Analysis of xx-top500-293-base.sdk
Contents
Original Sudoku
level: medium
position: 2..7......5.....3.......2......13.5.4.....6............13.....4..46.........29... initial
Autosolve
position: 23.7...4..5.142.3.14.3..2...62.1345.4..2..6.33...64..2613...924924631...5..4293.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 6,9 => CTR => C3: 7,8 * DIS # C3: 6,9 => CTR => C3: 7,8 * PRF # B6: 9 => SOL * DIS # I4: 9 => CTR => I4: 7,8 * DIS # B6: 7 => CTR => B6: 8,9 * DIS # I4: 7 => CTR => I4: 8,9 * PRF # B6: 9 => SOL * DIS # C3: 6,9 => CTR => C3: 7,8 * DIS # D6: 9 => CTR => D6: 5,8 * CNT 9 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 6,9 => CTR => C3: 7,8 * PRF C3: 7,8 # B6: 9 => SOL * STA C3: 7,8 + B6: 9 * CNT 2 HDP CHAINS / 11 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2..7......5.....3.......2......13.5.4.....6............13.....4..46.........29... | initial |
| 23.7...4..5.142.3.14.3..2...62.1345.4..2..6.33...64..2613...924924631...5..4293.. | autosolve |
| 239756841856142739147398265762913458481275693395864172613587924924631587578429316 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A2: 7,8 C2: 6,9 G2: 7,8 I2: 6,9 A4: 7,8 B5: 8,9 C5: 1,5 C6: 1,5 D4: 8,9 B9: 7,8 C9: 7,8 D7: 5,8 H8: 7,8 H9: 1,6 I9: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,I1: 1.. / G1 = 1 => 15 pairs (_) / I1 = 1 => 18 pairs (_) C5,C6: 1.. / C5 = 1 => 18 pairs (_) / C6 = 1 => 17 pairs (_) H9,I9: 1.. / H9 = 1 => 18 pairs (_) / I9 = 1 => 15 pairs (_) C5,H5: 1.. / C5 = 1 => 18 pairs (_) / H5 = 1 => 17 pairs (_) G1,G6: 1.. / G1 = 1 => 15 pairs (_) / G6 = 1 => 18 pairs (_) I1,I9: 1.. / I1 = 1 => 18 pairs (_) / I9 = 1 => 15 pairs (_) C5,C6: 5.. / C5 = 5 => 17 pairs (_) / C6 = 5 => 18 pairs (_) G8,I8: 5.. / G8 = 5 => 17 pairs (_) / I8 = 5 => 20 pairs (_) C6,D6: 5.. / C6 = 5 => 18 pairs (_) / D6 = 5 => 17 pairs (_) D6,D7: 5.. / D6 = 5 => 17 pairs (_) / D7 = 5 => 18 pairs (_) G1,G8: 5.. / G1 = 5 => 20 pairs (_) / G8 = 5 => 17 pairs (_) F1,F3: 6.. / F1 = 6 => 17 pairs (_) / F3 = 6 => 16 pairs (_) H9,I9: 6.. / H9 = 6 => 15 pairs (_) / I9 = 6 => 18 pairs (_) C2,I2: 6.. / C2 = 6 => 15 pairs (_) / I2 = 6 => 14 pairs (_) H3,H9: 6.. / H3 = 6 => 18 pairs (_) / H9 = 6 => 15 pairs (_) A2,C3: 7.. / A2 = 7 => 0 pairs (X) / C3 = 7 => 17 pairs (_) A4,B6: 7.. / A4 = 7 => 17 pairs (_) / B6 = 7 => 0 pairs (X) E5,F5: 7.. / E5 = 7 => 17 pairs (_) / F5 = 7 => 17 pairs (_) B9,C9: 7.. / B9 = 7 => 17 pairs (_) / C9 = 7 => 0 pairs (X) E7,F7: 7.. / E7 = 7 => 17 pairs (_) / F7 = 7 => 17 pairs (_) A2,G2: 7.. / A2 = 7 => 0 pairs (X) / G2 = 7 => 17 pairs (_) A4,I4: 7.. / A4 = 7 => 17 pairs (_) / I4 = 7 => 0 pairs (X) A2,A4: 7.. / A2 = 7 => 0 pairs (X) / A4 = 7 => 17 pairs (_) B6,B9: 7.. / B6 = 7 => 0 pairs (X) / B9 = 7 => 17 pairs (_) C3,C9: 7.. / C3 = 7 => 17 pairs (_) / C9 = 7 => 0 pairs (X) E5,E7: 7.. / E5 = 7 => 17 pairs (_) / E7 = 7 => 17 pairs (_) F5,F7: 7.. / F5 = 7 => 17 pairs (_) / F7 = 7 => 17 pairs (_) B9,C9: 8.. / B9 = 8 => 0 pairs (X) / C9 = 8 => 17 pairs (_) A2,G2: 8.. / A2 = 8 => 17 pairs (_) / G2 = 8 => 0 pairs (X) A2,A4: 8.. / A2 = 8 => 17 pairs (_) / A4 = 8 => 0 pairs (X) E1,E3: 9.. / E1 = 9 => 17 pairs (_) / E3 = 9 => 17 pairs (_) B5,B6: 9.. / B5 = 9 => 16 pairs (_) / B6 = 9 => 0 pairs (*) D4,D6: 9.. / D4 = 9 => 16 pairs (_) / D6 = 9 => 0 pairs (X) C2,I2: 9.. / C2 = 9 => 14 pairs (_) / I2 = 9 => 15 pairs (_) D4,I4: 9.. / D4 = 9 => 16 pairs (_) / I4 = 9 => 0 pairs (X) B5,H5: 9.. / B5 = 9 => 16 pairs (_) / H5 = 9 => 0 pairs (*) * DURATION: 0:01:09.884773 START: 12:58:16.807795 END: 12:59:26.692568 2017-05-04 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B5,B9,C2,C5,C6,C9,D4,D7,G2,H8,H9,I2,I9) * 23.7...4..5.142.3.14.3..2...62.1345.4..2..6.33...64..2613...924924631...5..4293.. * PAIR A2: 7,8 BLK 1 C3: 7,8,6,9 # reduction candidate for 7,8 C3: 6,9 => CTR * 23.7...4.75.14283.14.3..2..86291345749.2..6.337..64192613...92492463178.5..4293.. C3: 7,8 # 17 pairs * PAIR C2: 6,9 BLK 1 C1: 6,9,8 # reduction candidate for 6,9 C1: 6,9 # 17 pairs C3: 6,9,7,8 # reduction candidate for 6,9 C3: 6,9 => CTR * 23.7...4.75.14283.14.3..2..86291345749.2..6.337..64192613...92492463178.5..4293.. C3: 7,8 # 17 pairs * PAIR G2: 7,8 BLK 3 H3: 7,8,6,9 # reduction candidate for 7,8 H3: 7,8 # 19 pairs I3: 7,8,5,6,9 # reduction candidate for 7,8 I3: 7,8 # 21 pairs * PAIR G2: 7,8 COL G G6: 7,8,1 # reduction candidate for 7,8 G6: 7,8 # 15 pairs G8: 7,8,5 # reduction candidate for 7,8 G8: 7,8 # 20 pairs * PAIR I2: 6,9 BLK 3 I1: 6,9,1,5,8 # reduction candidate for 6,9 I1: 6,9 # 22 pairs H3: 6,9,7,8 # reduction candidate for 6,9 H3: 6,9 # 16 pairs I3: 6,9,5,7,8 # reduction candidate for 6,9 I3: 6,9 # 22 pairs * PAIR A4: 7,8 BLK 4 B6: 7,8,9 # reduction candidate for 7,8 B6: 9 => SOLVED * 239756841856142739147398265762913458481275693395864172613587924924631587578429316 B6: 7,8 # 16 pairs * PAIR A4: 7,8 ROW 4 I4: 7,8,9 # reduction candidate for 7,8 I4: 9 => CTR * 23.7...4.8591427361473.629.7628134594912..6833859641.26135..924924631.7.5784293.. I4: 