Analysis of xx-top500-418-base.sdk
Contents
Original Sudoku
level: medium
position: ....1..632.9..................9.51.....28.....3.......5.....9...6..3.......8...4. initial
Autosolve
position: .5..192632.9368...3.6.52...6..9.513..9.2836...3.6.1...5.312.9.696.53.......896345 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B3: 4,7 => SOL * DIS # I3: 4,7 => CTR => I3: 1,8,9 * DIS # I4: 4,7 => CTR => I4: 2,8 * DIS # C6: 4,7 => CTR => C6: 2,5,8 * DIS # I6: 4,7 => CTR => I6: 2,8,9 * DIS # H6: 5,7 => CTR => H6: 2,8,9 * PRF # H2: 5,7 => SOL * DIS # I4: 4,7 => CTR => I4: 2,8 * DIS # I6: 4,7 => CTR => I6: 2,8,9 * DIS # I3: 4,7 => CTR => I3: 1,8,9 * DIS # B4: 2,7 => CTR => B4: 4,8 * DIS # C4: 4,8 => CTR => C4: 2,7 * DIS # C6: 4,8 => CTR => C6: 2,5,7 * DIS # C9: 2 => CTR => C9: 1,7 * DIS # B4: 2,7 => CTR => B4: 4,8 * DIS # H6: 7,8 => CTR => H6: 2,5,9 * DIS # G6: 7,8 => CTR => G6: 4,5 * CNT 17 HDP CHAINS / 55 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B3: 4,7 => SOL * STA B3: 4,7 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....1..632.9..................9.51.....28.....3.......5.....9...6..3.......8...4. | initial |
| .5..192632.9368...3.6.52...6..9.513..9.2836...3.6.1...5.312.9.696.53.......896345 | autosolve |
| 854719263219368457376452819687945132195283674432671598543127986968534721721896345 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) D1: 4,7 D3: 4,7 E4: 4,7 E6: 4,7 H5: 5,7 I5: 4,7 B7: 4,8 C8: 4,8 A9: 1,7 B9: 2,7 F7: 4,7 F8: 4,7 H7: 7,8 G8: 7,8 H8: 1,2 I8: 1,2 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,B3: 1.. / B2 = 1 => 0 pairs (*) / B3 = 1 => 0 pairs (X) A5,C5: 1.. / A5 = 1 => 16 pairs (_) / C5 = 1 => 19 pairs (_) A9,C9: 1.. / A9 = 1 => 19 pairs (_) / C9 = 1 => 16 pairs (_) H8,I8: 1.. / H8 = 1 => 0 pairs (X) / I8 = 1 => 17 pairs (_) A5,A9: 1.. / A5 = 1 => 16 pairs (_) / A9 = 1 => 19 pairs (_) C5,C9: 1.. / C5 = 1 => 19 pairs (_) / C9 = 1 => 16 pairs (_) B9,C9: 2.. / B9 = 2 => 16 pairs (_) / C9 = 2 => 0 pairs (X) H8,I8: 2.. / H8 = 2 => 17 pairs (_) / I8 = 2 => 0 pairs (X) B4,B9: 2.. / B4 = 2 => 0 pairs (X) / B9 = 2 => 16 pairs (_) H6,H8: 2.. / H6 = 2 => 0 pairs (X) / H8 = 2 => 17 pairs (_) D1,D3: 4.. / D1 = 4 => 0 pairs (X) / D3 = 4 => 26 pairs (_) E4,E6: 4.. / E4 = 4 => 15 pairs (_) / E6 = 4 => 16 pairs (_) B7,C8: 4.. / B7 = 4 => 0 pairs (*) / C8 = 4 => 0 pairs (X) F7,F8: 4.. / F7 = 4 => 14 pairs (_) / F8 = 4 => 0 pairs (*) B7,F7: 4.. / B7 = 4 => 0 pairs (*) / F7 = 4 => 0 pairs (X) C8,F8: 4.. / C8 = 4 => 14 pairs (_) / F8 = 4 => 0 pairs (*) G2,H2: 5.. / G2 = 5 => 19 pairs (_) / H2 = 5 => 0 pairs (*) C5,C6: 5.. / C5 = 5 => 0 pairs (*) / C6 = 5 => 0 pairs (X) C5,H5: 5.. / C5 = 5 => 0 pairs (*) / H5 = 5 => 0 pairs (X) G2,G6: 5.. / G2 = 5 => 19 pairs (_) / G6 = 5 => 0 pairs (*) D1,D3: 7.. / D1 = 7 => 26 pairs (_) / D3 = 7 => 0 pairs (X) E4,E6: 7.. / E4 = 7 => 16 pairs (_) / E6 = 7 => 15 pairs (_) F7,F8: 7.. / F7 = 7 => 0 pairs (*) / F8 = 7 => 0 pairs (X) H7,G8: 7.. / H7 = 7 => 14 pairs (_) / G8 = 7 => 0 pairs (*) F7,H7: 7.. / F7 = 7 => 0 pairs (*) / H7 = 7 => 0 pairs (X) F8,G8: 7.. / F8 = 7 => 14 pairs (_) / G8 = 7 => 0 pairs (*) A1,C1: 8.. / A1 = 8 => 20 pairs (_) / C1 = 8 => 14 pairs (_) B7,C8: 8.. / B7 = 8 => 14 pairs (_) / C8 = 8 => 0 pairs (*) H7,G8: 8.. / H7 = 8 => 0 pairs (*) / G8 = 8 => 0 pairs (X) B7,H7: 8.. / B7 = 8 => 14 pairs (_) / H7 = 8 => 0 pairs (*) C8,G8: 8.. / C8 = 8 => 0 pairs (*) / G8 = 8 => 0 pairs (X) A1,A6: 8.. / A1 = 8 => 20 pairs (_) / A6 = 8 => 14 pairs (_) B4,B7: 8.. / B4 = 8 => 0 pairs (*) / B7 = 8 => 0 pairs (X) H3,I3: 9.. / H3 = 9 => 16 pairs (_) / I3 = 9 => 17 pairs (_) H6,I6: 9.. / H6 = 9 => 17 pairs (_) / I6 = 9 => 16 pairs (_) H3,H6: 9.. / H3 = 9 => 16 pairs (_) / H6 = 9 => 17 pairs (_) I3,I6: 9.. / I3 = 9 => 17 pairs (_) / I6 = 9 => 16 pairs (_) * DURATION: 0:01:07.749797 START: 17:06:29.763375 END: 17:07:37.513172 2017-05-04 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B7,B9,C8,D1,D3,E4,E6,F7,F8,G8,H5,H7,H8,I5,I8) * .5..192632.9368...3.6.52...6..9.513..9.2836...3.6.1...5.312.9.696.53.......896345 * PAIR D1: 4,7 ROW 1 A1: 4,7,8 # reduction candidate for 4,7 A1: 4,7 # 14 pairs C1: 4,7,8 # reduction candidate for 4,7 C1: 4,7 # 20 pairs * PAIR D3: 4,7 ROW 3 B3: 4,7,1 # reduction candidate for 4,7 B3: 4,7 => SOLVED * 854719263219368457376452819687945132195283674432671598543127986968534721721896345 B3: 1 # 17 pairs G3: 4,7,8 # reduction candidate for 4,7 G3: 4,7 # 20 pairs I3: 4,7,1,8,9 # reduction candidate for 4,7 I3: 4,7 => CTR * .5..192632.9368...316.5289.6..9.5138.9.2836...3.6.1.2958312497696.53.......896345 I3: 1,8,9 # 16 pairs * PAIR E4: 4,7 ROW 4 B4: 4,7,2,8 # reduction candidate for 4,7 B4: 4,7 # 14 pairs C4: 4,7,2,8 # reduction candidate for 4,7 C4: 4,7 # 22 pairs I4: 4,7,2,8 # reduction candidate for 4,7 I4: 4,7 => CTR * 8547192632.93685.1316.524.86..9.513..9.28365..356.18.95.312.986968534712...896345 I4: 2,8 # 17 pairs * PAIR E6: 4,7 ROW 6 A6: 4,7,8 # reduction candidate for 4,7 A6: 4,7 # 20 pairs C6: 4,7,2,5,8 # reduction candidate for 4,7 C6: 4,7 => CTR * 85..192632.9368...3.6.52...6829.513..95283674.3.6.1...5.31279869685347....1896345 C6: 2,5,8 # 16 pairs G6: 4,7,5,8 # reduction candidate for 4,7 G6: 4,7 # 14 pairs I6: 4,7,2,8,9 # reduction candidate for 4,7 I6: 4,7 => CTR * .5..192632.9368...3.6.52..96..9.5138.9.2836...3.6.1...5.312.9.696.53.......896345 I6: 2,8,9 # 16 pairs * PAIR H5: 5,7 BLK 6 G6: 5,7,4,8 # reduction candidate for 5,7 G6: 5,7 # 24 pairs H6: 5,7,2,8,9 # reduction candidate for 5,7 H6: 5,7 => CTR * 85471926327936851.316.52.9.68.9.5132.9.2836...326.1859543127986968534721.2.896345 H6: 2,8,9 # 16 pairs * PAIR H5: 5,7 ROW 5 C5: 5,7,1,4 # reduction candidate for 5,7 C5: 1,4 # 19 pairs C5: 5,7 # 17 pairs * PAIR H5: 5,7 COL H H2: 5,7,1 # reduction candidate for 5,7 H2: 5,7 => SOLVED * 