Analysis of xx-top500-429-base.sdk
Contents
Original Sudoku
level: medium
position: ..3.....7...5...1..8..........8..3...6.4.....1........5...37.......2.6....2...8.. initial
Autosolve
position: ..32...877.658..13.8.37......78..3..86.4.37..13.7.2..85986371..3..9286756721..839 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 2 => CTR => A3: 4,9 * DIS # E1: 4,9 => CTR => E1: 1,6 * PRF # F1: 4,9 => SOL * PRF # B4: 5 => SOL * DIS # E1: 4,9 => CTR => E1: 1,6 * PRF # F1: 4,9 => SOL * DIS # G2: 2 => CTR => G2: 4,9 * DIS # H3: 4,6 => CTR => H3: 5,9 * PRF # B4: 5 => SOL * PRF # C6: 4 => SOL * CNT 10 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 2 => CTR => A3: 4,9 * DIS A3: 4,9 # E1: 4,9 => CTR => E1: 1,6 * PRF A3: 4,9 + E1: 1,6 # F1: 4,9 => SOL * STA A3: 4,9 + E1: 1,6 + F1: 4,9 * CNT 3 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..3.....7...5...1..8..........8..3...6.4.....1........5...37.......2.6....2...8.. | initial |
| ..32...877.658..13.8.37......78..3..86.4.37..13.7.2..85986371..3..9286756721..839 | autosolve |
| 913264587726589413485371296257896341869413752134752968598637124341928675672145839 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A1: 4,9 B1: 1,5 B2: 2,4 C3: 1,5 F2: 4,9 I3: 4,6 A4: 2,4 C5: 5,9 I5: 1,2 B8: 1,4 C8: 1,4 E9: 4,5 F9: 4,5 H7: 2,4 I7: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,C3: 1.. / B1 = 1 => 0 pairs (*) / C3 = 1 => 0 pairs (X) I4,I5: 1.. / I4 = 1 => 12 pairs (_) / I5 = 1 => 14 pairs (_) B8,C8: 1.. / B8 = 1 => 19 pairs (_) / C8 = 1 => 0 pairs (*) C3,F3: 1.. / C3 = 1 => 19 pairs (_) / F3 = 1 => 0 pairs (*) E5,I5: 1.. / E5 = 1 => 12 pairs (_) / I5 = 1 => 14 pairs (_) B1,B8: 1.. / B1 = 1 => 0 pairs (*) / B8 = 1 => 0 pairs (X) C3,C8: 1.. / C3 = 1 => 19 pairs (_) / C8 = 1 => 0 pairs (*) B2,A3: 2.. / B2 = 2 => 16 pairs (_) / A3 = 2 => 0 pairs (X) G2,G3: 2.. / G2 = 2 => 0 pairs (X) / G3 = 2 => 16 pairs (_) A4,B4: 2.. / A4 = 2 => 16 pairs (_) / B4 = 2 => 0 pairs (X) H5,I5: 2.. / H5 = 2 => 14 pairs (_) / I5 = 2 => 12 pairs (_) H7,I7: 2.. / H7 = 2 => 12 pairs (_) / I7 = 2 => 14 pairs (_) B2,G2: 2.. / B2 = 2 => 16 pairs (_) / G2 = 2 => 0 pairs (X) A3,G3: 2.. / A3 = 2 => 0 pairs (X) / G3 = 2 => 16 pairs (_) A3,A4: 2.. / A3 = 2 => 0 pairs (X) / A4 = 2 => 16 pairs (_) B2,B4: 2.. / B2 = 2 => 16 pairs (_) / B4 = 2 => 0 pairs (X) H5,H7: 2.. / H5 = 2 => 14 pairs (_) / H7 = 2 => 12 pairs (_) I5,I7: 2.. / I5 = 2 => 12 pairs (_) / I7 = 2 => 14 pairs (_) B8,C8: 4.. / B8 = 4 => 0 pairs (*) / C8 = 4 => 0 pairs (X) E9,F9: 4.. / E9 = 4 => 13 pairs (_) / F9 = 4 => 0 pairs (X) H7,I7: 4.. / H7 = 4 => 14 pairs (_) / I7 = 4 => 12 pairs (_) C6,C8: 4.. / C6 = 4 => 0 pairs (*) / C8 = 4 => 0 pairs (X) E1,E9: 4.. / E1 = 4 => 0 pairs (X) / E9 = 4 => 13 pairs (_) B1,C3: 5.. / B1 = 5 => 19 pairs (_) / C3 = 5 => 0 pairs (*) E9,F9: 5.. / E9 = 5 => 0 pairs (X) / F9 = 5 => 13 pairs (_) B1,G1: 5.. / B1 = 5 => 19 pairs (_) / G1 = 5 => 0 pairs (*) B1,B4: 5.. / B1 = 5 => 19 pairs (_) / B4 = 5 => 0 