Analysis of xx-top500-226-base.sdk
Contents
Original Sudoku
level: medium
position: .8..7.1..5....4..3..........7....82...13........5.....6...8..7.3..2.............. initial
Autosolve
position: .8..731525128.47.373.152.8..73.1.8252513.8..786.527.31625.8137.3.72..5181.87352.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C1: 4,9 => SOL * DIS # C1: 6 => CTR => C1: 4,9 * DIS # C1: 6,9 => CTR => C1: 4 * PRF # C1: 4 => SOL * PRF # G3: 6,9 => SOL * DIS # G3: 4 => CTR => G3: 6,9 * DIS # I3: 6,9 => CTR => I3: 4 * PRF # I3: 4 => SOL * DIS # C1: 6,9 => CTR => C1: 4 * PRF # C1: 4 => SOL * PRF # D4: 6,9 => SOL * DIS # D4: 4 => CTR => D4: 6,9 * PRF # E8: 6,9 => SOL * DIS # E8: 4 => CTR => E8: 6,9 * PRF # G3: 6,9 => SOL * DIS # G3: 4 => CTR => G3: 6,9 * DIS # I3: 6,9 => CTR => I3: 4 * PRF # I3: 4 => SOL * PRF # H5: 6,9 => SOL * DIS # H5: 4 => CTR => H5: 6,9 * DIS # H9: 6,9 => CTR => H9: 4 * PRF # H9: 4 => SOL * PRF # D4: 4,9 => SOL * DIS # D4: 6 => CTR => D4: 4,9 * PRF # C1: 4,9 => SOL * DIS # C1: 6 => CTR => C1: 4,9 * PRF # D4: 6,9 => SOL * DIS # D4: 4 => CTR => D4: 6,9 * PRF # D4: 4,9 => SOL * DIS # D4: 6 => CTR => D4: 4,9 * DIS # G5: 4,9 => CTR => G5: 6 * DIS # E8: 4,9 => CTR => E8: 6 * PRF # E8: 6 => SOL * DIS # G5: 4,9 => CTR => G5: 6 * DIS # G3: 6 => CTR => G3: 4,9 * DIS # E8: 4,9 => CTR => E8: 6 * PRF # E8: 6 => SOL * DIS # I9: 4,9 => CTR => I9: 6 * DIS # E8: 4,9 => CTR => E8: 6 * PRF # E8: 6 => SOL * PRF # D4: 4,9 => SOL * DIS # D4: 6 => CTR => D4: 4,9 * PRF # E8: 6,9 => SOL * DIS # E8: 4 => CTR => E8: 6,9 * DIS # I9: 4,9 => CTR => I9: 6 * DIS # I3: 6 => CTR => I3: 4,9 * CNT 46 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:
* PRF # C1: 4,9 => SOL * STA C1: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .8..7.1..5....4..3..........7....82...13........5.....6...8..7.3..2.............. | initial |
| .8..731525128.47.373.152.8..73.1.8252513.8..786.527.31625.8137.3.72..5181.87352.. | autosolve |
| 984673152512894763736152984473916825251348697869527431625481379347269518198735246 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A1: 4,9 C3: 6,9 D1: 6,9 E2: 6,9 H2: 6,9 A4: 4,9 C6: 4,9 F4: 6,9 E5: 4,9 G6: 4,9 B8: 4,9 B9: 4,9 D7: 4,9 F8: 6,9 I7: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,C1: 4.. / A1 = 4 => 0 pairs (X) / C1 = 4 => 0 pairs (_) G3,I3: 4.. / G3 = 4 => 0 pairs (X) / I3 = 4 => 0 pairs (_) A4,C6: 4.. / A4 = 4 => 0 pairs (*) / C6 = 4 => 0 pairs (X) D4,E5: 4.. / D4 = 4 => 0 pairs (X) / E5 = 4 => 0 pairs (_) B8,B9: 4.. / B8 = 4 => 0 pairs (*) / B9 = 4 => 0 pairs (X) D7,E8: 4.. / D7 = 4 => 0 pairs (*) / E8 = 4 => 0 pairs (X) A4,D4: 4.. / A4 = 4 => 0 pairs (*) / D4 = 4 => 0 pairs (X) C6,G6: 4.. / C6 = 4 => 0 pairs (X) / G6 = 4 => 0 pairs (_) D7,I7: 4.. / D7 = 4 => 0 pairs (*) / I7 = 4 => 0 pairs (X) B8,E8: 4.. / B8 = 4 => 0 pairs (*) / E8 = 4 => 0 pairs (X) A1,A4: 4.. / A1 = 4 => 0 pairs (X) / A4 = 4 => 0 pairs (_) C1,C6: 4.. / C1 = 4 => 0 pairs (*) / C6 = 4 => 0 pairs (X) D4,D7: 4.. / D4 = 4 => 0 pairs (X) / D7 = 4 => 0 