Analysis of xx-top500-050-base.sdk
Contents
Original Sudoku
level: medium
position: .784...........1.....6.....1.....34....7....52.........6.....843...1.........2... initial
Autosolve
position: 6784.1.2.4..2..1...126..4..1.7...3428..72..152..1..8...613..28432.81.7..78...2.31 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E1: 3 => CTR => E1: 5,9 * DIS # I3: 3,9 => CTR => I3: 7,8 * DIS # E1: 5 => CTR => E1: 3,9 * PRF # E6: 5,9 => SOL * DIS # C5: 3 => CTR => C5: 6,9 * DIS # G9: 5 => CTR => G9: 6,9 * DIS # H8: 6,9 => CTR => H8: 5 * CNT 7 HDP CHAINS / 41 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E1: 3 => CTR => E1: 5,9 * PRF E1: 5,9 # E6: 5,9 => SOL * STA E1: 5,9 + E6: 5,9 * CNT 2 HDP CHAINS / 20 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .784...........1.....6.....1.....34....7....52.........6.....843...1.........2... | initial |
| 6784.1.2.4..2..1...126..4..1.7...3428..72..152..1..8...613..28432.81.7..78...2.31 | autosolve |
| 678491523435287196912635478157968342846723915293154867561379284324816759789542631 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A3: 5,9 G1: 5,9 I1: 3,9 B4: 5,9 D4: 5,9 E4: 6,8 F4: 6,8 G5: 6,9 A7: 5,9 F8: 4,6 D9: 5,9 E9: 4,6 I8: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,C2: 3.. / B2 = 3 => 17 pairs (_) / C2 = 3 => 18 pairs (_) I1,I3: 3.. / I1 = 3 => 13 pairs (_) / I3 = 3 => 0 pairs (X) E1,I1: 3.. / E1 = 3 => 0 pairs (X) / I1 = 3 => 13 pairs (_) B5,B6: 4.. / B5 = 4 => 14 pairs (_) / B6 = 4 => 15 pairs (_) C8,C9: 4.. / C8 = 4 => 15 pairs (_) / C9 = 4 => 17 pairs (_) F8,E9: 4.. / F8 = 4 => 17 pairs (_) / E9 = 4 => 15 pairs (_) B5,F5: 4.. / B5 = 4 => 14 pairs (_) / F5 = 4 => 15 pairs (_) C8,F8: 4.. / C8 = 4 => 15 pairs (_) / F8 = 4 => 17 pairs (_) C9,E9: 4.. / C9 = 4 => 17 pairs (_) / E9 = 4 => 15 pairs (_) E6,E9: 4.. / E6 = 4 => 17 pairs (_) / E9 = 4 => 15 pairs (_) H8,G9: 5.. / H8 = 5 => 16 pairs (_) / G9 = 5 => 0 pairs (X) E1,G1: 5.. / E1 = 5 => 0 pairs (X) / G1 = 5 => 16 pairs (_) B4,D4: 5.. / B4 = 5 => 22 pairs (_) / D4 = 5 => 17 pairs (_) C8,H8: 5.. / C8 = 5 => 0 pairs (X) / H8 = 5 => 16 pairs (_) A3,A7: 5.. / A3 = 5 => 17 pairs (_) / A7 = 5 => 22 pairs (_) D4,D9: 5.. / D4 = 5 => 17 pairs (_) / D9 = 5 => 22 pairs (_) G1,G9: 5.. / G1 = 5 => 16 pairs (_) / G9 = 5 => 0 pairs (X) H2,I2: 6.. / H2 = 6 => 15 pairs (_) / I2 = 6 => 16 pairs (_) C5,C6: 6.. / C5 = 6 => 15 pairs (_) / C6 = 6 => 17 pairs (_) E4,F4: 6.. / E4 = 6 => 15 pairs (_) / F4 = 6 => 17 pairs (_) F8,E9: 6.. / F8 = 6 => 15 pairs (_) / E9 = 6 => 17 pairs (_) C5,G5: 6.. / C5 = 6 => 15 pairs (_) / G5 = 6 => 17 pairs (_) E9,G9: 6.. / E9 = 6 => 17 pairs (_) / G9 = 6 => 15 pairs (_) E4,E9: 6.. / E4 = 6 => 15 