Analysis of xx-top500-065-base.sdk
Contents
Original Sudoku
level: medium
position: ....7..421..6............7.52.1.....3.....5......8.......3..6...74........8...... initial
Autosolve
position: 863.7..421976.....452....7652.1.....38....5..74..8.....153..6...74.......38...... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F7: 2,4 => CTR => F7: 7,8,9 * PRF # F5: 4,7 => SOL * PRF # I5: 1,9 => SOL * PRF # I4: 4,7 => SOL * DIS # G8: 8 => CTR => G8: 2,3 * DIS # F7: 2,9 => CTR => F7: 4,7,8 * PRF # H7: 2,9 => SOL * PRF # F7: 2,8,9 => SOL * PRF # F7: 2,8,9 => SOL * PRF # I4: 4,7 => SOL * CNT 10 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:
* DIS # F7: 2,4 => CTR => F7: 7,8,9 * PRF F7: 7,8,9 # F5: 4,7 => SOL * STA F7: 7,8,9 + F5: 4,7 * CNT 2 HDP CHAINS / 31 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....7..421..6............7.52.1.....3.....5......8.......3..6...74........8...... | initial |
| 863.7..421976.....452....7652.1.....38....5..74..8.....153..6...74.......38...... | autosolve |
| 863579142197624853452813976529136784386497521741285369215348697674951238938762415 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) D1: 5,9 E2: 2,4 F2: 2,4 D3: 8,9 G1: 1,9 G2: 3,8 G3: 1,9 C4: 6,9 D5: 4,7 G4: 4,7 G6: 2,3 A7: 2,9 D9: 4,7 I7: 4,7 G9: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,G3: 1.. / G1 = 1 => 16 pairs (_) / G3 = 1 => 16 pairs (_) C5,C6: 1.. / C5 = 1 => 16 pairs (_) / C6 = 1 => 17 pairs (_) F1,G1: 1.. / F1 = 1 => 16 pairs (_) / G1 = 1 => 16 pairs (_) E2,F2: 2.. / E2 = 2 => 14 pairs (_) / F2 = 2 => 20 pairs (_) D6,D8: 2.. / D6 = 2 => 19 pairs (_) / D8 = 2 => 17 pairs (_) G6,G8: 2.. / G6 = 2 => 17 pairs (_) / G8 = 2 => 19 pairs (_) E3,F3: 3.. / E3 = 3 => 17 pairs (_) / F3 = 3 => 16 pairs (_) E3,E4: 3.. / E3 = 3 => 17 pairs (_) / E4 = 3 => 16 pairs (_) E2,F2: 4.. / E2 = 4 => 20 pairs (_) / F2 = 4 => 14 pairs (_) I7,G9: 4.. / I7 = 4 => 0 pairs (X) / G9 = 4 => 0 pairs (_) D9,G9: 4.. / D9 = 4 => 0 pairs (X) / G9 = 4 => 0 pairs (_) D5,D9: 4.. / D5 = 4 => 0 pairs (*) / D9 = 4 => 0 pairs (X) G4,G9: 4.. / G4 = 4 => 0 pairs (X) / G9 = 4 => 0 pairs (_) D1,F1: 5.. / D1 = 5 => 16 pairs (_) / F1 = 5 => 15 pairs (_) H2,I2: 5.. / H2 = 5 => 16 pairs (_) / I2 = 5 => 17 pairs (_) D6,F6: 5.. / D6 = 5 => 15 pairs (_) / F6 = 5 => 16 pairs (_) E8,E9: 5.. / E8 = 5 => 15 pairs (_) / E9 = 5 => 16 pairs (_) D1,D6: 5.. / D1 = 5 => 16 pairs (_) / D6 = 5 => 15 pairs (_) F1,F6: 5.. / F1 = 5 => 15 pairs (_) / F6 = 5 => 16 pairs (_) A8,A9: 6.. / A8 = 6 => 16 pairs (_) / A9 = 6 => 16 pairs (_) F7,D9: 7.. / F7 = 7 => 0 pairs (X) / D9 = 7 => 0 pairs (_) I7,G9: 7.. / I7 = 7 => 