Analysis of xx-top500-219-base.sdk
Contents
Original Sudoku
level: medium
position: .5.9........4...7........3.....7...5.1....8..4...........1.56..7...6.2....3...... initial
Autosolve
position: 35.9.7......4.3.7..7.....3.....7.3.5.173..8..43....7.....1356.77..86.2.3.637..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H1: 1,4 => CTR => H1: 2,6,8 * DIS # G3: 1,4 => CTR => G3: 5,9 * DIS # G9: 9 => CTR => G9: 1,4 * PRF # F5: 2,6 => SOL * DIS # F5: 4,9 => CTR => F5: 2,6 * DIS # D6: 2,6 => CTR => D6: 5 * PRF # D6: 5 => SOL * DIS # F6: 2,6 => CTR => F6: 1,8,9 * PRF # D3: 2,6 => SOL * DIS # D3: 5 => CTR => D3: 2,6 * DIS # H1: 1,4 => CTR => H1: 2,6,8 * DIS # H9: 1,4 => CTR => H9: 5,8,9 * DIS # B7: 2,8 => CTR => B7: 4,9 * PRF # H9: 1,5 => SOL * DIS # H9: 4,8,9 => CTR => H9: 1,5 * DIS # F9: 4,9 => CTR => F9: 2 * DIS # F5: 4,9 => CTR => F5: 2,6 * PRF # F5: 2,6 => SOL * DIS # H9: 4,9 => CTR => H9: 1,5,8 * DIS # I9: 4,9 => CTR => I9: 1,8 * DIS # B7: 2,8 => CTR => B7: 4,9 * DIS # H5: 4,9 => CTR => H5: 2,6 * PRF # H9: 1,5 => SOL * DIS # H9: 4,8,9 => CTR => H9: 1,5 * CNT 24 HDP CHAINS / 44 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H1: 1,4 => CTR => H1: 2,6,8 * DIS H1: 2,6,8 # G3: 1,4 => CTR => G3: 5,9 * DIS H1: 2,6,8 + G3: 5,9 # G9: 9 => CTR => G9: 1,4 * PRF H1: 2,6,8 + G3: 5,9 + G9: 1,4 # F5: 2,6 => SOL * STA H1: 2,6,8 + G3: 5,9 + G9: 1,4 + F5: 2,6 * CNT 4 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5.9........4...7........3.....7...5.1....8..4...........1.56..7...6.2....3...... | initial |
| 35.9.7......4.3.7..7.....3.....7.3.5.173..8..43....7.....1356.77..86.2.3.637..... | autosolve |
| 356927184821453976974618532689271345517346829432589761248135697795864213163792458 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) G1: 1,4 D4: 2,6 F4: 1,4 H4: 1,4 B8: 4,9 C8: 1,5 A9: 1,5 F8: 4,9 H7: 4,9 H8: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C8,A9: 1.. / C8 = 1 => 0 pairs (X) / A9 = 1 => 0 pairs (_) F4,H4: 1.. / F4 = 1 => 0 pairs (*) / H4 = 1 => 0 pairs (X) C8,H8: 1.. / C8 = 1 => 0 pairs (X) / H8 = 1 => 0 pairs (_) E9,F9: 2.. / E9 = 2 => 0 pairs (X) / F9 = 2 => 11 pairs (_) C1,C3: 4.. / C1 = 4 => 13 pairs (_) / C3 = 4 => 10 pairs (_) B7,B8: 4.. / B7 = 4 => 0 pairs (*) / B8 = 4 => 0 pairs (X) F4,H4: 4.. / F4 = 4 => 0 pairs (X) / H4 = 4 => 0 pairs (_) B7,H7: 4.. / B7 = 4 => 0 pairs (*) / H7 = 4 => 0 pairs (X) B8,F8: 4.. / B8 = 4 => 0 pairs (X) / F8 = 4 => 0 pairs (_) E5,E9: 4.. / E5 = 4 => 0 pairs (*) / E9 = 4 => 0 pairs (X) G2,G3: 5.. / G2 = 5 => 10 pairs (_) / G3 = 5 => 0 pairs (*) A5,C6: 5.. / A5 = 5 => 0 pairs (*) / C6 = 5 => 0 pairs (X) C8,A9: 5.. / C8 = 5 => 0 pairs (*) / A9 = 5 => 0 pairs (X) H8,H9: 5.. / H8 = 5 => 0 pairs (X) / H9 = 5 => 0 pairs (_) E2,G2: 5.. / E2 = 5 => 0 pairs (*) / G2 = 5 => 0 pairs (X) A5,E5: 5.. / A5 = 5 => 0 pairs (*) / E5 = 5 => 0 pairs (X) C8,H8: 5.. / C8 = 5 => 0 pairs (*) / H8 = 5 => 0 pairs (X) A9,H9: 5.. / A9 = 5 => 0 pairs (X) / H9 = 5 => 0 pairs (_) A5,A9: 5.. / A5 = 5 => 0 pairs (*) / A9 = 5 => 0 pairs (X) C6,C8: 5.. / C6 = 5 => 0 pairs (X) / C8 = 5 => 0 pairs (_) D3,D6: 5.. / D3 = 5 => 0 pairs (X) / D6 = 5 => 0 pairs (_) D3,F3: 6.. / D3 = 6 => 0 pairs (*) / F3 = 6 => 0 pairs (X) E6,F6: 8.. / E6 = 8 => 0 pairs (*) / F6 = 8 => 0 pairs (X) H9,I9: 8.. / H9 = 8 => 0 pairs (X) / I9 = 8 => 18 pairs (_) F3,F6: 8.. / F3 = 8 => 0 pairs (*) / F6 = 8 => 0 pairs (X) H1,H9: 8.. / H1 = 8 => 18 pairs (_) / H9 = 8 => 0 pairs (X) B8,F8: 9.. / B8 = 9 => 0 pairs (*) / F8 = 9 => 0 pairs (X) * DURATION: 0:00:48.931631 START: 10:15:30.666649 END: 10:16:19.598280 2017-05-04 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B8,C8,D4,F4,F8,G1,H4,H7,H8) * 35.9.7......4.3.7..7.....3.....7.3.5.173..8..43....7.....1356.77..86.2.3.637..... * PAIR G1: 1,4 BLK 3 H1: 1,4,2,6,8 # reduction candidate for 1,4 H1: 1,4 => CTR * 35.9.7......4.357..7.5.6.3.....7.3.5.1735.8..435.987.....135647741869253563742.8. H1: 2,6,8 # 10 pairs I1: 1,4,2,6,8 # reduction candidate for 1,4 I1: 1,4 # 16 pairs G3: 1,4,5,9 # reduction candidate for 1,4 G3: 1,4 => CTR * 35.9.7......4.357..7.....3.....74315.173568944352..7.....135647741869253563742981 G3: 5,9 # 11 pairs I3: 1,4,2,8,9 # reduction candidate for 1,4 I3: 1,4 # 14 pairs * PAIR G1: 1,4 ROW 1 C1: 1,4,2,6,8 # reduction candidate for 1,4 C1: 1,4 # 12 pairs C1: 2,6,8 # 10 pairs * PAIR G1: 1,4 COL G G9: 1,4,9 # reduction candidate for 1,4 G9: 9 => CTR * 35.9.7......4.3.7..7.....3.....74315.173568944352..7.....135647741869253563742981 G9: 1,4 # 13 pairs * PAIR D4: 2,6 BLK 5 F5: 2,6,4,9 # reduction candidate for 2,6 F5: 2,6 => SOLVED * 356927184821453976974618532689271345517346829432589761248135697795864213163792458 F5: 4,9 => CTR * 35.9.7......4.3.7..7.....3.....713455173498..43....719.4.13569779.8642.3.63792... D6: 2,6,5 # reduction candidate for 2,6 D6: 2,6 => CTR * 35.9.7......4.357..7.5.693.....71345.1734.8..43..587.9.4.135697795864213163792458 D6: 5 => SOLVED * 356927184821453976974618532689271345517346829432589761248135697795864213163792458 F6: 2,6,1,8,9 # reduction candidate for 2,6 F6: 2,6 => CTR * 35.9.7......4.3.7..7.6.8.3....271345.173498..43.5867.9.4.135697795864213163792458 