pairs (*) F4,F9: 5.. / F4 = 5 => 0 pairs (X) / F9 = 5 => 13 pairs (_) E1,F1: 6.. / E1 = 6 => 14 pairs (_) / F1 = 6 => 15 pairs (_) H3,I3: 6.. / H3 = 6 => 0 pairs (X) / I3 = 6 => 15 pairs (_) E6,H6: 6.. / E6 = 6 => 15 pairs (_) / H6 = 6 => 16 pairs (_) F1,F4: 6.. / F1 = 6 => 15 pairs (_) / F4 = 6 => 14 pairs (_) I3,I4: 6.. / I3 = 6 => 15 pairs (_) / I4 = 6 => 0 pairs (X) A1,A3: 9.. / A1 = 9 => 16 pairs (_) / A3 = 9 => 15 pairs (_) C5,C6: 9.. / C5 = 9 => 17 pairs (_) / C6 = 9 => 21 pairs (_) F2,G2: 9.. / F2 = 9 => 16 pairs (_) / G2 = 9 => 15 pairs (_) * DURATION: 0:01:09.539315 START: 17:26:25.440454 END: 17:27:34.979769 2017-05-04 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B1,B2,B8,C3,C5,C8,E9,F2,F9,H7,I3,I5,I7) * ..32...877.658..13.8.37......78..3..86.4.37..13.7.2..85986371..3..9286756721..839 * PAIR A1: 4,9 BLK 1 A3: 4,9,2 # reduction candidate for 4,9 A3: 2 => CTR * 953261487746589213281374..64278.63.186.4137.213.7.2.48598637124314928675672145839 A3: 4,9 # 16 pairs * PAIR A1: 4,9 ROW 1 E1: 4,9,1,6 # reduction candidate for 4,9 E1: 4,9 => CTR * .132.65877.658..13.85371....578.93..8694.37..1347.29.85986371..3419286756721.5839 E1: 1,6 # 15 pairs F1: 4,9,1,6 # reduction candidate for 4,9 F1: 4,9 => SOLVED * 913264587726589413485371296257896341869413752134752968598637124341928675672145839 F1: 1,6 # 16 pairs G1: 4,9,5 # reduction candidate for 4,9 G1: 4,9 # 19 pairs * PAIR B2: 2,4 BLK 1 A3: 2,4,9 # reduction candidate for 2,4 A3: 2,4 # 16 pairs A3: 9 # 15 pairs * PAIR B2: 2,4 ROW 2 G2: 2,4,9 # reduction candidate for 2,4 G2: 2,4 # 16 pairs G2: 9 # 15 pairs * PAIR B2: 2,4 COL B B4: 2,4,5 # reduction candidate for 2,4 B4: 5 => SOLVED * 913264587726589413485371296257896341869413752134752968598637124341928675672145839 B4: 2,4 # 19 pairs * PAIR F2: 4,9 BLK 2 E1: 4,9,1,6 # reduction candidate for 4,9 E1: 4,9 => CTR * .132.65877.658..13.85371....578.93..8694.37..1347.29.85986371..3419286756721.5839 E1: 1,6 # 15 pairs F1: 4,9,1,6 # reduction candidate for 4,9 F1: 4,9 => SOLVED * 913264587726589413485371296257896341869413752134752968598637124341928675672145839 F1: 1,6 # 16 pairs F3: 4,9,1 # reduction candidate for 4,9 F3: 4,9 # 19 pairs * PAIR F2: 4,9 ROW 2 G2: 4,9,2 # reduction candidate for 4,9 G2: 2 => CTR * 953261487746589213281374..64278.63.186.4137.213.7.2.48598637124314928675672145839 G2: 4,9 # 16 pairs * PAIR I3: 4,6 BLK 3 H3: 4,6,5,9 # reduction candidate for 4,6 H3: 4,6 => CTR * .532..9877.6589213.8137.5....78..3..86.4.37..13.7.24.85986371..3149286756721..839 H3: 5,9 # 17 pairs * PAIR I3: 4,6 COL I I4: 4,6,1 # reduction candidate for 4,6 I4: 4,6 # 14 pairs I4: 1 # 12 pairs * PAIR A4: 2,4 BLK 4 B4: 2,4,5 # reduction candidate for 2,4 B4: 5 => SOLVED * 913264587726589413485371296257896341869413752134752968598637124341928675672145839 B4: 2,4 # 19 pairs * PAIR A4: 2,4 COL A A3: 2,4,9 # reduction candidate for 2,4 A3: 2,4 # 16 pairs A3: 9 # 15 pairs * PAIR C5: 5,9 BLK 4 C6: 5,9,4 # reduction candidate for 