0 pairs (*) / G9 = 7 => 0 pairs (X) F7,I7: 7.. / F7 = 7 => 0 pairs (X) / I7 = 7 => 0 pairs (_) D9,G9: 7.. / D9 = 7 => 0 pairs (*) / G9 = 7 => 0 pairs (X) D5,D9: 7.. / D5 = 7 => 0 pairs (X) / D9 = 7 => 0 pairs (_) G4,G9: 7.. / G4 = 7 => 0 pairs (*) / G9 = 7 => 0 pairs (X) D3,F3: 8.. / D3 = 8 => 15 pairs (_) / F3 = 8 => 0 pairs (X) H4,I4: 8.. / H4 = 8 => 0 pairs (*) / I4 = 8 => 0 pairs (X) F7,H7: 8.. / F7 = 8 => 0 pairs (*) / H7 = 8 => 0 pairs (X) D3,D8: 8.. / D3 = 8 => 15 pairs (_) / D8 = 8 => 0 pairs (X) G2,G8: 8.. / G2 = 8 => 17 pairs (_) / G8 = 8 => 0 pairs (X) G1,G3: 9.. / G1 = 9 => 16 pairs (_) / G3 = 9 => 16 pairs (_) * DURATION: 0:00:57.168066 START: 04:51:51.085183 END: 04:52:48.253249 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,C4,D1,D3,D5,D9,E2,F2,G1,G2,G3,G4,G6,G9,I7) * 863.7..421976.....452....7652.1.....38....5..74..8.....153..6...74.......38...... * PAIR D1: 5,9 BLK 2 F1: 5,9,1 # reduction candidate for 5,9 F1: 5,9 # 16 pairs F1: 1 # 16 pairs * PAIR D1: 5,9 COL D D6: 5,9,2 # reduction candidate for 5,9 D6: 2 # 19 pairs D6: 5,9 # 17 pairs * PAIR E2: 2,4 COL E E5: 2,4,6,9 # reduction candidate for 2,4 E5: 2,4 # 21 pairs E7: 2,4,9 # reduction candidate for 2,4 E7: 2,4 # 17 pairs * PAIR F2: 2,4 COL F F5: 2,4,6,7,9 # reduction candidate for 2,4 F5: 2,4 # 16 pairs F7: 2,4,7,8,9 # reduction candidate for 2,4 F7: 2,4 => CTR * 863.7..421976..8..452....7652.1..7.838.4.75..74..8.....153..687.74.......387..4.. F7: 7,8,9 # 15 pairs * PAIR D3: 8,9 BLK 2 F3: 8,9,1,3 # reduction candidate for 8,9 F3: 8,9 # 16 pairs F3: 1,3 # 16 pairs * PAIR D3: 8,9 COL D D8: 8,9,2 # reduction candidate for 8,9 D8: 8,9 # 19 pairs D8: 2 # 17 pairs * PAIR G1: 1,9 ROW 1 F1: 1,9,5 # reduction candidate for 1,9 F1: 1,9 # 16 pairs F1: 5 # 15 pairs * PAIR G2: 3,8 BLK 3 H2: 3,8,5 # reduction candidate for 3,8 H2: 3,8 # 17 pairs I2: 3,8,5 # reduction candidate for 3,8 I2: 3,8 # 16 pairs * PAIR G2: 3,8 COL G G8: 3,8,2 # reduction candidate for 3,8 G8: 2 # 19 pairs G8: 3,8 # 17 pairs * PAIR G3: 1,9 ROW 3 E3: 1,9,3 # reduction candidate for 1,9 E3: 1,9 # 16 pairs F3: 1,9,3,8 # reduction candidate for 1,9 F3: 1,9 # 18 pairs * PAIR C4: 6,9 BLK 4 C5: 6,9,1 # reduction candidate for 6,9 C5: 6,9 # 17 pairs C6: 6,9,1 # reduction candidate for 6,9 C6: 6,9 # 16 pairs * PAIR C4: 6,9 ROW 4 E4: 6,9,3,4 # reduction candidate for 6,9 E4: 6,9 # 19 pairs F4: 6,9,3,4,7 # reduction candidate for 6,9 F4: 6,9 # 18 pairs H4: 6,9,3,8 # reduction candidate for 6,9 H4: 6,9 # 19 pairs * PAIR D5: 4,7 BLK 5 F4: 4,7,3,6,9 # reduction candidate for 4,7 F4: 4,7 # 17 pairs F5: 4,7,2,6,9 # reduction candidate for 4,7 F5: 