pairs (_) / E9 = 6 => 17 pairs (_) F4,F8: 6.. / F4 = 6 => 17 pairs (_) / F8 = 6 => 15 pairs (_) G5,G9: 6.. / G5 = 6 => 17 pairs (_) / G9 = 6 => 15 pairs (_) H6,I6: 7.. / H6 = 7 => 18 pairs (_) / I6 = 7 => 14 pairs (_) E7,F7: 7.. / E7 = 7 => 14 pairs (_) / F7 = 7 => 14 pairs (_) I2,I3: 8.. / I2 = 8 => 15 pairs (_) / I3 = 8 => 13 pairs (_) E4,F4: 8.. / E4 = 8 => 17 pairs (_) / F4 = 8 => 15 pairs (_) B4,D4: 9.. / B4 = 9 => 17 pairs (_) / D4 = 9 => 22 pairs (_) A3,A7: 9.. / A3 = 9 => 22 pairs (_) / A7 = 9 => 17 pairs (_) D4,D9: 9.. / D4 = 9 => 22 pairs (_) / D9 = 9 => 17 pairs (_) * DURATION: 0:01:05.786062 START: 04:22:03.889868 END: 04:23:09.675930 2017-05-04 * CP COUNT: (33) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A7,B4,D4,D9,E4,E9,F4,F8,G1,G5,I1,I8) * 6784.1.2.4..2..1...126..4..1.7...3428..72..152..1..8...613..28432.81.7..78...2.31 * PAIR A3: 5,9 BLK 1 B2: 5,9,3 # reduction candidate for 5,9 B2: 5,9 # 18 pairs C2: 5,9,3 # reduction candidate for 5,9 C2: 5,9 # 17 pairs * PAIR A3: 5,9 ROW 3 E3: 5,9,3,7,8 # reduction candidate for 5,9 E3: 5,9 # 17 pairs F3: 5,9,3,7,8 # reduction candidate for 5,9 F3: 5,9 # 17 pairs H3: 5,9,7 # reduction candidate for 5,9 H3: 5,9 # 16 pairs * PAIR G1: 5,9 BLK 3 H2: 5,9,6,7 # reduction candidate for 5,9 H2: 5,9 # 19 pairs H3: 5,9,7 # reduction candidate for 5,9 H3: 5,9 # 16 pairs * PAIR G1: 5,9 ROW 1 E1: 5,9,3 # reduction candidate for 5,9 E1: 3 => CTR * 6784315294..2..168.126..4731.79863428..72.6152.6145897.613..284329814756784562931 E1: 5,9 # 13 pairs * PAIR G1: 5,9 COL G G9: 5,9,6 # reduction candidate for 5,9 G9: 5,9 # 17 pairs G9: 6 # 15 pairs * PAIR I1: 3,9 BLK 3 I3: 3,9,7,8 # reduction candidate for 3,9 I3: 3,9 => CTR * 6784.152.4.52..1689126584731579863428..72.6152.614.897.613..284329814756784562931 I3: 7,8 # 14 pairs * PAIR I1: 3,9 ROW 1 E1: 3,9,5 # reduction candidate for 3,9 E1: 5 => CTR * 6784519234..2..1565126394..1.75863428..72.6152561438...613.52843258147..784962531 E1: 3,9 # 16 pairs * PAIR B4: 5,9 BLK 4 B6: 5,9,3,4 # reduction candidate for 5,9 B6: 5,9 # 18 pairs C6: 5,9,3,6 # reduction candidate for 5,9 C6: 5,9 # 18 pairs * PAIR B4: 5,9 COL B B2: 5,9,3 # reduction candidate for 5,9 B2: 5,9 # 18 pairs B2: 3 # 17 pairs * PAIR D4: 5,9 BLK 5 E6: 5,9,3,4 # reduction candidate for 5,9 E6: 5,9 => SOLVED * 678491523435287196912635478157968342846723915293154867561379284324816759789542631 E6: 3,4 # 14 pairs F6: 5,9,3,4 # reduction candidate for 5,9 F6: 5,9 # 16 pairs * PAIR G5: 6,9 BLK 6 H6: 6,9,7 # reduction candidate for 6,9 H6: 6,9 # 14 pairs I6: 6,9,7 # reduction candidate for 6,9 I6: 6,9 # 18 pairs * PAIR G5: 6,9 ROW 5 C5: 6,9,3 # reduction candidate for 6,9 C5: 3 => CTR * 