Analysis of xx-top95-012-base.sdk
Contents
Original Sudoku
level: medium
position: .6.5.1.9.1...9..539....7....4.8...7.......5.8.817.5.3.....5.2............76..8... initial
Autosolve
position: .6.5.1.9.12..9..539....7....4.8...7.......5.8.817.5.3.....5.2.7....7.....76..8... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 3,5 => CTR => C3: 4,8 * DIS # E3: 2,3 => CTR => E3: 8 * DIS # I3: 2,4 => CTR => I3: 1,6 * DIS # G1: 4 => CTR => G1: 7,8 * DIS # I6: 2,6 => CTR => I6: 4,9 * PRF # H5: 1,6 => SOL * DIS # E4: 1,6 => CTR => E4: 2,3 * DIS # G8: 1,6 => CTR => G8: 3,4,8,9 * DIS # G9: 1,4 => CTR => G9: 3,9 * DIS # I9: 1,4 => CTR => I9: 5,9 * DIS # D9: 1,4 => CTR => D9: 2,3,9 * DIS # H3: 1,4 => CTR => H3: 2,6,8 * CNT 12 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 # C3: 3,5 => CTR => C3: 4,8 * DIS C3: 4,8 # E3: 2,3 => CTR => E3: 8 * DIS C3: 4,8 + E3: 8 # C4: 3,9 => CTR => C4: 2,5 * DIS C3: 4,8 + E3: 8 + C4: 2,5 # I6: 2,6 => CTR => I6: 9 * PRF C3: 4,8 + E3: 8 + C4: 2,5 + I6: 9 => SOL * STA C3: 4,8 + E3: 8 + C4: 2,5 + I6: 9 * CNT 5 HDP CHAINS / 17 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .6.5.1.9.1...9..539....7....4.8...7.......5.8.817.5.3.....5.2............76..8... | initial |
| .6.5.1.9.12..9..539....7....4.8...7.......5.8.817.5.3.....5.2.7....7.....76..8... | autosolve |
| 863521794127496853954387621645839172739142568281765439498653217512974386376218945 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) C2: 7,8 B3: 3,5 D2: 4,6 F2: 4,6 D3: 2,3 I1: 2,4 G2: 7,8 B5: 3,9 A6: 2,6 G4: 1,6 H9: 1,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B7,B8: 1.. / B7 = 1 => 11 pairs (_) / B8 = 1 => 11 pairs (_) E1,I1: 2.. / E1 = 2 => 12 pairs (_) / I1 = 2 => 0 pairs (X) H3,H5: 2.. / H3 = 2 => 13 pairs (_) / H5 = 2 => 0 pairs (X) G8,G9: 3.. / G8 = 3 => 11 pairs (_) / G9 = 3 => 11 pairs (_) D2,F2: 4.. / D2 = 4 => 9 pairs (_) / F2 = 4 => 9 pairs (_) B3,C3: 5.. / B3 = 5 => 10 pairs (_) / C3 = 5 => 0 pairs (X) A4,C4: 5.. / A4 = 5 => 11 pairs (_) / C4 = 5 => 10 pairs (_) I8,I9: 5.. / I8 = 5 => 0 pairs (X) / I9 = 5 => 11 pairs (_) A9,I9: 5.. / A9 = 5 => 0 pairs (X) / I9 = 5 => 11 pairs (_) B3,B8: 5.. / B3 = 5 => 10 pairs (_) / B8 = 5 => 0 pairs (X) D2,F2: 6.. / D2 = 6 => 9 pairs (_) / F2 = 6 => 9 pairs (_) G1,G2: 7.. / G1 = 7 => 9 pairs (_) / G2 = 7 => 10 pairs (_) A5,C5: 7.. / A5 = 7 => 11 pairs (_) / C5 = 7 => 12 pairs (_) C2,G2: 7.. / C2 = 7 => 9 pairs (_) / G2 = 7 => 10 pairs (_) A1,A5: 7.. / A1 = 7 => 12 pairs (_) / A5 = 7 => 11 pairs (_) E1,E3: 