F6: 1,8,9 # 10 pairs * PAIR D4: 2,6 ROW 4 A4: 2,6,8,9 # reduction candidate for 2,6 A4: 2,6 # 13 pairs C4: 2,6,8,9 # reduction candidate for 2,6 C4: 2,6 # 13 pairs * PAIR D4: 2,6 COL D D3: 2,6,5 # reduction candidate for 2,6 D3: 2,6 => SOLVED * 356927184821453976974618532689271345517346829432589761248135697795864213163792458 D3: 5 => CTR * 35.9.7......4.357..7.5.693.....71345.1734.8..43..587.9.4.135697795864213163792458 * PAIR H4: 1,4 COL H H1: 1,4,2,6,8 # reduction candidate for 1,4 H1: 1,4 => CTR * 35.9.7......4.357..7.5.6.3.....7.3.5.1735.8..435.987.....135647741869253563742.8. H1: 2,6,8 # 10 pairs H9: 1,4,5,8,9 # reduction candidate for 1,4 H9: 1,4 => CTR * 35.9.7.8....4.3.7..7.....3.....7.3.5.1735.8..435...7.....1356.77.186.253563742918 H9: 5,8,9 # 10 pairs * PAIR B8: 4,9 BLK 7 B7: 4,9,2,8 # reduction candidate for 4,9 B7: 2,8 => CTR * 35.9.7......4.3.7..7.....3.....74315.173568944352..7.....135647741869253563742... B7: 4,9 # 15 pairs * PAIR A9: 1,5 ROW 9 H9: 1,5,4,8,9 # reduction candidate for 1,5 H9: 1,5 => SOLVED * 356927184821453976974618532689271345517346829432589761248135697795864213163792458 H9: 4,8,9 => CTR * 35.9.7......4.357..7.5.6.3.....7.3.5.1735.8..435.987.....135647741869253563742... * PAIR F8: 4,9 BLK 8 E9: 4,9,2 # reduction candidate for 4,9 E9: 4,9 # 11 pairs F9: 4,9,2 # reduction candidate for 4,9 F9: 4,9 => CTR * 35.9.718....4.3.7..7.....3.....7134551734.8..43.5987...4.135697795864213163729458 F9: 2 # 11 pairs * PAIR F8: 4,9 COL F F5: 4,9,2,6 # reduction candidate for 4,9 F5: 4,9 => CTR * 35.9.7......4.3.7..7.....3.....713455173498..43....719.4.13569779.8642.3.63792... F5: 2,6 => SOLVED * 356927184821453976974618532689271345517346829432589761248135697795864213163792458 * PAIR H7: 4,9 BLK 9 G9: 4,9,1 # reduction candidate for 4,9 G9: 4,9 # 12 pairs H9: 4,9,1,5,8 # reduction candidate for 4,9 H9: 4,9 => CTR * 35.9.748....4.357..745.693.....7.3.5.1735.8.4435.9.7.....1356.77.186.253563742198 H9: 1,5,8 # 10 pairs I9: 4,9,1,8 # reduction candidate for 4,9 I9: 4,9 => CTR * 35.9.74.....4.357..745.693.....7.3.5.1735.8.4435.9.7.....1356.77.186.253563742189 I9: 1,8 # 11 pairs * PAIR H7: 4,9 ROW 7 B7: 4,9,2,8 # reduction candidate for 4,9 B7: 2,8 => CTR * 35.9.7......4.3.7..7.....3.....74315.173568944352..7.....135647741869253563742... B7: 4,9 # 15 pairs * PAIR H7: 4,9 COL H H5: 4,9,2,6 # reduction candidate for 4,9 H5: 4,9 => CTR * 35.9.7......4.3.7..7.....3.....74315.173568..4352..7.....1356.7741869253563742.8. H5: 2,6 # 11 pairs * PAIR H8: 1,5 BLK 9 H9: 1,5,4,8,9 # reduction