SOL * INC # C8: 7 => UNS * INC # C9: 4,8 => UNS * INC # I8: 6,8 => UNS * PRF # I9: 6,8 => SOL * INC # I9: 7 => UNS * DIS # H5: 6,8 => CTR => H5: 4 * PRF # H5: 4 => SOL * CNT 31 HDP CHAINS / 31 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E1: 4,6 => UNS * DIS # E1: 8 => CTR => E1: 4,6 * PRF E1: 4,6 # C8: 4,8 => SOL * STA E1: 4,6 + C8: 4,8 * CNT 3 HDP CHAINS / 3 HYP OPENED