4,7 => SOLVED * 863579142197624853452813976529136784386497521741285369215348697674951238938762415 F5: 2,6,9 # 15 pairs * PAIR D5: 4,7 ROW 5 I5: 4,7,1,9 # reduction candidate for 4,7 I5: 1,9 => SOLVED * 863579142197624853452813976529136784386497521741285369215348697674951238938762415 I5: 4,7 # 16 pairs * PAIR G4: 4,7 BLK 6 I4: 4,7,3,8,9 # reduction candidate for 4,7 I4: 4,7 => SOLVED * 863579142197624853452813976529136784386497521741285369215348697674951238938762415 I4: 3,8,9 # 16 pairs I5: 4,7,1,9 # reduction candidate for 4,7 I5: 4,7 # 16 pairs * PAIR G4: 4,7 ROW 4 F4: 4,7,3,6,9 # reduction candidate for 4,7 F4: 4,7 # 17 pairs F4: 3,6,9 # 15 pairs * PAIR G6: 2,3 BLK 6 H6: 2,3,1,6,9 # reduction candidate for 2,3 H6: 2,3 # 19 pairs H6: 1,6,9 # 15 pairs * PAIR G6: 2,3 ROW 6 F6: 2,3,5,6,9 # reduction candidate for 2,3 F6: 2,3 # 21 pairs F6: 5,6,9 # 15 pairs * PAIR G6: 2,3 COL G G8: 2,3,8 # reduction candidate for 2,3 G8: 8 => CTR * 863.7..421976..3..4528...7652.1..7..38.4.75..74..8.2...153486.7.742..8...387..4.. G8: 2,3 # 17 pairs * PAIR A7: 2,9 BLK 7 A8: 2,9,6 # reduction candidate for 2,9 A8: 2,9 # 16 pairs A9: 2,9,6 # reduction candidate for 2,9 A9: 2,9 # 16 pairs * PAIR A7: 2,9 ROW 7 E7: 2,9,4 # reduction candidate for 2,9 E7: 2,9 # 20 pairs F7: 2,9,4,7,8 # reduction candidate for 2,9 F7: 2,9 => CTR * 863.7..421976..8..452....7652.1..7.838.4.75..74..8.....1534.687.74.......387..4.. F7: 4,7,8 # 15 pairs H7: 2,9,8 # reduction candidate for 2,9 H7: 2,9 => SOLVED * 863579142197624853452813976529136784386497521741285369215348697674951238938762415 H7: 8 # 18 pairs * PAIR D9: 4,7 BLK 8 F7: 4,7,2,8,9 # reduction candidate for 4,7 F7: 2,8,9 => SOLVED * 863579142197624853452813976529136784386497521741285369215348697674951238938762415 F7: 4,7 # 20 pairs * PAIR I7: 4,7 ROW 7 F7: 4,7,2,8,9 # reduction candidate for 4,7 F7: 2,8,9 => SOLVED * 863579142197624853452813976529136784386497521741285369215348697674951238938762415 F7: 4,7 # 20 pairs * PAIR I7: 4,7 COL I I4: 4,7,3,8,9 # reduction candidate for 4,7 I4: 4,7 => SOLVED * 863579142197624853452813976529136784386497521741285369215348697674951238938762415 I4: 3,8,9 # 16 pairs I5: 4,7,1,9 # reduction candidate for 4,7 I5: 4,7 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-065-base-pr-000.dot * REASONING * DIS # F7: 2,4 => CTR => F7: 7,8,9 * PRF # F5: 4,7 => SOL * PRF # I5: 1,9 => SOL * PRF # I4: 4,7 => SOL * DIS # G8: 8 => CTR => G8: 2,3 * DIS # F7: 2,9 => CTR => F7: 4,7,8 * PRF # H7: 2,9 => SOL * PRF # F7: 2,8,9 => SOL * PRF # F7: 2,8,9 => SOL * PRF # I4: 4,7 => SOL * CNT 10 HDP CHAINS / 56 