candidate for 1,5 H9: 1,5 => SOLVED * 356927184821453976974618532689271345517346829432589761248135697795864213163792458 H9: 4,8,9 => CTR * 35.9.7......4.357..7.5.6.3.....7.3.5.1735.8..435.987.....135647741869253563742... * INCONCLUSIVE * SAVE PR GRAPH xx-top500-219-base-pr-000.dot * REASONING * DIS # H1: 1,4 => CTR => H1: 2,6,8 * DIS # G3: 1,4 => CTR => G3: 5,9 * DIS # G9: 9 => CTR => G9: 1,4 * PRF # F5: 2,6 => SOL * DIS # F5: 4,9 => CTR => F5: 2,6 * DIS # D6: 2,6 => CTR => D6: 5 * PRF # D6: 5 => SOL * DIS # F6: 2,6 => CTR => F6: 1,8,9 * PRF # D3: 2,6 => SOL * DIS # D3: 5 => CTR => D3: 2,6 * DIS # H1: 1,4 => CTR => H1: 2,6,8 * DIS # H9: 1,4 => CTR => H9: 5,8,9 * DIS # B7: 2,8 => CTR => B7: 4,9 * PRF # H9: 1,5 => SOL * DIS # H9: 4,8,9 => CTR => H9: 1,5 * DIS # F9: 4,9 => CTR => F9: 2 * DIS # F5: 4,9 => CTR => F5: 2,6 * PRF # F5: 2,6 => SOL * DIS # H9: 4,9 => CTR => H9: 1,5,8 * DIS # I9: 4,9 => CTR => I9: 1,8 * DIS # B7: 2,8 => CTR => B7: 4,9 * DIS # H5: 4,9 => CTR => H5: 2,6 * PRF # H9: 1,5 => SOL * DIS # H9: 4,8,9 => CTR => H9: 1,5 * CNT 24 HDP CHAINS / 44 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B8,C8,D4,F4,F8,G1,H4,H7,H8) * 35.9.7......4.3.7..7.....3.....7.3.5.173..8..43....7.....1356.77..86.2.3.637..... * PAIR G1: 1,4 BLK 3 H1: 1,4,2,6,8 # reduction candidate for 1,4 H1: 1,4 => CTR * 35.9.7......4.357..7.5.6.3.....7.3.5.1735.8..435.987.....135647741869253563742.8. I1: 1,4,2,6,8 # reduction candidate for 1,4 I1: 1,4 # 16 pairs G3: 1,4,5,9 # reduction candidate for 1,4 G3: 1,4 => CTR * 35.9.7......4.357..7.....3.....74315.173568944352..7.....135647741869253563742981 I3: 1,4,2,8,9 # reduction candidate for 1,4 I3: 1,4 # 14 pairs * PAIR G1: 1,4 ROW 1 C1: 1,4,2,6,8 # reduction candidate for 1,4 C1: 1,4 # 13 pairs C1: 2,6,8 # 11 pairs * PAIR G1: 1,4 COL G G9: 1,4,9 # reduction candidate for 1,4 G9: 9 => CTR * 35.9.74.....4.317..74...53.....7.3.5.173..8..43.5..7.....1356.77.586.2131637..958 * PAIR RESTART * PAIR G1: 1,4 BLK 3 I1: 1,4,2,6,8 # reduction candidate for 1,4 I1: 1,4 # 16 pairs I3: 1,4,2,8 # reduction candidate for 1,4 I3: 1,4 # 14 pairs * PAIR G1: 1,4 ROW 1 C1: 1,4,2,6,8 # reduction candidate for 1,4 C1: 1,4 # 15 pairs C1: 2,6,8 # 13 pairs * PAIR D4: 2,6 BLK 5 F5: 2,6,4,9 # reduction candidate for 2,6 F5: 2,6 => SOLVED * 356927184821453976974618532689271345517346829432589761248135697795864213163792458 * DURATION: 0:00:13.520930 START: 10:17:02.320587 END: 10:17:15.841517 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-219-base-pr-001.dot * REASONING * DIS # H1: 1,4 => CTR => H1: 2,6,8 * DIS H1: 2,6,8 # G3: 1,4 => CTR => G3: 5,9 * DIS H1: 2,6,8 + G3: 5,9 # G9: 9 => CTR => G9: 1,4 * PRF H1: 2,6,8 + G3: 5,9 + G9: 1,4 # F5: 2,6 => SOL * STA H1: 2,6,8 + G3: 5,9 + G9: 1,4 + F5: 2,6 * CNT 4 HDP CHAINS / 13 HYP OPENED