7,8 # 16 pairs * PAIR B5: 8,9 BLK 4 B6: 8,9,7 # reduction candidate for 8,9 B6: 7 => CTR * 23.7...4.75.14283.14.3..2..86291345749.2..6.337..64192613...92492463178.5874293.. B6: 8,9 # 17 pairs * PAIR B5: 8,9 ROW 5 H5: 8,9,1 # reduction candidate for 8,9 H5: 8,9 # 18 pairs H5: 1 # 17 pairs * PAIR D4: 8,9 BLK 5 D6: 8,9,5 # reduction candidate for 8,9 D6: 8,9 # 18 pairs D6: 5 # 17 pairs * PAIR D4: 8,9 ROW 4 I4: 8,9,7 # reduction candidate for 8,9 I4: 7 => CTR * 23.7...4.75.14283.14.3..27.86291345749.2..68337..64.92613...924924631...5874293.. I4: 8,9 # 17 pairs * PAIR B9: 7,8 COL B B6: 7,8,9 # reduction candidate for 7,8 B6: 9 => SOLVED * 239756841856142739147398265762913458481275693395864172613587924924631587578429316 B6: 7,8 # 16 pairs * PAIR C9: 7,8 COL C C3: 7,8,6,9 # reduction candidate for 7,8 C3: 6,9 => CTR * 23.7...4.75.14283.14.3..2..86291345749.2..6.337..64192613...92492463178.5..4293.. C3: 7,8 # 17 pairs * PAIR D7: 5,8 BLK 8 E7: 5,8,7 # reduction candidate for 5,8 E7: 5,8 # 17 pairs F7: 5,8,7 # reduction candidate for 5,8 F7: 5,8 # 17 pairs * PAIR D7: 5,8 COL D D6: 5,8,9 # reduction candidate for 5,8 D6: 9 => CTR * 23.7...4.8591427361473.629.7628134594912..6833859641.26135..924924631.7.5784293.. D6: 5,8 # 16 pairs * PAIR H8: 7,8 BLK 9 G8: 7,8,5 # reduction candidate for 7,8 G8: 7,8 # 20 pairs I8: 7,8,5 # reduction candidate for 7,8 I8: 7,8 # 17 pairs * PAIR H8: 7,8 COL H H3: 7,8,6,9 # reduction candidate for 7,8 H3: 7,8 # 19 pairs H6: 7,8,1,9 # reduction candidate for 7,8 H6: 7,8 # 18 pairs * PAIR I9: 1,6 COL I I1: 1,6,5,8,9 # reduction candidate for 1,6 I1: 1,6 # 16 pairs I1: 5,8,9 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-293-base-pr-000.dot * REASONING * DIS # C3: 6,9 => CTR => C3: 7,8 * DIS # C3: 6,9 => CTR => C3: 7,8 * PRF # B6: 9 => SOL * DIS # I4: 9 => CTR => I4: 7,8 * DIS # B6: 7 => CTR => B6: 8,9 * DIS # I4: 7 => CTR => I4: 8,9 * PRF # B6: 9 => SOL * DIS # C3: 6,9 => CTR => C3: 7,8 * DIS # D6: 9 => CTR => D6: 5,8 * CNT 9 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B5,B9,C2,C5,C6,C9,D4,D7,G2,H8,H9,I2,I9) * 23.7...4..5.142.3.14.3..2...62.1345.4..2..6.33...64..2613...924924631...5..4293.. * PAIR A2: 7,8 BLK 1 C3: 7,8,6,9 # reduction candidate for 7,8 C3: 6,9 => CTR * 23.7...4.75.14283.14.3..2..86291345749.2..6.337..64192613...92492463178.5..4293.. * PAIR G2: 7,8 BLK 3 H3: 7,8,6,9 # reduction candidate for 7,8 H3: 7,8 # 23 pairs I3: 7,8,5,6,9 # reduction candidate for 7,8 I3: 7,8 # 25 pairs * PAIR G2: 