Analysis of xx-top95-075-base.sdk
Contents
Original Sudoku
level: medium
position: .52..68.......7.2.......6....48..9..2..41......1.....8..61..38.....9...63..6..1.9 initial
Autosolve
position: .52..68.......7.2......16....48..9..2..41......1.....8..61..38.....9...63..6..1.9 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D3: 3,9 => CTR => D3: 2,5 * PRF # E3: 3,4 => SOL * DIS # H3: 4,5 => CTR => H3: 3,7,9 * DIS # E2: 4,5 => CTR => E2: 3,8 * DIS # G8: 4,5 => CTR => G8: 2,7 * DIS # H4: 5,7 => CTR => H4: 1,3,6 * DIS # I4: 5,7 => CTR => I4: 1,2,3 * DIS # H5: 5,7 => CTR => H5: 3,6 * DIS # H6: 5,7 => CTR => H6: 3,4,6 * DIS # G8: 5,7 => CTR => G8: 2,4 * CNT 10 HDP CHAINS / 33 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D3: 3,9 => CTR => D3: 2,5 * PRF D3: 2,5 # E3: 3,4 => SOL * STA D3: 2,5 + E3: 3,4 * CNT 2 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .52..68.......7.2.......6....48..9..2..41......1.....8..61..38.....9...63..6..1.9 | initial |
| .52..68.......7.2......16....48..9..2..41......1.....8..61..38.....9...63..6..1.9 | autosolve |
| 152946837963587421847231695574863912289415763631729548796152384415398276328674159 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) D1: 3,9 E1: 3,4 G2: 4,5 G5: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H4,I4: 1.. / H4 = 1 => 4 pairs (_) / I4 = 1 => 0 pairs (X) A8,B8: 1.. / A8 = 1 => 6 pairs (_) / B8 = 1 => 4 pairs (_) B2,B8: 1.. / B2 = 1 => 6 pairs (_) / B8 = 1 => 4 pairs (_) H1,H4: 1.. / H1 = 1 => 0 pairs (X) / H4 = 1 => 4 pairs (_) D3,E3: 2.. / D3 = 2 => 4 pairs (_) / E3 = 2 => 0 pairs (X) I4,G6: 2.. / I4 = 2 => 6 pairs (_) / G6 = 2 => 0 pairs (X) I7,G8: 2.. / I7 = 2 => 0 pairs (X) / G8 = 2 => 6 pairs (_) G6,G8: 2.. / G6 = 2 => 0 pairs (X) / G8 = 2 => 6 pairs (_) I4,I7: 2.. / I4 = 2 => 6 pairs (_) / I7 = 2 => 0 pairs (X) D8,F8: 3.. / D8 = 3 => 13 pairs (_) / F8 = 3 => 15 pairs (_) G6,H6: 4.. / G6 = 4 => 17 pairs (_) / H6 = 4 => 11 pairs (_) A2,B2: 6.. / A2 = 6 => 5 pairs (_) / B2 = 6 => 5 pairs (_) E4,E6: 6.. / E4 = 6 => 6 pairs (_) / E6 = 6 => 4 pairs (_) B5,H5: 6.. / B5 = 6 => 15 pairs (_) / H5 = 6 => 4 pairs (_) D6,D8: 7.. / D6 = 7 => 4 pairs (_) / D8 = 7 => 0 pairs (X) E2,E3: 8.. / E2 = 8 => 5 pairs (_) / E3 = 8 => 17 pairs (_) B5,C5: 8.. / B5 = 8 => 4 pairs (_) / C5 = 8 => 9 pairs (_) F8,F9: 8.. / F8 = 8 => 16 pairs (_) / F9 = 8 => 5 pairs (_) H1,H3: 9.. / H1 = 9 => 15 pairs (_) / H3 = 9 => 4 pairs (_) F5,F6: 9.. / F5 = 9 => 4 pairs (_) / F6 = 9 => 7 pairs (_) A7,B7: 9.. / A7 = 9 => 4 pairs (_) / B7 = 9 => 4 pairs (_) * DURATION: 0:00:24.867761 START: 00:38:33.273881 END: 00:38:58.141642 2017-05-04 * CP COUNT: (21) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D1,E1,G2,G5) * .52..68.......7.2......16....48..9..2..41......1.....8..61..38.....9...63..6..1.9 * PAIR D1: 3,9 BLK 2 D2: 3,9,5 # reduction candidate for 3,9 D2: 3,9 # 15 pairs D3: 3,9,2,5 # reduction candidate for 3,9 D3: 3,9 => CTR * .52.468.....58742.....216....48..9.22..41......12...48..61..384...7932563..65.1.9 D3: 2,5 # 5 pairs * PAIR D1: 3,9 ROW 1 H1: 3,9,1,4,7 # reduction candidate for 3,9 H1: 1,4,7 # 10 pairs H1: 3,9 # 6 pairs * PAIR E1: 3,4 BLK 2 E2: 3,4,5,8 # reduction candidate for 3,4 E2: 3,4 # 17 pairs E3: 3,4,2,5,8 # reduction candidate for 3,4 E3: 3,4 => SOLVED * 152946837963587421847231695574863912289415763631729548796152384415398276328674159 E3: 2,5,8 # 4 pairs * PAIR E1: 3,4 ROW 1 H1: 3,4,1,7,9 # reduction candidate for 3,4 H1: 3,4 # 8 pairs I1: 3,4,1,7 # reduction candidate for 3,4 I1: 3,4 # 13 pairs * PAIR G2: 4,5 BLK 3 I2: 4,5,1,3 # reduction candidate for 4,5 I2: 4,5 # 20 pairs H3: 4,5,3,7,9 # reduction candidate for 4,5 H3: 4,5 => CTR * .5234689......7.2......16....48..91.2..41......1.....8..61.438.....93..63..6.81.9 H3: 3,7,9 # 4 pairs I3: 4,5,3,7 # reduction candidate for 4,5 I3: 4,5 # 6 pairs * PAIR G2: 4,5 ROW 2 E2: 4,5,3,8 # reduction candidate for 4,5 E2: 4,5 => CTR * 152.468.7....57421...2816.5..48..9122..41..63..1....48..61..384.1..932.63..6..1.9 E2: 3,8 # 5 pairs * PAIR G2: 4,5 COL G G6: 4,5,2,7 # reduction candidate for 4,5 G6: 4,5 # 6 pairs G8: 4,5,2,7 # reduction candidate for 4,5 G8: 4,5 => CTR * .52.468...1..875244..2516....48.29.52.54197.39.17..248596174382.2.593476347628159 G8: 2,7 # 5 pairs * PAIR G5: 5,7 BLK 6 H4: 5,7,1,3,6 # reduction candidate for 5,7 H4: 5,7 => CTR * .52..681......7.2......169...48..9.12..41......1...248..61..382....9.4.63..6..1.9 H4: 1,3,6 # 4 pairs I4: 5,7,1,2,3 # reduction candidate for 5,7 I4: 5,7 => CTR * .52.468...1..875244..2516.7.7483291528.41.763..17..248596174382.2.593476347628159 I4: 1,2,3 # 4 pairs H5: 5,7,3,6 # reduction candidate for 5,7 H5: 5,7 => CTR * .52.468..61..875244..2516...34865912268419753591732468926174385..7593246345628179 H5: 3,6 # 5 pairs I5: 5,7,3 # reduction candidate for 5,7 I5: 5,7 # 8 pairs G6: 5,7,2,4 # reduction candidate for 5,7 G6: 5,7 # 13 pairs H6: 5,7,3,4,6 # reduction candidate for 5,7 H6: 5,7 => CTR * .52.468......8752......16....48..9122..41.763..17.2458..61.4385...5932.63.56.81.9 H6: 3,4,6 # 4 pairs * PAIR G5: 5,7 ROW 5 C5: 5,7,3,8,9 # reduction candidate for 5,7 C5: 5,7 # 13 pairs C5: 3,8,9 # 4 pairs * PAIR G5: 5,7 COL G G8: 5,7,2,4 # reduction candidate for 5,7 G8: 5,7 => CTR * .52..68.......7.2......16....48..9..2..41......1...248..61..38.....9...63..6..1.9 G8: 2,4 # 6 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-075-base-pr-000.dot * REASONING * DIS # D3: 3,9 => CTR => D3: 2,5 * PRF # E3: 3,4 => SOL * DIS # H3: 4,5 => CTR => H3: 3,7,9 * DIS # E2: 4,5 => CTR => E2: 3,8 * DIS # G8: 4,5 => CTR => G8: 2,7 * DIS # H4: 5,7 => CTR => H4: 1,3,6 * DIS # I4: 5,7 => CTR => I4: 1,2,3 * DIS # H5: 5,7 => CTR => H5: 3,6 * DIS # H6: 5,7 => CTR => H6: 3,4,6 * DIS # G8: 5,7 => CTR => G8: 2,4 * CNT 10 HDP CHAINS / 33 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D1,E1,G2,G5) * .52..68.......7.2......16....48..9..2..41......1.....8..61..38.....9...63..6..1.9 * PAIR D1: 3,9 BLK 2 D2: 3,9,5 # reduction candidate for 3,9 D2: 3,9 # 15 pairs D3: 3,9,2,5 # reduction candidate for 3,9 D3: 3,9 => CTR * .52.468.....58742.....216....48..9.22..41......12...48..61..384...7932563..65.1.9 * RESTART * PAIR D1: 3,9 BLK 2 D2: 3,9,5 # reduction candidate for 3,9 D2: 3,9 # 15 pairs D2: 5 # 13 pairs * PAIR D1: 3,9 ROW 1 H1: 3,9,1,4,7 # reduction candidate for 3,9 H1: 1,4,7 # 11 pairs H1: 3,9 # 7 pairs * PAIR E1: 3,4 BLK 2 E2: 3,4,5,8 # reduction candidate for 3,4 E2: 3,4 # 17 pairs E3: 3,4,2,5,8 # reduction candidate for 3,4 E3: 3,4 => SOLVED * 152946837963587421847231695574863912289415763631729548796152384415398276328674159 * DURATION: 0:00:07.893919 START: 00:39:20.764544 END: 00:39:28.658463 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-075-base-pr-001.dot * REASONING * DIS # D3: 3,9 => CTR => D3: 2,5 * PRF D3: 2,5 # E3: 3,4 => SOL * STA D3: 2,5 + E3: 3,4 * CNT 2 HDP CHAINS / 8 HYP OPENED
Header Info
Top 95 Sudokus 075 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 152946837963587421847231695574863912289415763631729548796152384415398276328674159 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 # D2: 3,9 => UNS * DIS # D3: 3,9 => CTR => D3: 2,5 * INC # D3: 2,5 => UNS * INC # H1: 3,9 => UNS * INC # H1: 1,4,7 => UNS * INC # E2: 3,4 => UNS * PRF # E3: 3,4 => SOL * INC # E3: 2,5,8 => UNS * INC # H1: 3,4 => UNS * INC # I1: 3,4 => UNS * INC # I2: 4,5 => UNS * DIS # H3: 4,5 => CTR => H3: 3,7,9 * INC # H3: 3,7,9 => UNS * INC # I3: 4,5 => UNS * DIS # E2: 4,5 => CTR => E2: 3,8 * INC # E2: 3,8 => UNS * INC # G6: 4,5 => UNS * DIS # G8: 4,5 => CTR => G8: 2,7 * INC # G8: 2,7 => UNS * DIS # H4: 5,7 => CTR => H4: 1,3,6 * INC # H4: 1,3,6 => UNS * DIS # I4: 5,7 => CTR => I4: 1,2,3 * INC # I4: 1,2,3 => UNS * DIS # H5: 5,7 => CTR => H5: 3,6 * INC # H5: 3,6 => UNS * INC # I5: 5,7 => UNS * INC # G6: 5,7 => UNS * DIS # H6: 5,7 => CTR => H6: 3,4,6 * INC # H6: 3,4,6 => UNS * INC # C5: 5,7 => UNS * INC # C5: 3,8,9 => UNS * DIS # G8: 5,7 => CTR => G8: 2,4 * INC # G8: 2,4 => UNS * CNT 33 HDP CHAINS / 33 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D2: 3,9 => UNS * DIS # D3: 3,9 => CTR => D3: 2,5 * INC D3: 2,5 # D2: 3,9 => UNS * INC D3: 2,5 # D2: 5 => UNS * INC D3: 2,5 # H1: 3,9 => UNS * INC D3: 2,5 # H1: 1,4,7 => UNS * INC D3: 2,5 # E2: 3,4 => UNS * PRF D3: 2,5 # E3: 3,4 => SOL * STA D3: 2,5 + E3: 3,4 * CNT 8 HDP CHAINS / 8 HYP OPENED