Header Info
Top 500 Minimum 17 219 solution: 356927184821453976974618532689271345517346829432589761248135697795864213163792458 info: 1957 FNBTHWY S8.f 40482 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 356927184821453976974618532689271345517346829432589761248135697795864213163792458 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:
* DIS # H1: 1,4 => CTR => H1: 2,6,8 * INC # H1: 2,6,8 => UNS * INC # I1: 1,4 => UNS * DIS # G3: 1,4 => CTR => G3: 5,9 * INC # G3: 5,9 => UNS * INC # I3: 1,4 => UNS * INC # C1: 1,4 => UNS * INC # C1: 2,6,8 => UNS * INC # G9: 1,4 => UNS * DIS # G9: 9 => CTR => G9: 1,4 * PRF # F5: 2,6 => SOL * DIS # F5: 4,9 => CTR => F5: 2,6 * DIS # D6: 2,6 => CTR => D6: 5 * PRF # D6: 5 => SOL * DIS # F6: 2,6 => CTR => F6: 1,8,9 * INC # F6: 1,8,9 => UNS * INC # A4: 2,6 => UNS * INC # C4: 2,6 => UNS * PRF # D3: 2,6 => SOL * DIS # D3: 5 => CTR => D3: 2,6 * DIS # H1: 1,4 => CTR => H1: 2,6,8 * INC # H1: 2,6,8 => UNS * DIS # H9: 1,4 => CTR => H9: 5,8,9 * INC # H9: 5,8,9 => UNS * INC # B7: 4,9 => UNS * DIS # B7: 2,8 => CTR => B7: 4,9 * PRF # H9: 1,5 => SOL * DIS # H9: 4,8,9 => CTR => H9: 1,5 * INC # E9: 4,9 => UNS * DIS # F9: 4,9 => CTR => F9: 2 * INC # F9: 2 => UNS * DIS # F5: 4,9 => CTR => F5: 2,6 * PRF # F5: 2,6 => SOL * INC # G9: 4,9 => UNS * DIS # H9: 4,9 => CTR => H9: 1,5,8 * INC # H9: 1,5,8 => UNS * DIS # I9: 4,9 => CTR => I9: 1,8 * INC # I9: 1,8 => UNS * INC # B7: 4,9 => UNS * DIS # B7: 2,8 => CTR => B7: 4,9 * DIS # H5: 4,9 => CTR => H5: 2,6 * INC # H5: 2,6 => UNS * PRF # H9: 1,5 => SOL * DIS # H9: 4,8,9 => CTR => H9: 1,5 * CNT 44 HDP CHAINS / 44 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # H1: 1,4 => CTR => H1: 2,6,8 * INC H1: 2,6,8 # I1: 1,4 => UNS * DIS H1: 2,6,8 # G3: 1,4 => CTR => G3: 5,9 * INC H1: 2,6,8 + G3: 5,9 # I3: 1,4 => UNS * INC H1: 2,6,8 + G3: 5,9 # C1: 1,4 => UNS * INC H1: 2,6,8 + G3: 5,9 # C1: 2,6,8 => UNS * INC H1: 2,6,8 + G3: 5,9 # G9: 1,4 => UNS * DIS H1: 2,6,8 + G3: 5,9 # G9: 9 => CTR => G9: 1,4 * INC H1: 2,6,8 + G3: 5,9 + G9: 1,4 # I1: 1,4 => UNS * INC H1: 2,6,8 + G3: 5,9 + G9: 1,4 # I3: 1,4 => UNS * INC H1: 2,6,8 + G3: 5,9 + G9: 1,4 # C1: 1,4 => UNS * INC H1: 2,6,8 + G3: 5,9 + G9: 1,4 # C1: 2,6,8 => UNS * PRF H1: 2,6,8 + G3: 5,9 + G9: 1,4 # F5: 2,6 => SOL * STA H1: 2,6,8 + G3: 5,9 + G9: 1,4 + F5: 2,6 * CNT 13 HDP CHAINS / 13 HYP OPENED