Analysis of xx-top500-326-base.sdk
Contents
Original Sudoku
level: medium
position: ....3.9..5.1......4.........3..8...6..2....4........51.7....2..6..4........1..... initial
Autosolve
position: ....3.9..5.1......4.3.......3..8.726..2....49.......51.7....2..6..4........1..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F2: 4,6 => CTR => F2: 2,7,8,9 * DIS # G9: 5 => CTR => G9: 4,6 * DIS # F4: 1,9 => CTR => F4: 4,5 * PRF # F4: 4,5 => SOL * DIS # A7: 1,9 => CTR => A7: 3 * PRF # A7: 3 => SOL * PRF # E6: 6,7 => SOL * DIS # F4: 5,9 => CTR => F4: 1,4 * PRF # C4: 5,9 => SOL * DIS # C4: 4 => CTR => C4: 5,9 * DIS # D3: 5,9 => CTR => D3: 2,6,7,8 * DIS # D7: 5,9 => CTR => D7: 3,6,8 * DIS # B8: 2 => CTR => B8: 1,5 * DIS # G3: 6 => CTR => G3: 1,5 * CNT 14 HDP CHAINS / 25 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F2: 4,6 => CTR => F2: 2,7,8,9 * DIS F2: 2,7,8,9 # E2: 2,7,9 => CTR => E2: 4,6 * DIS F2: 2,7,8,9 + E2: 4,6 # G9: 5 => CTR => G9: 4,6 * DIS F2: 2,7,8,9 + E2: 4,6 + G9: 4,6 # F4: 1,9 => CTR => F4: 4,5 * PRF F2: 2,7,8,9 + E2: 4,6 + G9: 4,6 + F4: 4,5 => SOL * STA F2: 2,7,8,9 + E2: 4,6 + G9: 4,6 + F4: 4,5 * CNT 5 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....3.9..5.1......4.........3..8...6..2....4........51.7....2..6..4........1..... | initial |
| ....3.9..5.1......4.3.......3..8.726..2....49.......51.7....2..6..4........1..... | autosolve |
| 726531984591847632483296175135984726862715349947362851374659218618423597259178463 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) C1: 6,7 G2: 4,6 A4: 1,9 C6: 6,7 D4: 5,9 G5: 3,8 G6: 3,8 G8: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A7,B8: 1.. / A7 = 1 => 0 pairs (X) / B8 = 1 => 0 pairs (_) F1,H1: 1.. / F1 = 1 => 0 pairs (*) / H1 = 1 => 0 pairs (X) A4,F4: 1.. / A4 = 1 => 0 pairs (*) / F4 = 1 => 0 pairs (X) A7,H7: 1.. / A7 = 1 => 0 pairs (X) / H7 = 1 => 0 pairs (_) B5,B8: 1.. / B5 = 1 => 0 pairs (X) / B8 = 1 => 0 pairs (_) E3,E5: 1.. / E3 = 1 => 0 pairs (X) / E5 = 1 => 0 pairs (_) G3,G8: 1.. / G3 = 1 => 0 pairs (*) / G8 = 1 => 0 pairs (X) A1,A9: 2.. / A1 = 2 => 0 pairs (X) / A9 = 2 => 0 pairs (_) H2,I2: 3.. / H2 = 3 => 8 pairs (_) / I2 = 3 => 8 pairs (_) G5,G6: 3.. / G5 = 3 => 8 pairs (_) / G6 = 3 => 7 pairs (_) A7,A9: 3.. / A7 = 3 => 0 pairs (*) / A9 = 3 => 0 pairs (X) C4,B6: 4.. / C4 = 4 => 0 pairs (X) / B6 = 4 => 0 pairs (_) F1,I1: 4.. / F1 = 4 => 0 pairs (X) / I1 = 4 => 0 pairs (_) C4,F4: 4.. / C4 = 4 => 0 pairs (X) / F4 = 4 => 0 pairs (_) C7,I7: 4.. / C7 = 4 => 0 pairs (*) / I7 = 4 => 0 pairs (X) B6,B9: 4.. / B6 = 4 => 0 pairs (*) / B9 = 4 => 0 pairs (X) E2,E6: 4.. / E2 = 4 => 0 pairs (*) / E6 = 4 => 0 pairs (X) G2,G9: 4.. / G2 = 4 => 0 pairs (X) / G9 = 4 => 0 pairs (_) C4,B5: 5.. / C4 = 5 => 0 pairs (*) / B5 = 5 => 0 pairs (X) C1,C6: 6.. / C1 = 6 => 0 pairs (*) / C6 = 6 => 0 pairs (X) A1,C1: 7.. / A1 = 7 => 0 pairs (*) / C1 = 7 => 0 pairs (X) C1,C6: 7.. / C1 = 7 => 8 pairs (_) / C6 = 7 => 0 pairs (*) G5,G6: 8.. / G5 = 8 => 7 pairs (_) / G6 = 8 => 8 pairs (_) B2,B3: 9.. / B2 = 9 => 8 pairs (_) / B3 = 9 => 8 pairs (_) * DURATION: 0:00:39.457264 START: 14:00:29.893062 