67845192343.2..1...1263.4..1975863428437296152561438..9613752843258147..784962531 C5: 6,9 # 16 pairs * PAIR G5: 6,9 COL G G9: 6,9,5 # reduction candidate for 6,9 G9: 5 => CTR * 6784519234..2..1565126394..1.75863428..72.6152561438...613.52843258147..784962531 G9: 6,9 # 16 pairs * PAIR A7: 5,9 BLK 7 C8: 5,9,4 # reduction candidate for 5,9 C8: 5,9 # 17 pairs C9: 5,9,4 # reduction candidate for 5,9 C9: 5,9 # 15 pairs * PAIR A7: 5,9 ROW 7 E7: 5,9,7 # reduction candidate for 5,9 E7: 5,9 # 14 pairs F7: 5,9,7 # reduction candidate for 5,9 F7: 5,9 # 14 pairs * PAIR D9: 5,9 BLK 8 E7: 5,9,7 # reduction candidate for 5,9 E7: 5,9 # 14 pairs F7: 5,9,7 # reduction candidate for 5,9 F7: 5,9 # 14 pairs * PAIR D9: 5,9 ROW 9 C9: 5,9,4 # reduction candidate for 5,9 C9: 5,9 # 15 pairs G9: 5,9,6 # reduction candidate for 5,9 G9: 5,9 # 17 pairs * PAIR I8: 6,9 BLK 9 H8: 6,9,5 # reduction candidate for 6,9 H8: 6,9 => CTR * 6784519234..2..1..5126..4781.758634284.72.6152561438979613752843258147..784.62531 H8: 5 # 16 pairs G9: 6,9,5 # reduction candidate for 6,9 G9: 6,9 # 16 pairs * PAIR I8: 6,9 COL I I2: 6,9,7,8 # reduction candidate for 6,9 I2: 6,9 # 15 pairs I6: 6,9,7 # reduction candidate for 6,9 I6: 6,9 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-050-base-pr-000.dot * REASONING * DIS # E1: 3 => CTR => E1: 5,9 * DIS # I3: 3,9 => CTR => I3: 7,8 * DIS # E1: 5 => CTR => E1: 3,9 * PRF # E6: 5,9 => SOL * DIS # C5: 3 => CTR => C5: 6,9 * DIS # G9: 5 => CTR => G9: 6,9 * DIS # H8: 6,9 => CTR => H8: 5 * CNT 7 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A7,B4,D4,D9,E4,E9,F4,F8,G1,G5,I1,I8) * 6784.1.2.4..2..1...126..4..1.7...3428..72..152..1..8...613..28432.81.7..78...2.31 * PAIR A3: 5,9 BLK 1 B2: 5,9,3 # reduction candidate for 5,9 B2: 5,9 # 18 pairs C2: 5,9,3 # reduction candidate for 5,9 C2: 5,9 # 17 pairs * PAIR A3: 5,9 ROW 3 E3: 5,9,3,7,8 # reduction candidate for 5,9 E3: 5,9 # 17 pairs F3: 5,9,3,7,8 # reduction candidate for 5,9 F3: 5,9 # 17 pairs H3: 5,9,7 # reduction candidate for 5,9 H3: 5,9 # 16 pairs * PAIR G1: 5,9 BLK 3 H2: 5,9,6,7 # reduction candidate for 5,9 H2: 5,9 # 19 pairs H3: 5,9,7 # reduction candidate for 5,9 H3: 5,9 # 16 pairs * PAIR G1: 5,9 ROW 1 E1: 5,9,3 # reduction candidate for 5,9 E1: 3 => CTR * 6784315294..2..168.126..4731.79863428..72.6152.6145897.613..284329814756784562931 * PAIR G1: 5,9 COL G G9: 5,9,6 # reduction candidate for 5,9 G9: 5,9 # 17 pairs G9: 6 # 15 pairs * PAIR RESTART * PAIR G1: 5,9 BLK 3 H2: 5,9,6,7 # reduction candidate for 5,9 H2: 5,9 # 19 pairs H3: 5,9,7 # reduction candidate for 5,9 H3: 5,9 # 16 pairs * PAIR G1: 5,9 COL G G9: 5,9,6 # reduction candidate for 5,9 G9: 5,9 # 17 pairs G9: 6 # 15 