8.. / E1 = 8 => 0 pairs (X) / E3 = 8 => 13 pairs (_) C2,G2: 8.. / C2 = 8 => 10 pairs (_) / G2 = 8 => 9 pairs (_) G6,I6: 9.. / G6 = 9 => 13 pairs (_) / I6 = 9 => 14 pairs (_) C4,F4: 9.. / C4 = 9 => 0 pairs (X) / F4 = 9 => 11 pairs (_) * DURATION: 0:00:23.654789 START: 23:05:33.591546 END: 23:05:57.246335 2017-05-03 * CP COUNT: (19) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B3,B5,C2,D2,D3,F2,G2,G4,H9,I1) * .6.5.1.9.12..9..539....7....4.8...7.......5.8.817.5.3.....5.2.7....7.....76..8... * PAIR C2: 7,8 BLK 1 A1: 7,8,3,4 # reduction candidate for 7,8 A1: 7,8 # 13 pairs C1: 7,8,3,4 # reduction candidate for 7,8 C1: 7,8 # 13 pairs * PAIR B3: 3,5 BLK 1 C3: 3,5,4,8 # reduction candidate for 3,5 C3: 3,5 => CTR * .6.531.9212..9..539..287....4.82..7.6.7...528281765.3.....5.2.7..2.7.....76..8... C3: 4,8 # 12 pairs * PAIR B3: 3,5 COL B B8: 3,5,1,9 # reduction candidate for 3,5 B8: 3,5 # 11 pairs B8: 1,9 # 11 pairs * PAIR D2: 4,6 COL D D7: 4,6,1,3,9 # reduction candidate for 4,6 D7: 4,6 # 12 pairs D8: 4,6,1,2,3,9 # reduction candidate for 4,6 D8: 4,6 # 12 pairs * PAIR F2: 4,6 COL F F7: 4,6,3,9 # reduction candidate for 4,6 F7: 4,6 # 12 pairs F8: 4,6,2,3,9 # reduction candidate for 4,6 F8: 4,6 # 14 pairs * PAIR D3: 2,3 BLK 2 E1: 2,3,8 # reduction candidate for 2,3 E1: 2,3 # 13 pairs E3: 2,3,8 # reduction candidate for 2,3 E3: 2,3 => CTR * .6.581.9212..9..5395...7....4.8.9.7.6.7...528281765.3...9.5.2.7..2.7.....762.8... E3: 8 # 13 pairs * PAIR D3: 2,3 COL D D5: 2,3,1,4,9 # reduction candidate for 2,3 D5: 2,3 # 12 pairs D8: 2,3,1,4,6,9 # reduction candidate for 2,3 D8: 2,3 # 12 pairs D9: 2,3,1,4,9 # reduction candidate for 2,3 D9: 2,3 # 12 pairs * PAIR I1: 2,4 BLK 3 H3: 2,4,1,6,8 # reduction candidate for 2,4 H3: 2,4 # 16 pairs I3: 2,4,1,6 # reduction candidate for 2,4 I3: 2,4 => CTR * 763521894128.9.753954387..2.4.832.7.637...528281765439....5.2.7..2.7.3..3762.89.5 I3: 1,6 # 12 pairs * PAIR I1: 2,4 COL I I6: 2,4,6,9 # reduction candidate for 2,4 I6: 2,4 # 22 pairs I6: 6,9 # 12 pairs * PAIR G2: 7,8 BLK 3 G1: 7,8,4 # reduction candidate for 7,8 G1: 4 => CTR * .6.581492128.9.753954..7....4.8.9.7.6.7...528281765934..9.5.2.7..2.7.....762.83.9 G1: 7,8 # 12 pairs * PAIR B5: 3,9 BLK 4 C4: 3,9,2,5 # reduction candidate for 3,9 C4: 3,9 # 13 pairs C5: 3,9,2,7 # reduction candidate for 3,9 C5: 3,9 # 23 pairs * PAIR B5: 3,9 ROW 5 D5: 3,9,1,2,4 # reduction candidate for 3,9 D5: 3,9 # 15 pairs F5: 3,9,2,4 # reduction candidate for 3,9 F5: 3,9 # 14 pairs * PAIR B5: 3,9 COL