854719263219368457376452819687945132195283674432671598543127986968534721721896345 H2: 1 # 21 pairs * PAIR I5: 4,7 BLK 6 I4: 4,7,2,8 # reduction candidate for 4,7 I4: 4,7 => CTR * 8547192632.93685.1316.524.86..9.513..9.28365..356.18.95.312.986968534712...896345 I4: 2,8 # 17 pairs G6: 4,7,5,8 # reduction candidate for 4,7 G6: 4,7 # 14 pairs I6: 4,7,2,8,9 # reduction candidate for 4,7 I6: 4,7 => CTR * .5..192632.9368...3.6.52..96..9.5138.9.2836...3.6.1...5.312.9.696.53.......896345 I6: 2,8,9 # 16 pairs * PAIR I5: 4,7 ROW 5 A5: 4,7,1 # reduction candidate for 4,7 A5: 4,7 # 19 pairs C5: 4,7,1,5 # reduction candidate for 4,7 C5: 4,7 # 19 pairs * PAIR I5: 4,7 COL I I2: 4,7,1 # reduction candidate for 4,7 I2: 4,7 # 18 pairs I3: 4,7,1,8,9 # reduction candidate for 4,7 I3: 4,7 => CTR * .5..192632.9368...316.5289.6..9.5138.9.2836...3.6.1.2958312497696.53.......896345 I3: 1,8,9 # 16 pairs * PAIR B7: 4,8 COL B B4: 4,8,2,7 # reduction candidate for 4,8 B4: 2,7 => CTR * .5..192632493685173167524..6..9.513..9.283654435671...583124976964537821...896345 B4: 4,8 # 26 pairs * PAIR C8: 4,8 COL C C1: 4,8,7 # reduction candidate for 4,8 C1: 4,8 # 18 pairs C4: 4,8,2,7 # reduction candidate for 4,8 C4: 4,8 => CTR * 8574192632.9368...3.67524..6.89.513..9.28365..356.17..5831249769645378....2896345 C4: 2,7 # 17 pairs C6: 4,8,2,5,7 # reduction candidate for 4,8 C6: 4,8 => CTR * 85..192632.9368...3.6.52...6829.513..95283674.3.6.1...5.31279869685347....1896345 C6: 2,5,7 # 16 pairs * PAIR A9: 1,7 BLK 7 C9: 1,7,2 # reduction candidate for 1,7 C9: 2 => CTR * .5..192632.93685173167524..62.9.513.791283654435671...5831249769645378..172896345 C9: 1,7 # 16 pairs * PAIR A9: 1,7 COL A A5: 1,7,4 # reduction candidate for 1,7 A5: 4 # 22 pairs A5: 1,7 # 19 pairs * PAIR B9: 2,7 BLK 7 C9: 2,7,1 # reduction candidate for 2,7 C9: 2,7 # 19 pairs C9: 1 # 16 pairs * PAIR B9: 2,7 COL B B4: 2,7,4,8 # reduction candidate for 2,7 B4: 2,7 => CTR * .5..192632493685173167524..6..9.513..9.283654435671...583124976964537821...896345 B4: 4,8 # 26 pairs * PAIR H7: 7,8 COL H H3: 7,8,1,9 # reduction candidate for 7,8 H3: 7,8 # 14 pairs H6: 7,8,2,5,9 # reduction candidate for 7,8 H6: 7,8 => CTR * .5..192632.9368.1.316.52.9.6..9.5132.9.28365..3.6.1..95.312.9.696.53..21...896345 H6: 2,5,9 # 16 pairs * PAIR G8: 7,8 COL G G3: 7,8,4 # reduction candidate for 7,8 G3: 7,8 # 21 pairs G6: 7,8,4,5 # reduction candidate for 7,8 G6: 7,8 => CTR * .5.4192632493685173167524..6..9.513..9.283654435671...5831249769645378.....896345 G6: 4,5 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-418-base-pr-000.dot * REASONING * PRF # B3: 4,7 => SOL * DIS # I3: 4,7 => CTR => I3: 1,8,9 * DIS # I4: 4,7 => CTR => I4: 2,8 * DIS # C6: 4,7 => CTR => C6: 2,5,8 * DIS # I6: 4,7 => CTR => I6: 2,8,9 * DIS # H6: 5,7 => CTR => H6: 2,8,9 * PRF # H2: 5,7 => SOL * DIS # I4: 4,7 => CTR => I4: 2,8 * DIS # I6: 4,7 => CTR => I6: 2,8,9 * DIS # I3: 4,7 => CTR => I3: 1,8,9 * DIS # B4: 2,7 => CTR => B4: 