pairs * PAIR B4: 5,9 BLK 4 B6: 5,9,3,4 # reduction candidate for 5,9 B6: 5,9 # 18 pairs C6: 5,9,3,6 # reduction candidate for 5,9 C6: 5,9 # 18 pairs * PAIR B4: 5,9 COL B B2: 5,9,3 # reduction candidate for 5,9 B2: 5,9 # 18 pairs B2: 3 # 17 pairs * PAIR D4: 5,9 BLK 5 E6: 5,9,3,4 # reduction candidate for 5,9 E6: 5,9 => SOLVED * 678491523435287196912635478157968342846723915293154867561379284324816759789542631 * DURATION: 0:00:21.618535 START: 04:23:52.106618 END: 04:24:13.725153 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-050-base-pr-001.dot * REASONING * DIS # E1: 3 => CTR => E1: 5,9 * PRF E1: 5,9 # E6: 5,9 => SOL * STA E1: 5,9 + E6: 5,9 * CNT 2 HDP CHAINS / 20 HYP OPENED
Header Info
Top 500 Minimum 17 050 solution: 678491523435287196912635478157968342846723915293154867561379284324816759789542631 info: 1386 FNBTHXY S8.f 23211 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 678491523435287196912635478157968342846723915293154867561379284324816759789542631 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 # B2: 5,9 => UNS * INC # C2: 5,9 => UNS * INC # E3: 5,9 => UNS * INC # F3: 5,9 => UNS * INC # H3: 5,9 => UNS * INC # H2: 5,9 => UNS * INC # H3: 5,9 => UNS * INC # E1: 5,9 => UNS * DIS # E1: 3 => CTR => E1: 5,9 * INC # G9: 5,9 => UNS * INC # G9: 6 => UNS * DIS # I3: 3,9 => CTR => I3: 7,8 * INC # I3: 7,8 => UNS * INC # E1: 3,9 => UNS * DIS # E1: 5 => CTR => E1: 3,9 * INC # B6: 5,9 => UNS * INC # C6: 5,9 => UNS * INC # B2: 5,9 => UNS * INC # B2: 3 => UNS * PRF # E6: 5,9 => SOL * INC # E6: 3,4 => UNS * INC # F6: 5,9 => UNS * INC # H6: 6,9 => UNS * INC # I6: 6,9 => UNS * INC # C5: 6,9 => UNS * DIS # C5: 3 => CTR => C5: 6,9 * INC # G9: 6,9 => UNS * DIS # G9: 5 => CTR => G9: 6,9 * INC # C8: 5,9 => UNS * INC # C9: 5,9 => UNS * INC # E7: 5,9 => UNS * INC # F7: 5,9 => UNS * INC # E7: 5,9 => UNS * INC # F7: 5,9 => UNS * INC # C9: 5,9 => UNS * INC # G9: 5,9 => UNS * DIS # H8: 6,9 => CTR => H8: 5 * INC # H8: 5 => UNS * INC # G9: 6,9 => UNS * INC # I2: 6,9 => UNS * INC # I6: 6,9 => UNS * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 5,9 => UNS * INC # C2: 5,9 => UNS * INC # E3: 5,9 => UNS * INC # F3: 5,9 => UNS * INC # H3: 5,9 => UNS * INC # H2: 5,9 => UNS * INC # H3: 5,9 => UNS * INC # E1: 5,9 => UNS * DIS # E1: 3 => CTR => E1: 5,9 * INC E1: 5,9 # G9: 5,9 => UNS * INC E1: 5,9 # G9: 6 => UNS * INC E1: 5,9 # H2: 5,9 => UNS * INC E1: 5,9 # H3: 5,9 => UNS * INC E1: 5,9 # G9: 5,9 => UNS * INC E1: 5,9 # G9: 6 => UNS * INC E1: 5,9 # B6: 5,9 => UNS * INC E1: 5,9 # C6: 5,9 => UNS * INC E1: 5,9 # B2: 5,9 => UNS * INC E1: 5,9 # B2: 3 => UNS * PRF E1: 5,9 # E6: 5,9 => SOL * STA E1: 5,9 + E6: 5,9 * CNT 20 HDP CHAINS / 20 HYP OPENED