pairs (_) E5,E8: 4.. / E5 = 4 => 0 pairs (*) / E8 = 4 => 0 pairs (X) H5,H9: 4.. / H5 = 4 => 0 pairs (X) / H9 = 4 => 0 pairs (_) C1,C3: 6.. / C1 = 6 => 0 pairs (X) / C3 = 6 => 0 pairs (_) D1,E2: 6.. / D1 = 6 => 0 pairs (*) / E2 = 6 => 0 pairs (X) D4,F4: 6.. / D4 = 6 => 0 pairs (X) / F4 = 6 => 0 pairs (_) G5,H5: 6.. / G5 = 6 => 17 pairs (_) / H5 = 6 => 0 pairs (X) E8,F8: 6.. / E8 = 6 => 0 pairs (*) / F8 = 6 => 0 pairs (X) H9,I9: 6.. / H9 = 6 => 0 pairs (X) / I9 = 6 => 17 pairs (_) C1,D1: 6.. / C1 = 6 => 0 pairs (X) / D1 = 6 => 0 pairs (_) E2,H2: 6.. / E2 = 6 => 0 pairs (X) / H2 = 6 => 0 pairs (_) D1,D4: 6.. / D1 = 6 => 0 pairs (*) / D4 = 6 => 0 pairs (X) E2,E8: 6.. / E2 = 6 => 0 pairs (X) / E8 = 6 => 0 pairs (_) F4,F8: 6.. / F4 = 6 => 0 pairs (*) / F8 = 6 => 0 pairs (X) G3,G5: 6.. / G3 = 6 => 0 pairs (X) / G5 = 6 => 17 pairs (_) I3,I9: 6.. / I3 = 6 => 0 pairs (X) / I9 = 6 => 17 pairs (_) D1,E2: 9.. / D1 = 9 => 0 pairs (X) / E2 = 9 => 0 pairs (_) A4,C6: 9.. / A4 = 9 => 0 pairs (X) / C6 = 9 => 0 pairs (_) B8,B9: 9.. / B8 = 9 => 0 pairs (X) / B9 = 9 => 0 pairs (_) E2,H2: 9.. / E2 = 9 => 0 pairs (*) / H2 = 9 => 0 pairs (X) C6,G6: 9.. / C6 = 9 => 0 pairs (*) / G6 = 9 => 0 pairs (X) D7,I7: 9.. / D7 = 9 => 0 pairs (X) / I7 = 9 => 0 pairs (_) A1,A4: 9.. / A1 = 9 => 0 pairs (*) / A4 = 9 => 0 pairs (X) F4,F8: 9.. / F4 = 9 => 0 pairs (X) / F8 = 9 => 0 pairs (_) * DURATION: 0:00:59.004030 START: 10:34:32.902944 END: 10:35:31.906974 2017-05-04 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B8,B9,C3,C6,D1,D7,E2,E5,F4,F8,G6,H2,I7) * .8..731525128.47.373.152.8..73.1.8252513.8..786.527.31625.8137.3.72..5181.87352.. * PAIR A1: 4,9 BLK 1 C1: 4,9,6 # reduction candidate for 4,9 C1: 4,9 => SOLVED * 984673152512894763736152984473916825251348697869527431625481379347269518198735246 C1: 6 => CTR * 4869731525128.47.373.152.8..73.1.8252513.8..786.527.31625.8137.3.72..5181.87352.. * PAIR C3: 6,9 BLK 1 C1: 6,9,4 # reduction candidate for 6,9 C1: 6,9 => CTR * 48..731525128.47.373.152.8.973416825251398..786.527.31625.8137.3.72..5181.87352.. C1: 4 => SOLVED * 984673152512894763736152984473916825251348697869527431625481379347269518198735246 * PAIR C3: 6,9 ROW 3 G3: 6,9,4 # reduction candidate for 6,9 G3: 6,9 => SOLVED * 984673152512894763736152984473916825251348697869527431625481379347269518198735246 G3: 4 => CTR * .8..731525128.47.373.15248..73.1.8252513.8647864527931625.8137.3.72465181487352.. I3: 6,9,4 # reduction candidate for 6,9 I3: 6,9 => CTR * .8..731525128.47.373.15248..73.1.8252513.8647864527931625.8137.3.72465181487352.. I3: 4 => SOLVED * 984673152512894763736152984473916825251348697869527431625481379347269518198735246 * PAIR D1: 6,9 ROW 1 C1: 6,9,4 # reduction candidate for 6,9 C1: 6,9 => CTR * 48..731525128.47.373.152.8.973416825251398..786.527.31625.8137.3.72..5181.87352.. C1: 4 => SOLVED * 984673152512894763736152984473916825251348697869527431625481379347269518198735246 * PAIR D1: 6,9 COL D D4: 6,9,4 # reduction candidate for 6,9 D4: 6,9 => SOLVED * 