B B7: 3,9,1 # reduction candidate for 3,9 B7: 3,9 # 11 pairs B8: 3,9,1,5 # reduction candidate for 3,9 B8: 3,9 # 11 pairs * PAIR A6: 2,6 BLK 4 A4: 2,6,3,5 # reduction candidate for 2,6 A4: 2,6 # 23 pairs A5: 2,6,3,7 # reduction candidate for 2,6 A5: 2,6 # 15 pairs * PAIR A6: 2,6 ROW 6 E6: 2,6,4 # reduction candidate for 2,6 E6: 2,6 # 14 pairs I6: 2,6,4,9 # reduction candidate for 2,6 I6: 2,6 => CTR * 763521894128.9.7539543876213458691726.7.1.548281745936....5.2.7..2.7.3..576238419 I6: 4,9 # 12 pairs * PAIR G4: 1,6 BLK 6 I4: 1,6,2 # reduction candidate for 1,6 I4: 1,6 # 19 pairs H5: 1,6,2,4 # reduction candidate for 1,6 H5: 1,6 => SOLVED * 863521794127496853954387621645839172739142568281765439498653217512974386376218945 H5: 2,4 # 12 pairs * PAIR G4: 1,6 ROW 4 E4: 1,6,2,3 # reduction candidate for 1,6 E4: 1,6 => CTR * 763521894128.9.753954387.2.3458.9.72697.325.82817.5936..9.5.2.7..297.4.55762483.9 E4: 2,3 # 16 pairs * PAIR G4: 1,6 COL G G3: 1,6,4,8 # reduction candidate for 1,6 G3: 1,6 # 13 pairs G8: 1,6,3,4,8,9 # reduction candidate for 1,6 G8: 1,6 => CTR * 76.5.1.92128.9.7539..3278...4.832.7.637...528281765934....5.2.7..2.7...55762.83.9 G8: 3,4,8,9 # 11 pairs * PAIR H9: 1,4 BLK 9 H7: 1,4,6,8 # reduction candidate for 1,4 H7: 1,4 # 21 pairs G8: 1,4,3,6,8,9 # reduction candidate for 1,4 G8: 1,4 # 16 pairs H8: 1,4,6,8 # reduction candidate for 1,4 H8: 1,4 # 21 pairs I8: 1,4,5,6,9 # reduction candidate for 1,4 I8: 1,4 # 17 pairs G9: 1,4,3,9 # reduction candidate for 1,4 G9: 1,4 => CTR * 76.521894128.9.7539.4387621.45869172697...5.82817.5936....5.2.7..2.7.3...76..8... G9: 3,9 # 12 pairs I9: 1,4,5,9 # reduction candidate for 1,4 I9: 1,4 => CTR * .6.521.9412..9..53954387.26.458.9.72.....25.82817.5.39....5.2.7..2.7.3.5576238941 I9: 5,9 # 12 pairs * PAIR H9: 1,4 ROW 9 D9: 1,4,2,3,9 # reduction candidate for 1,4 D9: 1,4 => CTR * 76.5.1.9.128.9.7539....7.2..4.8...726.7...5.82817.5.3.....5.2.7..2.7.....76.28... D9: 2,3,9 # 11 pairs E9: 1,4,2,3 # reduction candidate for 1,4 E9: 1,4 # 14 pairs * PAIR H9: 1,4 COL H H3: 1,4,2,6,8 # reduction candidate for 1,4 H3: 1,4 => CTR * 7635.1.9.128.9.7539543.7....4.832.7.637...528281765.3.....5.2.7..2.7.....762.8... H3: 2,6,8 # 11 pairs H5: 1,4,2,6 # reduction candidate for 1,4 H5: 1,4 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-012-base-pr-000.dot * REASONING * DIS # C3: 3,5 => CTR => C3: 4,8 * DIS # E3: 2,3 => CTR => E3: 8 * DIS # I3: 2,4 => CTR => I3: 1,6 * DIS # G1: 4 => CTR => G1: 7,8 * DIS # I6: 2,6 => CTR => I6: 4,9 * PRF # H5: 1,6 => SOL * DIS # E4: 1,6 => CTR => E4: 2,3 * DIS # G8: 1,6 => CTR => G8: 3,4,8,9 * DIS # G9: 1,4 => CTR => G9: 3,9 * DIS # I9: 1,4 => CTR => I9: 5,9 * DIS # D9: 1,4 => CTR => D9: 2,3,9 * DIS # H3: 1,4 => CTR => H3: 2,6,8 * CNT 12 HDP CHAINS / 56 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B3,B5,C2,D2,D3,F2,G2,G4,H9,I1) * .6.5.1.9.12..9..539....7....4.8...7.......5.8.817.5.3.....5.2.7....7.....76..8... * PAIR C2: 7,8 BLK 1 A1: 7,8,3,4 # reduction candidate for 7,8 A1: 7,8 # 13 pairs C1: 7,8,3,4 # reduction candidate for 7,8 C1: 7,8 # 13 pairs * PAIR B3: 3,5 BLK 1 C3: 3,5,4,8 # reduction candidate for 3,5 C3: 3,5 => CTR * .6.531.9212..9..539..287....4.82..7.6.7...528281765.3.....5.2.7..2.7.....76..8... * PAIR D2: 4,6 COL D D7: 4,6,1,3,9 # reduction candidate for 4,6 D7: 4,6 # 13 pairs D8: 4,6,1,2,3,9 # reduction candidate for 4,6 D8: 4,6 # 13 pairs * PAIR F2: 4,6 COL F F7: 4,6,3,9 # reduction candidate for 4,6 F7: 4,6 # 13 pairs F8: 4,6,2,3,9 # reduction candidate for 4,6 F8: 4,6 # 15 pairs * PAIR D3: 2,3 BLK 2 E3: 2,3,8 # reduction candidate for 2,3 E3: 2,3 => CTR * .6.581.9212..9..5395...7....4.8.9.7.6.7...528281765.3...9.5.2.7..2.7.....762.8... * PAIR B5: 3,9 BLK 4 C4: 3,9,2,5 # reduction candidate for 3,9 C4: 3,9 => CTR * .6.521.9412..9..53954387.2.54.8.2.7.7.21.9548681745932.9..5.217..5.7...9.769.8..5 C5: 3,9,7 # reduction candidate for 3,9 C5: 3,9 # 23 pairs * RESTART * PAIR B5: 3,9 BLK 4 C5: 3,9,7 # reduction candidate for 3,9 C5: 3,9 # 23 pairs C5: 7 # 15 pairs * PAIR B5: 3,9 COL B B7: 3,9,1 # reduction candidate for 3,9 B7: 3,9 # 16 pairs B8: 3,9,1 # reduction candidate for 3,9 B8: 3,9 # 16 pairs * PAIR A6: 2,6 BLK 4 A4: 2,6,3,5 # reduction candidate for 2,6 A4: 2,6 # 23 pairs A4: 3,5 # 16 pairs * PAIR A6: 2,6 ROW 6 I6: 2,6,9 # reduction candidate for 2,6 I6: 2,6 => CTR * .6.521.9412..9..53954387.2.3458.9.72.97..3548281745936..9.5.2.7..2.7.3..576238419 I6: 9 => SOLVED * 863521794127496853954387621645839172739142568281765439498653217512974386376218945 * DURATION: 0:00:19.078164 START: 23:06:38.828031 END: 23:06:57.906195 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-012-base-pr-001.dot * REASONING * DIS # C3: 3,5 => CTR => C3: 4,8 * DIS C3: 4,8 # E3: 2,3 => CTR => E3: 8 * DIS C3: 4,8 + E3: 8 # C4: 3,9 => CTR => C4: 2,5 * DIS C3: 4,8 + E3: 8 + C4: 2,5 # I6: 2,6 => CTR => I6: 9 * PRF C3: 4,8 + E3: 8 + C4: 2,5 + I6: 9 => SOL * STA C3: 4,8 + E3: 8 + C4: 2,5 + I6: 9 * CNT 5 HDP CHAINS / 17 HYP OPENED
Header Info