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,C4,D1,D3,D5,D9,E2,F2,G1,G2,G3,G4,G6,G9,I7) * 863.7..421976.....452....7652.1.....38....5..74..8.....153..6...74.......38...... * PAIR D1: 5,9 BLK 2 F1: 5,9,1 # reduction candidate for 5,9 F1: 5,9 # 16 pairs F1: 1 # 16 pairs * PAIR D1: 5,9 COL D D6: 5,9,2 # reduction candidate for 5,9 D6: 2 # 19 pairs D6: 5,9 # 17 pairs * PAIR E2: 2,4 COL E E5: 2,4,6,9 # reduction candidate for 2,4 E5: 2,4 # 21 pairs E7: 2,4,9 # reduction candidate for 2,4 E7: 2,4 # 17 pairs * PAIR F2: 2,4 COL F F5: 2,4,6,7,9 # reduction candidate for 2,4 F5: 2,4 # 16 pairs F7: 2,4,7,8,9 # reduction candidate for 2,4 F7: 2,4 => CTR * 863.7..421976..8..452....7652.1..7.838.4.75..74..8.....153..687.74.......387..4.. * RESTART * PAIR F2: 2,4 COL F F5: 2,4,6,7,9 # reduction candidate for 2,4 F5: 2,4 # 16 pairs F5: 6,7,9 # 15 pairs * PAIR RESTART * PAIR F2: 2,4 COL F F5: 2,4,6,7,9 # reduction candidate for 2,4 F5: 2,4 # 16 pairs F5: 6,7,9 # 15 pairs * PAIR D3: 8,9 BLK 2 F3: 8,9,1,3 # reduction candidate for 8,9 F3: 8,9 # 16 pairs F3: 1,3 # 16 pairs * PAIR D3: 8,9 COL D D8: 8,9,2 # reduction candidate for 8,9 D8: 8,9 # 19 pairs D8: 2 # 17 pairs * PAIR G1: 1,9 ROW 1 F1: 1,9,5 # reduction candidate for 1,9 F1: 1,9 # 16 pairs F1: 5 # 15 pairs * PAIR G2: 3,8 BLK 3 H2: 3,8,5 # reduction candidate for 3,8 H2: 3,8 # 17 pairs I2: 3,8,5 # reduction candidate for 3,8 I2: 3,8 # 16 pairs * PAIR G2: 3,8 COL G G8: 3,8,2 # reduction candidate for 3,8 G8: 2 # 19 pairs G8: 3,8 # 17 pairs * PAIR G3: 1,9 ROW 3 E3: 1,9,3 # reduction candidate for 1,9 E3: 1,9 # 16 pairs F3: 1,9,3,8 # reduction candidate for 1,9 F3: 1,9 # 18 pairs * PAIR C4: 6,9 BLK 4 C5: 6,9,1 # reduction candidate for 6,9 C5: 6,9 # 17 pairs C6: 6,9,1 # reduction candidate for 6,9 C6: 6,9 # 16 pairs * PAIR C4: 6,9 ROW 4 E4: 6,9,3,4 # reduction candidate for 6,9 E4: 6,9 # 19 pairs F4: 6,9,3,4,7 # reduction candidate for 6,9 F4: 6,9 # 18 pairs H4: 6,9,3,8 # reduction candidate for 6,9 H4: 6,9 # 19 pairs * PAIR D5: 4,7 BLK 5 F4: 4,7,3,6,9 # reduction candidate for 4,7 F4: 4,7 # 17 pairs F5: 4,7,2,6,9 # reduction candidate for 4,7 F5: 4,7 => SOLVED * 863579142197624853452813976529136784386497521741285369215348697674951238938762415 * DURATION: 0:00:30.032609 START: 04:53:43.859062 END: 04:54:13.891671 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-065-base-pr-001.dot * REASONING * DIS # F7: 2,4 => CTR => F7: 7,8,9 * PRF F7: 7,8,9 # F5: 4,7 => SOL * STA F7: 7,8,9 + F5: 4,7 * CNT 2 HDP CHAINS / 31 HYP OPENED
Header Info