984673152512894763736152984473916825251348697869527431625481379347269518198735246 D4: 4 => CTR * .8.673152512894763736152.8..7341.8252513.8..786.527.31625.8137.3.72..5181.87352.. * PAIR E2: 6,9 COL E E8: 6,9,4 # reduction candidate for 6,9 E8: 6,9 => SOLVED * 984673152512894763736152984473916825251348697869527431625481379347269518198735246 E8: 4 => CTR * .8..73152512864793739152.8.973.1.8252513.8..786.527.31625.8137.3.72..5181.87352.. * PAIR H2: 6,9 BLK 3 G3: 6,9,4 # reduction candidate for 6,9 G3: 6,9 => SOLVED * 984673152512894763736152984473916825251348697869527431625481379347269518198735246 G3: 4 => CTR * .8..731525128.47.373.15248..73.1.8252513.8647864527931625.8137.3.72465181487352.. I3: 6,9,4 # reduction candidate for 6,9 I3: 6,9 => CTR * .8..731525128.47.373.15248..73.1.8252513.8647864527931625.8137.3.72465181487352.. I3: 4 => SOLVED * 984673152512894763736152984473916825251348697869527431625481379347269518198735246 * PAIR H2: 6,9 COL H H5: 6,9,4 # reduction candidate for 6,9 H5: 6,9 => SOLVED * 984673152512894763736152984473916825251348697869527431625481379347269518198735246 H5: 4 => CTR * .8..731525128.47.373.152.8..73.1.8252513.8647864527931625.8137.3.72465181487352.. H9: 6,9,4 # reduction candidate for 6,9 H9: 6,9 => CTR * .8..731525128.47.373.152.8..73.1.8252513.8.47864527931625.8137.3.72465181487352.. H9: 4 => SOLVED * 984673152512894763736152984473916825251348697869527431625481379347269518198735246 * PAIR A4: 4,9 ROW 4 D4: 4,9,6 # reduction candidate for 4,9 D4: 4,9 => SOLVED * 984673152512894763736152984473916825251348697869527431625481379347269518198735246 D4: 6 => CTR * .8..731525128.47.373.152.8.473619825251348..7869527.31625.8137.3.72..5181.87352.. * PAIR C6: 4,9 COL C C1: 4,9,6 # reduction candidate for 4,9 C1: 4,9 => SOLVED * 984673152512894763736152984473916825251348697869527431625481379347269518198735246 C1: 6 => CTR * 4869731525128.47.373.152.8..73.1.8252513.8..786.527.31625.8137.3.72..5181.87352.. * PAIR F4: 6,9 BLK 5 D4: 6,9,4 # reduction candidate for 6,9 D4: 6,9 => SOLVED * 984673152512894763736152984473916825251348697869527431625481379347269518198735246 D4: 4 => CTR * .8.673152512894763736152.8..7341.8252513.8..786.527.31625.8137.3.72..5181.87352.. * PAIR E5: 4,9 BLK 5 D4: 4,9,6 # reduction candidate for 4,9 D4: 4,9 => SOLVED * 984673152512894763736152984473916825251348697869527431625481379347269518198735246 D4: 6 => CTR * .8..731525128.47.373.152.8.473619825251348..7869527.31625.8137.3.72..5181.87352.. * PAIR E5: 4,9 ROW 5 G5: 4,9,6 # reduction candidate for 4,9 G5: 4,9 => CTR * .86973152512864793739152684.73.1.8252513.8.6786.527.316254813793472..518198735246 G5: 6 # 17 pairs H5: 4,9,6 # reduction candidate for 4,9 H5: 4,9 # 17 pairs * PAIR E5: 4,9 COL E E8: 4,9,6 # reduction candidate for 4,9 E8: 4,9 => CTR * .8..73152512864793739152.8.973.1.8252513.8..786.527.31625.8137.3.72..5181.87352.. E8: 6 => SOLVED * 984673152512894763736152984473916825251348697869527431625481379347269518198735246 * PAIR G6: 4,9 BLK 6 G5: 4,9,6 # reduction candidate for 4,9 G5: 4,9 => CTR * .86973152512864793739152684.73.1.8252513.8.6786.527.316254813793472..518198735246 G5: 6 # 17 pairs H5: 4,9,6 # reduction candidate for 4,9 H5: 4,9 # 17 pairs * PAIR G6: 4,9 COL G G3: 4,9,6 # reduction candidate for 4,9 G3: 6 => CTR * .86973152512864793739152684.73.1.8252513.8.6786.527.316254813793472..518198735246 G3: 4,9 # 17 pairs * PAIR B8: 4,9 ROW 8 E8: 4,9,6 # reduction candidate for 4,9 E8: 4,9 => CTR * .8..73152512864793739152.8.973.1.8252513.8..786.527.31625.8137.3.72..5181.87352.. E8: 6 => SOLVED * 984673152512894763736152984473916825251348697869527431625481379347269518198735246 * PAIR B9: 4,9 ROW 9 H9: 4,9,6 # reduction candidate for 4,9 H9: 4,9 # 17 pairs I9: 4,9,6 # reduction candidate for 4,9 I9: 4,9 => CTR * .86973152512864793739152486973.1.8252513.86.786.527.31625.8137.3.72..5181.873526. I9: 6 # 17 pairs * PAIR D7: 4,9 BLK 8 E8: 4,9,6 # reduction candidate for 4,9 E8: 4,9 => CTR * .8..73152512864793739152.8.973.1.8252513.8..786.527.31625.8137.3.72..5181.87352.. E8: 6 => SOLVED * 984673152512894763736152984473916825251348697869527431625481379347269518198735246 * PAIR D7: 4,9 COL D D4: 4,9,6 # reduction candidate for 4,9 D4: 4,9 => SOLVED * 984673152512894763736152984473916825251348697869527431625481379347269518198735246 D4: 6 => CTR * .8..731525128.47.373.152.8.473619825251348..7869527.31625.8137.3.72..5181.87352.. * PAIR F8: 6,9 BLK 8 E8: 6,9,4 # reduction candidate for 6,9 E8: 6,9 => SOLVED * 984673152512894763736152984473916825251348697869527431625481379347269518198735246 E8: 4 => CTR * .8..73152512864793739152.8.973.1.8252513.8..786.527.31625.8137.3.72..5181.87352.. * PAIR I7: 4,9 BLK 9 H9: 4,9,6 # reduction candidate for 4,9 H9: 4,9 # 17 pairs I9: 4,9,6 # reduction candidate for 4,9 I9: 4,9 => CTR * .86973152512864793739152486973.1.8252513.86.786.527.31625.8137.3.72..5181.873526. I9: 6 # 17 pairs * PAIR I7: 4,9 COL I I3: 4,9,6 # reduction candidate for 4,9 I3: 6 => CTR * .8..731525128.47.373.152486.73.1.8252513.8647864527931625.8137.3.7246518148735269 I3: 4,9 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-226-base-pr-000.dot * REASONING * PRF # C1: 4,9 => SOL * DIS # C1: 6 => CTR => C1: 4,9 * DIS # C1: 6,9 => CTR => C1: 4 * PRF # C1: 4 => SOL * PRF # G3: 6,9 => SOL * DIS # G3: 4 => CTR => G3: 6,9 * DIS # I3: 6,9 => CTR => I3: 4 * PRF # I3: 4 => SOL * DIS # C1: 6,9 => CTR => C1: 4 * PRF # C1: 4 => SOL * PRF # D4: 6,9 => SOL * DIS # D4: 4 => CTR => D4: 6,9 * PRF # E8: 6,9 => SOL * DIS # E8: 4 => CTR => E8: 6,9 * PRF # G3: 6,9 => SOL * DIS # G3: 4 => CTR => G3: 6,9 * DIS # I3: 6,9 => CTR => I3: 4 * PRF # I3: 4 => SOL * PRF # H5: 6,9 => SOL * DIS # H5: 4 => CTR => H5: 6,9 * DIS # H9: 6,9 => CTR => H9: 4 * PRF # H9: 4 => SOL * PRF # D4: 4,9 => SOL * DIS # D4: 6 => CTR => D4: 4,9 * PRF # C1: 4,9 => SOL * DIS # C1: 6 => CTR => C1: 4,9 * PRF # D4: 6,9 => SOL * DIS # D4: 4 => CTR => D4: 6,9 * PRF # D4: 4,9 => SOL * DIS # D4: 6 => CTR => D4: 4,9 * DIS # G5: 4,9 => CTR => G5: 6 * DIS # E8: 4,9 => CTR => E8: 6 * PRF # E8: 6 => SOL * DIS # G5: 4,9 => CTR => G5: 6 * DIS # G3: 6 => CTR => G3: 4,9 * DIS # E8: 4,9 => CTR => E8: 6 * PRF # E8: 6 => SOL * DIS # I9: 4,9 => CTR => I9: 6 * DIS # E8: 4,9 => CTR => E8: 6 * PRF # E8: 6 => SOL * PRF # D4: 4,9 => SOL * DIS # D4: 6 => CTR => D4: 4,9 * PRF # E8: 6,9 => SOL * DIS # E8: 4 => CTR => E8: 6,9 * DIS # I9: 4,9 => CTR => I9: 6 * DIS # I3: 6 => CTR => I3: 4,9 * CNT 46 HDP CHAINS / 56 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B8,B9,C3,C6,D1,D7,E2,E5,F4,F8,G6,H2,I7) * .8..731525128.47.373.152.8..73.1.8252513.8..786.527.31625.8137.3.72..5181.87352.. * PAIR A1: 4,9 BLK 1 C1: 4,9,6 # reduction candidate for 4,9 C1: 4,9 => SOLVED * 984673152512894763736152984473916825251348697869527431625481379347269518198735246 * DURATION: 0:00:01.900833 START: 10:36:29.246038 END: 10:36:31.146871 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-226-base-pr-001.dot * REASONING * PRF # C1: 4,9 => SOL * STA C1: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 226 solution: 984673152512894763736152984473916825251348697869527431625481379347269518198735246 info: 2063 FNBWXY S8.f 23620 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 984673152512894763736152984473916825251348697869527431625481379347269518198735246 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 # C1: 4,9 => SOL * DIS # C1: 6 => CTR => C1: 4,9 * DIS # C1: 6,9 => CTR => C1: 4 * PRF # C1: 4 => SOL * PRF # G3: 6,9 => SOL * DIS # G3: 4 => CTR => G3: 6,9 * DIS # I3: 6,9 => CTR => I3: 4 * PRF # I3: 4 => SOL * DIS # C1: 6,9 => CTR => C1: 4 * PRF # C1: 4 => SOL * PRF # D4: 6,9 => SOL * DIS # D4: 4 => CTR => D4: 6,9 * PRF # E8: 6,9 => SOL * DIS # E8: 4 => CTR => E8: 6,9 * PRF # G3: 6,9 => SOL * DIS # G3: 4 => CTR => G3: 6,9 * DIS # I3: 6,9 => CTR => I3: 4 * PRF # I3: 4 => SOL * PRF # H5: 6,9 => SOL * DIS # H5: 4 => CTR => H5: 6,9 * DIS # H9: 6,9 => CTR => H9: 4 * PRF # H9: 4 => SOL * PRF # D4: 4,9 => SOL * DIS # D4: 6 => CTR => D4: 4,9 * PRF # C1: 4,9 => SOL * DIS # C1: 6 => CTR => C1: 4,9 * PRF # D4: 6,9 => SOL * DIS # D4: 4 => CTR => D4: 6,9 * PRF # D4: 4,9 => SOL * DIS # D4: 6 => CTR => D4: 4,9 * DIS # G5: 4,9 => CTR => G5: 6 * INC # G5: 6 => UNS * INC # H5: 4,9 => UNS * DIS # E8: 4,9 => CTR => E8: 6 * PRF # E8: 6 => SOL * DIS # G5: 4,9 => CTR => G5: 6 * INC # G5: 6 => UNS * INC # H5: 4,9 => UNS * INC # G3: 4,9 => UNS * DIS # G3: 6 => CTR => G3: 4,9 * DIS # E8: 4,9 => CTR => E8: 6 * PRF # E8: 6 => SOL * INC # H9: 4,9 => UNS * DIS # I9: 4,9 => CTR => I9: 6 * INC # I9: 6 => UNS * DIS # E8: 4,9 => CTR => E8: 6 * PRF # E8: 6 => SOL * PRF # D4: 4,9 => SOL * DIS # D4: 6 => CTR => D4: 4,9 * PRF # E8: 6,9 => SOL * DIS # E8: 4 => CTR => E8: 6,9 * INC # H9: 4,9 => UNS * DIS # I9: 4,9 => CTR => I9: 6 * INC # I9: 6 => UNS * INC # I3: 4,9 => UNS * DIS # I3: 6 => CTR => I3: 4,9 * CNT 56 HDP CHAINS / 56 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C1: 4,9 => SOL * STA C1: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED