Analysis of xx-top500-466-base.sdk
Contents
Original Sudoku
level: medium
position: .....1.6....4.2....8......3......12..4..3..........7..2.1...5.....74....6........ initial
Autosolve
position: ...3.1.6....4.2....8......3......12..4..3..........73.2.1...54....74....6.4...... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # G1: 8,9 => SOL * DIS # I1: 8,9 => CTR => I1: 2,5,7 * DIS # H2: 8,9 => CTR => H2: 1,5,7 * DIS # I2: 8,9 => CTR => I2: 1,5,7 * DIS # G5: 8,9 => CTR => G5: 6 * DIS # G9: 8,9 => CTR => G9: 3 * DIS # D6: 1,2 => CTR => D6: 5,6,8,9 * DIS # B6: 5,6,9 => CTR => B6: 1,2 * DIS # D7: 6,9 => CTR => D7: 8 * DIS # F7: 6,9 => CTR => F7: 3,8 * DIS # I7: 7,8 => CTR => I7: 6,9 * DIS # D6: 1,2 => CTR => D6: 5,6,8,9 * PRF # I8: 1,9 => SOL * DIS # I8: 2,6 => CTR => I8: 1,9 * DIS # H2: 1,9 => CTR => H2: 5,7,8 * CNT 15 HDP CHAINS / 37 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # G1: 8,9 => SOL * STA G1: 8,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....1.6....4.2....8......3......12..4..3..........7..2.1...5.....74....6........ | initial |
| ...3.1.6....4.2....8......3......12..4..3..........73.2.1...54....74....6.4...... | autosolve |
| 459371862316482975782569413863957124147238659925614738271893546538746291694125387 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) G2: 8,9 E6: 1,2 E7: 6,9 D9: 1,2 E9: 1,2 H8: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D9,E9: 1.. / D9 = 1 => 0 pairs (*) / E9 = 1 => 0 pairs (X) H8,I8: 1.. / H8 = 1 => 0 pairs (X) / I8 = 1 => 0 pairs (_) A3,H3: 1.. / A3 = 1 => 0 pairs (X) / H3 = 1 => 0 pairs (_) A5,D5: 1.. / A5 = 1 => 0 pairs (*) / D5 = 1 => 0 pairs (X) B2,B6: 1.. / B2 = 1 => 0 pairs (*) / B6 = 1 => 0 pairs (X) E6,E9: 1.. / E6 = 1 => 0 pairs (*) / E9 = 1 => 0 pairs (X) I2,I8: 1.. / I2 = 1 => 0 pairs (X) / I8 = 1 => 0 pairs (_) D9,E9: 2.. / D9 = 2 => 0 pairs (X) / E9 = 2 => 0 pairs (_) G8,I8: 2.. / G8 = 2 => 0 pairs (*) / I8 = 2 => 0 pairs (X) C3,G3: 2.. / C3 = 2 => 0 pairs (*) / G3 = 2 => 0 pairs (X) C5,D5: 2.. / C5 = 2 => 0 pairs (X) / D5 = 2 => 0 pairs (_) B1,B6: 2.. / B1 = 2 => 0 pairs (X) / B6 = 2 => 0 pairs (_) E6,E9: 2.. / E6 = 2 => 0 pairs (X) / E9 = 2 => 0 pairs (_) I1,I8: 2.. / I1 = 2 => 0 pairs (*) / I8 = 2 => 0 pairs (X) G8,G9: 3.. / G8 = 3 => 0 pairs (X) / G9 = 3 => 6 pairs (_) B7,F7: 3.. / B7 = 3 => 0 pairs (X) / F7 = 3 => 7 pairs (_) A1,A3: 4.. / A1 = 4 => 0 pairs (*) / A3 = 4 => 0 pairs (X) G1,G3: 4.. / G1 = 4 => 0 pairs (X) / G3 = 4 => 0 pairs (_) F4,F6: 4.. / F4 = 4 => 6 pairs (_) / F6 = 4 => 6 pairs (_) I4,I6: 4.. / I4 = 4 => 6 pairs (_) / I6 = 4 => 6 pairs (_) A1,G1: 4.. / A1 = 4 => 0 pairs (*) / G1 = 4 => 0 pairs (X) A3,G3: 4.. / A3 = 4 => 0 pairs (X) / G3 = 4 => 0 pairs (_) F4,I4: 4.. / F4 = 4 => 6 pairs (_) / I4 = 4 => 6 pairs (_) F6,I6: 4.. / F6 = 4 => 6 pairs (_) / I6 = 4 => 6 pairs (_) F8,F9: 5.. / F8 = 5 => 0 pairs (X) / F9 = 5 => 6 pairs (_) B9,F9: 5.. / B9 = 5 => 0 pairs (X) / F9 = 5 => 6 pairs (_) G5,G8: 6.. / G5 = 6 => 6 pairs (_) / G8 = 6 => 0 pairs (X) B7,B9: 7.. / B7 = 7 => 6 pairs (_) / B9 = 7 => 0 pairs (X) B7,I7: 7.. / B7 = 7 => 6 pairs (_) / I7 = 7 => 0 pairs (X) E1,E2: 8.. / E1 = 8 => 6 pairs (_) / E2 = 8 => 9 pairs (_) A8,C8: 8.. / A8 = 8 => 6 pairs (_) / C8 = 8 => 6 pairs (_) * DURATION: 0:00:53.462703 START: 18:38:09.130417 END: 18:39:02.593120 2017-05-04 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D9,E6,E7,E9,G2,H8) * ...3.1.6....4.2....8......3......12..4..3..........73.2.1...54....74....6.4...... * PAIR G2: 8,9 BLK 3 G1: 8,9,2,4 # reduction candidate for 8,9 G1: 8,9 => SOLVED * 459371862316482975782569413863957124147238659925614738271893546538746291694125387 G1: 2,4 # 7 pairs I1: 8,9,2,5,7 # reduction candidate for 8,9 I1: 8,9 => CTR * 42.3.1.6....4.2..118....4.3......12..4213.....1..2.73.2.1...54....74..126.421.... I1: 2,5,7 # 6 pairs H2: 8,9,1,5,7 # reduction candidate for 8,9 H2: 8,9 => CTR * 42.381.6....4.2..118....4.3......12..4.13.....1..2.73.2.1...54....74..126.421.... H2: 1,5,7 # 6 pairs I2: 8,9,1,5,7 # reduction candidate for 8,9 I2: 8,9 => CTR * ...3.1.62.164.2....82....13.6....12.14.23.6...2..1.73.2.1...546...7462916.41253.7 I2: 1,5,7 # 6 pairs * PAIR G2: 8,9 ROW 2 E2: 8,9,5,6,7 # reduction candidate for 8,9 E2: 8,9 # 7 pairs E2: 5,6,7 # 7 pairs * PAIR G2: 8,9 COL G G5: 8,9,6 # reduction candidate for 8,9 G5: 8,9 => CTR * 42.3.1.6....4.2..118....4.3......12..4213.....1..2.73.2.1...54....74.6126.421.3.. G5: 6 # 6 pairs G9: 8,9,3 # reduction candidate for 8,9 G9: 8,9 => CTR * 42.3.1.6....4.2..118....4.3......12..4213.6...1..2.73.271.93546...746312634215... G9: 3 # 6 pairs * PAIR E6: 1,2 BLK 5 D5: 1,2,5,6,8,9 # reduction candidate for 1,2 D5: 1,2 # 7 pairs D6: 1,2,5,6,8,9 # reduction candidate for 1,2 D6: 1,2 => CTR * .2.3.1.6..1.4.2....8....213......12.142.37.........73.2.1...54....74..9.6.4...... D6: 5,6,8,9 # 7 pairs * PAIR E6: 1,2 ROW 6 B6: 1,2,5,6,9 # reduction candidate for 1,2 B6: 5,6,9 => CTR * .2.3.1.6..1.4.2....8....213......12..4..3..........73.2.1...54....74..9.6.4...... B6: 1,2 # 8 pairs * PAIR E7: 6,9 BLK 8 D7: 6,9,8 # reduction candidate for 6,9 D7: 6,9 => CTR * 42.3.1.6....4.2..118....4.3......12..4213.....1..2.73.2.1...54....74.2166.421.3.. D7: 8 # 6 pairs F7: 6,9,3,8 # reduction candidate for 6,9 F7: 6,9 => CTR * 42.3.1.6....4.2..118....4.3......12..4213.....1..2.73.2318..547...7432166742153.. F7: 3,8 # 7 pairs F8: 6,9,3,5 # reduction candidate for 6,9 F8: 6,9 # 8 pairs * PAIR E7: 6,9 ROW 7 I7: 6,9,7,8 # reduction candidate for 6,9 I7: 7,8 => CTR * 42.3.1.6....4.2..118....4.3......12..4213.....1..2.73.2.1...54....74.2166.421.3.. I7: 6,9 # 8 pairs * PAIR E7: 6,9 COL E E2: 6,9,5,7,8 # reduction candidate for 6,9 E2: 6,9 # 12 pairs E3: 6,9,5,7 # reduction candidate for 6,9 E3: 6,9 # 9 pairs E4: 6,9,5,7 # reduction candidate for 6,9 E4: 6,9 # 11 pairs * PAIR D9: 1,2 COL D D5: 1,2,5,6,8,9 # reduction candidate for 1,2 D5: 1,2 # 7 pairs D6: 1,2,5,6,8,9 # reduction candidate for 1,2 D6: 1,2 => CTR * .2.3.1.6..1.4.2....8....213......12.142.37.........73.2.1...54....74..9.6.4...... D6: 5,6,8,9 # 7 pairs * PAIR H8: 1,9 BLK 9 I8: 1,9,2,6 # reduction candidate for 1,9 I8: 1,9 => SOLVED * 459371862316482975782569413863957124147238659925614738271893546538746291694125387 I8: 2,6 => CTR * 42.3.1.6....4.2..118....4.3......12..4213.....1..2.73.2.1...54....74.2166.421.3.. * PAIR H8: 1,9 COL H H2: 1,9,5,7,8 # reduction candidate for 1,9 H2: 1,9 => CTR * 42.3.1.6....4.2...18....4.3......12..4213.....1..2.73.2.1...54....74.2..6.421.3.. H2: 5,7,8 # 6 pairs H3: 1,9,5,7 # reduction candidate for 1,9 H3: 1,9 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-466-base-pr-000.dot * REASONING * PRF # G1: 8,9 => SOL * DIS # I1: 8,9 => CTR => I1: 2,5,7 * DIS # H2: 8,9 => CTR => H2: 1,5,7 * DIS # I2: 8,9 => CTR => I2: 1,5,7 * DIS # G5: 8,9 => CTR => G5: 6 * DIS # G9: 8,9 => CTR => G9: 3 * DIS # D6: 1,2 => CTR => D6: 5,6,8,9 * DIS # B6: 5,6,9 => CTR => B6: 1,2 * DIS # D7: 6,9 => CTR => D7: 8 * DIS # F7: 6,9 => CTR => F7: 3,8 * DIS # I7: 7,8 => CTR => I7: 6,9 * DIS # D6: 1,2 => CTR => D6: 5,6,8,9 * PRF # I8: 1,9 => SOL * DIS # I8: 2,6 => CTR => I8: 1,9 * DIS # H2: 1,9 => CTR => H2: 5,7,8 * CNT 15 HDP CHAINS / 37 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D9,E6,E7,E9,G2,H8) * ...3.1.6....4.2....8......3......12..4..3..........73.2.1...54....74....6.4...... * PAIR G2: 8,9 BLK 3 G1: 8,9,2,4 # reduction candidate for 8,9 G1: 8,9 => SOLVED * 459371862316482975782569413863957124147238659925614738271893546538746291694125387 * DURATION: 0:00:02.860356 START: 18:39:32.789711 END: 18:39:35.650067 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-466-base-pr-001.dot * REASONING * PRF # G1: 8,9 => SOL * STA G1: 8,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 466 solution: 459371862316482975782569413863957124147238659925614738271893546538746291694125387 info: 95591 FNBTHYK S8.f 1796 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 459371862316482975782569413863957124147238659925614738271893546538746291694125387 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 # G1: 8,9 => SOL * INC # G1: 2,4 => UNS * DIS # I1: 8,9 => CTR => I1: 2,5,7 * INC # I1: 2,5,7 => UNS * DIS # H2: 8,9 => CTR => H2: 1,5,7 * INC # H2: 1,5,7 => UNS * DIS # I2: 8,9 => CTR => I2: 1,5,7 * INC # I2: 1,5,7 => UNS * INC # E2: 8,9 => UNS * INC # E2: 5,6,7 => UNS * DIS # G5: 8,9 => CTR => G5: 6 * INC # G5: 6 => UNS * DIS # G9: 8,9 => CTR => G9: 3 * INC # G9: 3 => UNS * INC # D5: 1,2 => UNS * DIS # D6: 1,2 => CTR => D6: 5,6,8,9 * INC # D6: 5,6,8,9 => UNS * INC # B6: 1,2 => UNS * DIS # B6: 5,6,9 => CTR => B6: 1,2 * DIS # D7: 6,9 => CTR => D7: 8 * INC # D7: 8 => UNS * DIS # F7: 6,9 => CTR => F7: 3,8 * INC # F7: 3,8 => UNS * INC # F8: 6,9 => UNS * INC # I7: 6,9 => UNS * DIS # I7: 7,8 => CTR => I7: 6,9 * INC # E2: 6,9 => UNS * INC # E3: 6,9 => UNS * INC # E4: 6,9 => UNS * INC # D5: 1,2 => UNS * DIS # D6: 1,2 => CTR => D6: 5,6,8,9 * INC # D6: 5,6,8,9 => UNS * PRF # I8: 1,9 => SOL * DIS # I8: 2,6 => CTR => I8: 1,9 * DIS # H2: 1,9 => CTR => H2: 5,7,8 * INC # H2: 5,7,8 => UNS * INC # H3: 1,9 => UNS * CNT 37 HDP CHAINS / 37 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # G1: 8,9 => SOL * STA G1: 8,9 * CNT 1 HDP CHAINS / 1 HYP OPENED