7,8 COL G G6: 7,8,1 # reduction candidate for 7,8 G6: 7,8 # 17 pairs G8: 7,8,5 # reduction candidate for 7,8 G8: 7,8 # 14 pairs * PAIR I2: 6,9 BLK 3 I1: 6,9,1,5,8 # reduction candidate for 6,9 I1: 6,9 # 24 pairs H3: 6,9,7,8 # reduction candidate for 6,9 H3: 6,9 # 18 pairs I3: 6,9,5,7,8 # reduction candidate for 6,9 I3: 6,9 # 26 pairs * PAIR A4: 7,8 BLK 4 B6: 7,8,9 # reduction candidate for 7,8 B6: 9 => SOLVED * 239756841856142739147398265762913458481275693395864172613587924924631587578429316 * DURATION: 0:00:13.049552 START: 13:00:06.722108 END: 13:00:19.771660 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-293-base-pr-001.dot * REASONING * DIS # C3: 6,9 => CTR => C3: 7,8 * PRF C3: 7,8 # B6: 9 => SOL * STA C3: 7,8 + B6: 9 * CNT 2 HDP CHAINS / 11 HYP OPENED
Header Info
Top 500 Minimum 17 293 solution: 239756841856142739147398265762913458481275693395864172613587924924631587578429316 info: 2404 FNBTHWXY S8.f 48963 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 239756841856142739147398265762913458481275693395864172613587924924631587578429316 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 # C3: 7,8 => UNS * DIS # C3: 6,9 => CTR => C3: 7,8 * INC # C1: 6,9 => UNS * DIS # C3: 6,9 => CTR => C3: 7,8 * INC # C3: 7,8 => UNS * INC # H3: 7,8 => UNS * INC # I3: 7,8 => UNS * INC # G6: 7,8 => UNS * INC # G8: 7,8 => UNS * INC # I1: 6,9 => UNS * INC # H3: 6,9 => UNS * INC # I3: 6,9 => UNS * INC # B6: 7,8 => UNS * PRF # B6: 9 => SOL * INC # I4: 7,8 => UNS * DIS # I4: 9 => CTR => I4: 7,8 * INC # B6: 8,9 => UNS * DIS # B6: 7 => CTR => B6: 8,9 * INC # H5: 8,9 => UNS * INC # H5: 1 => UNS * INC # D6: 8,9 => UNS * INC # D6: 5 => UNS * INC # I4: 8,9 => UNS * DIS # I4: 7 => CTR => I4: 8,9 * INC # B6: 7,8 => UNS * PRF # B6: 9 => SOL * INC # C3: 7,8 => UNS * DIS # C3: 6,9 => CTR => C3: 7,8 * INC # E7: 5,8 => UNS * INC # F7: 5,8 => UNS * INC # D6: 5,8 => UNS * DIS # D6: 9 => CTR => D6: 5,8 * INC # G8: 7,8 => UNS * INC # I8: 7,8 => UNS * INC # H3: 7,8 => UNS * INC # H6: 7,8 => UNS * INC # I1: 1,6 => UNS * INC # I1: 5,8,9 => UNS * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C3: 7,8 => UNS * DIS # C3: 6,9 => CTR => C3: 7,8 * INC C3: 7,8 # H3: 7,8 => UNS * INC C3: 7,8 # I3: 7,8 => UNS * INC C3: 7,8 # G6: 7,8 => UNS * INC C3: 7,8 # G8: 7,8 => UNS * INC C3: 7,8 # I1: 6,9 => UNS * INC C3: 7,8 # H3: 6,9 => UNS * INC C3: 7,8 # I3: 6,9 => UNS * INC C3: 7,8 # B6: 7,8 => UNS * PRF C3: 7,8 # B6: 9 => SOL * STA C3: 7,8 + B6: 9 * CNT 11 HDP CHAINS / 11 HYP OPENED