5,9 C6: 4 => SOLVED * 913264587726589413485371296257896341869413752134752968598637124341928675672145839 C6: 5,9 # 19 pairs * PAIR C5: 5,9 ROW 5 E5: 5,9,1 # reduction candidate for 5,9 E5: 5,9 # 14 pairs H5: 5,9,2 # reduction candidate for 5,9 H5: 5,9 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-429-base-pr-000.dot * REASONING * DIS # A3: 2 => CTR => A3: 4,9 * DIS # E1: 4,9 => CTR => E1: 1,6 * PRF # F1: 4,9 => SOL * PRF # B4: 5 => SOL * DIS # E1: 4,9 => CTR => E1: 1,6 * PRF # F1: 4,9 => SOL * DIS # G2: 2 => CTR => G2: 4,9 * DIS # H3: 4,6 => CTR => H3: 5,9 * PRF # B4: 5 => SOL * PRF # C6: 4 => SOL * CNT 10 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B1,B2,B8,C3,C5,C8,E9,F2,F9,H7,I3,I5,I7) * ..32...877.658..13.8.37......78..3..86.4.37..13.7.2..85986371..3..9286756721..839 * PAIR A1: 4,9 BLK 1 A3: 4,9,2 # reduction candidate for 4,9 A3: 2 => CTR * 953261487746589213281374..64278.63.186.4137.213.7.2.48598637124314928675672145839 * PAIR A1: 4,9 ROW 1 E1: 4,9,1,6 # reduction candidate for 4,9 E1: 4,9 => CTR * .132.658772658..13.853712..2578.93..8694.37..1347.29.85986371..3.19286756721..839 F1: 4,9,1,6 # reduction candidate for 4,9 F1: 4,9 => SOLVED * 913264587726589413485371296257896341869413752134752968598637124341928675672145839 * DURATION: 0:00:05.798031 START: 17:28:10.628032 END: 17:28:16.426063 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-429-base-pr-001.dot * REASONING * DIS # A3: 2 => CTR => A3: 4,9 * DIS A3: 4,9 # E1: 4,9 => CTR => E1: 1,6 * PRF A3: 4,9 + E1: 1,6 # F1: 4,9 => SOL * STA A3: 4,9 + E1: 1,6 + F1: 4,9 * CNT 3 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 429 solution: 913264587726589413485371296257896341869413752134752968598637124341928675672145839 info: 95185 FNBHWXYK S8.f 39923 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 913264587726589413485371296257896341869413752134752968598637124341928675672145839 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 # A3: 4,9 => UNS * DIS # A3: 2 => CTR => A3: 4,9 * DIS # E1: 4,9 => CTR => E1: 1,6 * INC # E1: 1,6 => UNS * PRF # F1: 4,9 => SOL * INC # F1: 1,6 => UNS * INC # G1: 4,9 => UNS * INC # A3: 2,4 => UNS * INC # A3: 9 => UNS * INC # G2: 2,4 => UNS * INC # G2: 9 => UNS * INC # B4: 2,4 => UNS * PRF # B4: 5 => SOL * DIS # E1: 4,9 => CTR => E1: 1,6 * INC # E1: 1,6 => UNS * PRF # F1: 4,9 => SOL * INC # F1: 1,6 => UNS * INC # F3: 4,9 => UNS * INC # G2: 4,9 => UNS * DIS # G2: 2 => CTR => G2: 4,9 * DIS # H3: 4,6 => CTR => H3: 5,9 * INC # H3: 5,9 => UNS * INC # I4: 4,6 => UNS * INC # I4: 1 => UNS * INC # B4: 2,4 => UNS * PRF # B4: 5 => SOL * INC # A3: 2,4 => UNS * INC # A3: 9 => UNS * INC # C6: 5,9 => UNS * PRF # C6: 4 => SOL * INC # E5: 5,9 => UNS * INC # H5: 5,9 => UNS * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 4,9 => UNS * DIS # A3: 2 => CTR => A3: 4,9 * DIS A3: 4,9 # E1: 4,9 => CTR => E1: 1,6 * PRF A3: 4,9 + E1: 1,6 # F1: 4,9 => SOL * STA A3: 4,9 + E1: 1,6 + F1: 4,9 * CNT 4 HDP CHAINS / 4 HYP OPENED