Top 95 Sudokus 012 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 863521794127496853954387621645839172739142568281765439498653217512974386376218945 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: 7,8 => UNS * INC # C1: 7,8 => UNS * DIS # C3: 3,5 => CTR => C3: 4,8 * INC # C3: 4,8 => UNS * INC # B8: 3,5 => UNS * INC # B8: 1,9 => UNS * INC # D7: 4,6 => UNS * INC # D8: 4,6 => UNS * INC # F7: 4,6 => UNS * INC # F8: 4,6 => UNS * INC # E1: 2,3 => UNS * DIS # E3: 2,3 => CTR => E3: 8 * INC # E3: 8 => UNS * INC # D5: 2,3 => UNS * INC # D8: 2,3 => UNS * INC # D9: 2,3 => UNS * INC # H3: 2,4 => UNS * DIS # I3: 2,4 => CTR => I3: 1,6 * INC # I3: 1,6 => UNS * INC # I6: 2,4 => UNS * INC # I6: 6,9 => UNS * INC # G1: 7,8 => UNS * DIS # G1: 4 => CTR => G1: 7,8 * INC # C4: 3,9 => UNS * INC # C5: 3,9 => UNS * INC # D5: 3,9 => UNS * INC # F5: 3,9 => UNS * INC # B7: 3,9 => UNS * INC # B8: 3,9 => UNS * INC # A4: 2,6 => UNS * INC # A5: 2,6 => UNS * INC # E6: 2,6 => UNS * DIS # I6: 2,6 => CTR => I6: 4,9 * INC # I6: 4,9 => UNS * INC # I4: 1,6 => UNS * PRF # H5: 1,6 => SOL * INC # H5: 2,4 => UNS * DIS # E4: 1,6 => CTR => E4: 2,3 * INC # E4: 2,3 => UNS * INC # G3: 1,6 => UNS * DIS # G8: 1,6 => CTR => G8: 3,4,8,9 * INC # G8: 3,4,8,9 => UNS * INC # H7: 1,4 => UNS * INC # G8: 1,4 => UNS * INC # H8: 1,4 => UNS * INC # I8: 1,4 => UNS * DIS # G9: 1,4 => CTR => G9: 3,9 * INC # G9: 3,9 => UNS * DIS # I9: 1,4 => CTR => I9: 5,9 * INC # I9: 5,9 => UNS * DIS # D9: 1,4 => CTR => D9: 2,3,9 * INC # D9: 2,3,9 => UNS * INC # E9: 1,4 => UNS * DIS # H3: 1,4 => CTR => H3: 2,6,8 * INC # H3: 2,6,8 => UNS * INC # H5: 1,4 => UNS * CNT 56 HDP CHAINS / 56 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 7,8 => UNS * INC # C1: 7,8 => UNS * DIS # C3: 3,5 => CTR => C3: 4,8 * INC C3: 4,8 # D7: 4,6 => UNS * INC C3: 4,8 # D8: 4,6 => UNS * INC C3: 4,8 # F7: 4,6 => UNS * INC C3: 4,8 # F8: 4,6 => UNS * DIS C3: 4,8 # E3: 2,3 => CTR => E3: 8 * DIS C3: 4,8 + E3: 8 # C4: 3,9 => CTR => C4: 2,5 * INC C3: 4,8 + E3: 8 + C4: 2,5 # C5: 3,9 => UNS * INC C3: 4,8 + E3: 8 + C4: 2,5 # C5: 3,9 => UNS * INC C3: 4,8 + E3: 8 + C4: 2,5 # C5: 7 => UNS * INC C3: 4,8 + E3: 8 + C4: 2,5 # B7: 3,9 => UNS * INC C3: 4,8 + E3: 8 + C4: 2,5 # B8: 3,9 => UNS * INC C3: 4,8 + E3: 8 + C4: 2,5 # A4: 2,6 => UNS * INC C3: 4,8 + E3: 8 + C4: 2,5 # A4: 3,5 => UNS * DIS C3: 4,8 + E3: 8 + C4: 2,5 # I6: 2,6 => CTR => I6: 9 * PRF C3: 4,8 + E3: 8 + C4: 2,5 + I6: 9 => SOL * STA C3: 4,8 + E3: 8 + C4: 2,5 + I6: 9 * CNT 18 HDP CHAINS / 17 HYP OPENED