END: 14:01:09.350326 2017-05-04 * CP COUNT: (24) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,C1,C6,D4,G2,G5,G6,G8) * ....3.9..5.1......4.3.......3..8.726..2....49.......51.7....2..6..4........1..... * PAIR G2: 4,6 ROW 2 E2: 4,6,2,7,9 # reduction candidate for 4,6 E2: 4,6 # 9 pairs F2: 4,6,2,7,8,9 # reduction candidate for 4,6 F2: 4,6 => CTR * ....3491.5.1...4..4.3.......34.8.726.52....49....4..51.7....2.461.4..5..24.1..6.. F2: 2,7,8,9 # 8 pairs * PAIR G2: 4,6 COL G G9: 4,6,5 # reduction candidate for 4,6 G9: 5 => CTR * ....3491.5.1...4..4.3...6...34.8.726..2....49....4..51.7....2..6..4..1...4.1..5.. G9: 4,6 # 10 pairs * PAIR A4: 1,9 ROW 4 F4: 1,9,4,5 # reduction candidate for 1,9 F4: 1,9 => CTR * ....3491.5.1......4.3.......3458.726.52....49.......51.7....2.461.4..5...4.1..6.. F4: 4,5 => SOLVED * 726531984591847632483296175135984726862715349947362851374659218618423597259178463 * PAIR A4: 1,9 COL A A7: 1,9,3 # reduction candidate for 1,9 A7: 1,9 => CTR * 2.7.319845.1.4.6..4.3...175139584726.52.1..49.46....51974.5.21.6184..59.3251..46. A7: 3 => SOLVED * 726531984591847632483296175135984726862715349947362851374659218618423597259178463 * PAIR C6: 6,7 ROW 6 D6: 6,7,2,3,9 # reduction candidate for 6,7 D6: 6,7 # 11 pairs E6: 6,7,2,4,9 # reduction candidate for 6,7 E6: 6,7 => SOLVED * 726531984591847632483296175135984726862715349947362851374659218618423597259178463 E6: 2,4,9 # 8 pairs F6: 6,7,2,3,4,9 # reduction candidate for 6,7 F6: 6,7 # 11 pairs * PAIR D4: 5,9 BLK 5 F4: 5,9,1,4 # reduction candidate for 5,9 F4: 5,9 => CTR * ....3.9..5.1......4.3......134.8.726.52....499......5137....21461.4..5..24.1..6.. F4: 1,4 # 9 pairs * PAIR D4: 5,9 ROW 4 C4: 5,9,4 # reduction candidate for 5,9 C4: 5,9 => SOLVED * 726531984591847632483296175135984726862715349947362851374659218618423597259178463 C4: 4 => CTR * ....3491.5.1......4.3.......34.8.726.52....49.......51.7....2.461.4..5...4.1..6.. * PAIR D4: 5,9 COL D D3: 5,9,2,6,7,8 # reduction candidate for 5,9 D3: 5,9 => CTR * 2.7.3.91.5.1......4.3......93.581726..2....49.......5117....2..6..4..1..3..1..... D3: 2,6,7,8 # 8 pairs D7: 5,9,3,6,8 # reduction candidate for 5,9 D7: 5,9 => CTR * 2.7.3.91.5.1......4.3......93.581726..2....49.......5117....2..6..4..1..3..1..... D7: 3,6,8 # 8 pairs * PAIR G8: 1,5 ROW 8 B8: 1,5,2 # reduction candidate for 1,5 B8: 2 => CTR * 2.7.3.9..5.1......4.3.1....935.8.726.12....49.......5117....2..62.4.....35.1..... B8: 1,5 # 10 pairs * PAIR G8: 1,5 COL G G3: 1,5,6 # reduction candidate for 1,5 G3: 6 => CTR * ....3.9..5.1...4..4.3...6...3..8.726.12....49....4..5117....2..65.4..1..3..1..5.. G3: 1,5 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-326-base-pr-000.dot * REASONING * DIS # F2: 4,6 => CTR => F2: 2,7,8,9 * DIS # G9: 5 => CTR => G9: 4,6 * DIS # F4: 1,9 => CTR => F4: 4,5 * PRF # F4: 4,5 => SOL * DIS # A7: 1,9 => CTR => A7: 3 * PRF # A7: 3 => SOL * PRF # E6: 6,7 => SOL * DIS # F4: 5,9 => CTR => F4: 1,4 * PRF # C4: 5,9 => SOL * DIS # C4: 4 => CTR => C4: 5,9 * DIS # D3: 5,9 => CTR => D3: 2,6,7,8 * DIS # D7: 5,9 => CTR => D7: 3,6,8 * DIS # B8: 2 => CTR => B8: 1,5 * DIS # G3: 6 => CTR => G3: 1,5 * CNT 14 HDP CHAINS / 25 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,C1,C6,D4,G2,G5,G6,G8) * ....3.9..5.1......4.3.......3..8.726..2....49.......51.7....2..6..4........1..... * PAIR G2: 4,6 ROW 2 E2: 4,6,2,7,9 # reduction candidate for 4,6 E2: 4,6 # 9 pairs F2: 4,6,2,7,8,9 # reduction candidate for 4,6 F2: 4,6 => CTR * ....3491.5.1...4..4.3.......34.8.726.52....49....4..51.7....2.461.4..5..24.1..6.. * RESTART * PAIR G2: 4,6 ROW 2 E2: 4,6,2,7,9 # reduction candidate for 4,6 E2: 2,7,9 => CTR * ....3491.5.1......4.3.......34.8.726.52....49....4..5117....2.462.4..1..34.1..... * PAIR G2: 4,6 COL G G9: 4,6,5 # reduction candidate for 4,6 G9: 5 => CTR * ....3491.5.1.6.4..4.3...6...34.8.726..2....49....4..51.7....2..6..4..1...4.1..5.. * PAIR RESTART * PAIR A4: 1,9 ROW 4 F4: 1,9,4,5 # reduction candidate for 1,9 F4: 1,9 => CTR * ....3491.5.1......4.3.......3458.726.52....49.......51.7....2.461.4..5...4.1..6.. F4: 4,5 => SOLVED * 726531984591847632483296175135984726862715349947362851374659218618423597259178463 * DURATION: 0:00:07.851887 START: 14:01:29.602302 END: 14:01:37.454189 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-326-base-pr-001.dot * REASONING * DIS # F2: 4,6 => CTR => F2: 2,7,8,9 * DIS F2: 2,7,8,9 # E2: 2,7,9 => CTR => E2: 4,6 * DIS F2: 2,7,8,9 + E2: 4,6 # G9: 5 => CTR => G9: 4,6 * DIS F2: 2,7,8,9 + E2: 4,6 + G9: 4,6 # F4: 1,9 => CTR => F4: 4,5 * PRF F2: 2,7,8,9 + E2: 4,6 + G9: 4,6 + F4: 4,5 => SOL * STA F2: 2,7,8,9 + E2: 4,6 + G9: 4,6 + F4: 4,5 * CNT 5 HDP CHAINS / 7 HYP OPENED
Header Info
Top 500 Minimum 17 326 solution: 726531984591847632483296175135984726862715349947362851374659218618423597259178463 info: 2963 FNBHWY S8.f 3944 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 726531984591847632483296175135984726862715349947362851374659218618423597259178463 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 # E2: 4,6 => UNS * DIS # F2: 4,6 => CTR => F2: 2,7,8,9 * INC # F2: 2,7,8,9 => UNS * INC # G9: 4,6 => UNS * DIS # G9: 5 => CTR => G9: 4,6 * DIS # F4: 1,9 => CTR => F4: 4,5 * PRF # F4: 4,5 => SOL * DIS # A7: 1,9 => CTR => A7: 3 * PRF # A7: 3 => SOL * INC # D6: 6,7 => UNS * PRF # E6: 6,7 => SOL * INC # E6: 2,4,9 => UNS * INC # F6: 6,7 => UNS * DIS # F4: 5,9 => CTR => F4: 1,4 * INC # F4: 1,4 => UNS * PRF # C4: 5,9 => SOL * DIS # C4: 4 => CTR => C4: 5,9 * DIS # D3: 5,9 => CTR => D3: 2,6,7,8 * INC # D3: 2,6,7,8 => UNS * DIS # D7: 5,9 => CTR => D7: 3,6,8 * INC # D7: 3,6,8 => UNS * INC # B8: 1,5 => UNS * DIS # B8: 2 => CTR => B8: 1,5 * INC # G3: 1,5 => UNS * DIS # G3: 6 => CTR => G3: 1,5 * CNT 25 HDP CHAINS / 25 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E2: 4,6 => UNS * DIS # F2: 4,6 => CTR => F2: 2,7,8,9 * INC F2: 2,7,8,9 # E2: 4,6 => UNS * DIS F2: 2,7,8,9 # E2: 2,7,9 => CTR => E2: 4,6 * INC F2: 2,7,8,9 + E2: 4,6 # G9: 4,6 => UNS * DIS F2: 2,7,8,9 + E2: 4,6 # G9: 5 => CTR => G9: 4,6 * DIS F2: 2,7,8,9 + E2: 4,6 + G9: 4,6 # F4: 1,9 => CTR => F4: 4,5 * PRF F2: 2,7,8,9 + E2: 4,6 + G9: 4,6 + F4: 4,5 => SOL * STA F2: 2,7,8,9 + E2: 4,6 + G9: 4,6 + F4: 4,5 * CNT 8 HDP CHAINS / 7 HYP OPENED