Top 500 Minimum 17 065 solution: 863579142197624853452813976529136784386497521741285369215348697674951238938762415 info: 1441 FNBTHWX S8.f 5673 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 863579142197624853452813976529136784386497521741285369215348697674951238938762415 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 # F1: 5,9 => UNS * INC # F1: 1 => UNS * INC # D6: 5,9 => UNS * INC # D6: 2 => UNS * INC # E5: 2,4 => UNS * INC # E7: 2,4 => UNS * INC # F5: 2,4 => UNS * DIS # F7: 2,4 => CTR => F7: 7,8,9 * INC # F7: 7,8,9 => UNS * INC # F3: 8,9 => UNS * INC # F3: 1,3 => UNS * INC # D8: 8,9 => UNS * INC # D8: 2 => UNS * INC # F1: 1,9 => UNS * INC # F1: 5 => UNS * INC # H2: 3,8 => UNS * INC # I2: 3,8 => UNS * INC # G8: 3,8 => UNS * INC # G8: 2 => UNS * INC # E3: 1,9 => UNS * INC # F3: 1,9 => UNS * INC # C5: 6,9 => UNS * INC # C6: 6,9 => UNS * INC # E4: 6,9 => UNS * INC # F4: 6,9 => UNS * INC # H4: 6,9 => UNS * INC # F4: 4,7 => UNS * PRF # F5: 4,7 => SOL * INC # F5: 2,6,9 => UNS * INC # I5: 4,7 => UNS * PRF # I5: 1,9 => SOL * PRF # I4: 4,7 => SOL * INC # I4: 3,8,9 => UNS * INC # I5: 4,7 => UNS * INC # F4: 4,7 => UNS * INC # F4: 3,6,9 => UNS * INC # H6: 2,3 => UNS * INC # H6: 1,6,9 => UNS * INC # F6: 2,3 => UNS * INC # F6: 5,6,9 => UNS * INC # G8: 2,3 => UNS * DIS # G8: 8 => CTR => G8: 2,3 * INC # A8: 2,9 => UNS * INC # A9: 2,9 => UNS * INC # E7: 2,9 => UNS * DIS # F7: 2,9 => CTR => F7: 4,7,8 * INC # F7: 4,7,8 => UNS * PRF # H7: 2,9 => SOL * INC # H7: 8 => UNS * INC # F7: 4,7 => UNS * PRF # F7: 2,8,9 => SOL * INC # F7: 4,7 => UNS * PRF # F7: 2,8,9 => SOL * PRF # I4: 4,7 => SOL * INC # I4: 3,8,9 => UNS * INC # I5: 4,7 => UNS * CNT 56 HDP CHAINS / 56 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F1: 5,9 => UNS * INC # F1: 1 => UNS * INC # D6: 5,9 => UNS * INC # D6: 2 => UNS * INC # E5: 2,4 => UNS * INC # E7: 2,4 => UNS * INC # F5: 2,4 => UNS * DIS # F7: 2,4 => CTR => F7: 7,8,9 * INC F7: 7,8,9 # F5: 2,4 => UNS * INC F7: 7,8,9 # F5: 6,7,9 => UNS * INC F7: 7,8,9 # F5: 2,4 => UNS * INC F7: 7,8,9 # F5: 6,7,9 => UNS * INC F7: 7,8,9 # F3: 8,9 => UNS * INC F7: 7,8,9 # F3: 1,3 => UNS * INC F7: 7,8,9 # D8: 8,9 => UNS * INC F7: 7,8,9 # D8: 2 => UNS * INC F7: 7,8,9 # F1: 1,9 => UNS * INC F7: 7,8,9 # F1: 5 => UNS * INC F7: 7,8,9 # H2: 3,8 => UNS * INC F7: 7,8,9 # I2: 3,8 => UNS * INC F7: 7,8,9 # G8: 3,8 => UNS * INC F7: 7,8,9 # G8: 2 => UNS * INC F7: 7,8,9 # E3: 1,9 => UNS * INC F7: 7,8,9 # F3: 1,9 => UNS * INC F7: 7,8,9 # C5: 6,9 => UNS * INC F7: 7,8,9 # C6: 6,9 => UNS * INC F7: 7,8,9 # E4: 6,9 => UNS * INC F7: 7,8,9 # F4: 6,9 => UNS * INC F7: 7,8,9 # H4: 6,9 => UNS * INC F7: 7,8,9 # F4: 4,7 => UNS * PRF F7: 7,8,9 # F5: 4,7 => SOL * STA F7: 7,8,9 + F5: 4,7 * CNT 31 HDP CHAINS / 31 HYP OPENED