4,8 * DIS # C4: 4,8 => CTR => C4: 2,7 * DIS # C6: 4,8 => CTR => C6: 2,5,7 * DIS # C9: 2 => CTR => C9: 1,7 * DIS # B4: 2,7 => CTR => B4: 4,8 * DIS # H6: 7,8 => CTR => H6: 2,5,9 * DIS # G6: 7,8 => CTR => G6: 4,5 * CNT 17 HDP CHAINS / 55 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B7,B9,C8,D1,D3,E4,E6,F7,F8,G8,H5,H7,H8,I5,I8) * .5..192632.9368...3.6.52...6..9.513..9.2836...3.6.1...5.312.9.696.53.......896345 * PAIR D1: 4,7 ROW 1 A1: 4,7,8 # reduction candidate for 4,7 A1: 4,7 # 14 pairs C1: 4,7,8 # reduction candidate for 4,7 C1: 4,7 # 20 pairs * PAIR D3: 4,7 ROW 3 B3: 4,7,1 # reduction candidate for 4,7 B3: 4,7 => SOLVED * 854719263219368457376452819687945132195283674432671598543127986968534721721896345 * DURATION: 0:00:04.793384 START: 17:08:32.743049 END: 17:08:37.536433 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-418-base-pr-001.dot * REASONING * PRF # B3: 4,7 => SOL * STA B3: 4,7 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 418 solution: 854719263219368457376452819687945132195283674432671598543127986968534721721896345 info: 95090 FNBTYK S8.f 2717 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 854719263219368457376452819687945132195283674432671598543127986968534721721896345 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 # A1: 4,7 => UNS * INC # C1: 4,7 => UNS * PRF # B3: 4,7 => SOL * INC # B3: 1 => UNS * INC # G3: 4,7 => UNS * DIS # I3: 4,7 => CTR => I3: 1,8,9 * INC # I3: 1,8,9 => UNS * INC # B4: 4,7 => UNS * INC # C4: 4,7 => UNS * DIS # I4: 4,7 => CTR => I4: 2,8 * INC # I4: 2,8 => UNS * INC # A6: 4,7 => UNS * DIS # C6: 4,7 => CTR => C6: 2,5,8 * INC # C6: 2,5,8 => UNS * INC # G6: 4,7 => UNS * DIS # I6: 4,7 => CTR => I6: 2,8,9 * INC # I6: 2,8,9 => UNS * INC # G6: 5,7 => UNS * DIS # H6: 5,7 => CTR => H6: 2,8,9 * INC # H6: 2,8,9 => UNS * INC # C5: 5,7 => UNS * INC # C5: 1,4 => UNS * PRF # H2: 5,7 => SOL * INC # H2: 1 => UNS * DIS # I4: 4,7 => CTR => I4: 2,8 * INC # I4: 2,8 => UNS * INC # G6: 4,7 => UNS * DIS # I6: 4,7 => CTR => I6: 2,8,9 * INC # I6: 2,8,9 => UNS * INC # A5: 4,7 => UNS * INC # C5: 4,7 => UNS * INC # I2: 4,7 => UNS * DIS # I3: 4,7 => CTR => I3: 1,8,9 * INC # I3: 1,8,9 => UNS * INC # B4: 4,8 => UNS * DIS # B4: 2,7 => CTR => B4: 4,8 * INC # C1: 4,8 => UNS * DIS # C4: 4,8 => CTR => C4: 2,7 * INC # C4: 2,7 => UNS * DIS # C6: 4,8 => CTR => C6: 2,5,7 * INC # C6: 2,5,7 => UNS * INC # C9: 1,7 => UNS * DIS # C9: 2 => CTR => C9: 1,7 * INC # A5: 1,7 => UNS * INC # A5: 4 => UNS * INC # C9: 2,7 => UNS * INC # C9: 1 => UNS * DIS # B4: 2,7 => CTR => B4: 4,8 * INC # B4: 4,8 => UNS * INC # H3: 7,8 => UNS * DIS # H6: 7,8 => CTR => H6: 2,5,9 * INC # H6: 2,5,9 => UNS * INC # G3: 7,8 => UNS * DIS # G6: 7,8 => CTR => G6: 4,5 * INC # G6: 4,5 => UNS * CNT 55 HDP CHAINS / 55 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 4,7 => UNS * INC # C1: 4,7 => UNS * PRF # B3: 4,7 => SOL * STA B3: 4,7 * CNT 3 HDP CHAINS / 3 HYP OPENED