Analysis of zz-menneske-no-06903546-base.sdk
Contents
Original Sudoku
level: medium
position: 9......534....9.....13....6....6.8..2.8.....9.......253....57......2....59...1... initial
Autosolve
position: 9......534....9.....13..9.6....6.8..2.8.....9.......253....57......2.5..59...1... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 2,6,7,8 => CTR => B2: 3,5 * DIS # C4: 3,5 => CTR => C4: 9 * DIS # B2: 7,8 => CTR => B2: 2,3,5,6 * DIS # B3: 7,8 => CTR => B3: 2,5 * DIS # E3: 7,8 => CTR => E3: 4,5 * DIS # F3: 7,8 => CTR => F3: 2,4 * DIS # D2: 1,2 => CTR => D2: 5,6,7,8 * DIS # B4: 1,7 => CTR => B4: 3,4,5 * DIS # A6: 1,7 => CTR => A6: 6 * DIS # D4: 1,7 => CTR => D4: 2,4,5,9 * DIS # C4: 5 => CTR => C4: 3,9 * DIS # E6: 1,4,7,8 => CTR => E6: 3,9 * CNT 12 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 2,6,7,8 => CTR => B2: 3,5 * PRF B2: 3,5 # I9: 2,4 => SOL * STA B2: 3,5 + I9: 2,4 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 9......534....9.....13....6....6.8..2.8.....9.......253....57......2....59...1... | initial |
| 9......534....9.....13..9.6....6.8..2.8.....9.......253....57......2.5..59...1... | autosolve |
| 967182453435679218821354976159263847248517369673498125316845792784926531592731684 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) C2: 3,5 A3: 7,8 G2: 1,2 A4: 1,7 C6: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D4,F4: 2.. / D4 = 2 => 18 pairs (_) / F4 = 2 => 0 pairs (X) B3,F3: 2.. / B3 = 2 => 18 pairs (_) / F3 = 2 => 0 pairs (X) B2,C2: 3.. / B2 = 3 => 18 pairs (_) / C2 = 3 => 0 pairs (X) F8,E9: 3.. / F8 = 3 => 0 pairs (X) / E9 = 3 => 18 pairs (_) F8,H8: 3.. / F8 = 3 => 0 pairs (X) / H8 = 3 => 18 pairs (_) G1,H3: 4.. / G1 = 4 => 9 pairs (_) / H3 = 4 => 9 pairs (_) B3,E3: 5.. / B3 = 5 => 0 pairs (X) / E3 = 5 => 18 pairs (_) C2,C4: 5.. / C2 = 5 => 18 pairs (_) / C4 = 5 => 0 pairs (X) B2,D2: 6.. / B2 = 6 => 0 pairs (X) / D2 = 6 => 18 pairs (_) A6,A8: 6.. / A6 = 6 => 5 pairs (_) / A8 = 6 => 0 pairs (X) F1,F8: 6.. / F1 = 6 => 0 pairs (X) / F8 = 6 => 18 pairs (_) I2,I4: 7.. / I2 = 7 => 8 pairs (_) / I4 = 7 => 6 pairs (_) A3,A8: 8.. / A3 = 8 => 5 pairs (_) / A8 = 8 => 8 pairs (_) C4,C6: 9.. / C4 = 9 => 18 pairs (_) / C6 = 9 => 0 pairs (X) H7,H8: 9.. / H7 = 9 => 18 pairs (_) / H8 = 9 => 0 pairs (X) C4,D4: 9.. / C4 = 9 => 18 pairs (_) / D4 = 9 => 0 pairs (X) D8,H8: 9.. / D8 = 9 => 18 pairs (_) / H8 = 9 => 0 pairs (X) E6,E7: 9.. / E6 = 9 => 18 pairs (_) / E7 = 9 => 0 pairs (X) * DURATION: 0:00:28.155879 START: 06:38:54.334863 END: 06:39:22.490742 2017-05-01 * CP COUNT: (18) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,C2,C6,G2) * 9......534....9.....13..9.6....6.8..2.8.....9.......253....57......2.5..59...1... * PAIR C2: 3,5 BLK 1 B2: 3,5,2,6,7,8 # reduction candidate for 3,5 B2: 2,6,7,8 => CTR * 9......534.3..9....513.29.6..5.6.8..2.8.....9.......253....57......2.5..59...1... B2: 3,5 # 18 pairs * PAIR C2: 3,5 COL C C4: 3,5,9 # reduction candidate for 3,5 C4: 3,5 => CTR * 9....6.5346...9....2135.9.6...9628..2.85....9..9....253...957......2359.59...1... C4: 9 # 18 pairs * PAIR A3: 7,8 BLK 1 B1: 7,8,2,6 # reduction candidate for 7,8 B1: 7,8 # 8 pairs B2: 7,8,2,3,5,6 # reduction candidate for 7,8 B2: 7,8 => CTR * 9......534.3659....513.29.6..5.6.8..2.8.....9.......253....57......2.5..59...1... B2: 2,3,5,6 # 5 pairs B3: 7,8,2,5 # reduction candidate for 7,8 B3: 7,8 => CTR * 9......534356.9.....1352946.592638.42.85..3.96.3...1253....57......2653.59..31... B3: 2,5 # 6 pairs * PAIR A3: 7,8 ROW 3 E3: 7,8,4,5 # reduction candidate for 7,8 E3: 7,8 => CTR * 9......534....9....513.2946..5.6.8..2.8.....9.......253....57......2.5..59...1... E3: 4,5 # 6 pairs F3: 7,8,2,4 # reduction candidate for 7,8 F3: 7,8 => CTR * 9.....153435619278.2135.946..9.638172.8.....96.3.9.4253....579....92653.59.73168. F3: 2,4 # 6 pairs H3: 7,8,4 # reduction candidate for 7,8 H3: 7,8 # 9 pairs * PAIR A3: 7,8 COL A A8: 7,8,1,6 # reduction candidate for 7,8 A8: 7,8 # 6 pairs A8: 1,6 # 6 pairs * PAIR G2: 1,2 BLK 3 G1: 1,2,4 # reduction candidate for 1,2 G1: 1,2 # 9 pairs I2: 1,2,7,8 # reduction candidate for 1,2 I2: 1,2 # 13 pairs * PAIR G2: 1,2 ROW 2 D2: 1,2,5,6,7,8 # reduction candidate for 1,2 D2: 1,2 => CTR * 9......53463.59....513.29.6..5.6.8..2.8.....9.......253....57......2.5..59...1... D2: 5,6,7,8 # 5 pairs * PAIR A4: 1,7 BLK 4 B4: 1,7,3,4,5 # reduction candidate for 1,7 B4: 1,7 => CTR * 9....6453463..9217..13..9.6....628342.8....796.....1253....57......235..59...13.. B4: 3,4,5 # 5 pairs B5: 1,7,3,4,5,6 # reduction candidate for 1,7 B5: 1,7 # 8 pairs A6: 1,7,6 # reduction candidate for 1,7 A6: 1,7 => CTR * 9.6....534..6.9...8.13..9.6....6.8..2.8.....9.......253....576.6...2.59.59...1... A6: 6 # 5 pairs B6: 1,7,3,4,6 # reduction candidate for 1,7 B6: 1,7 # 6 pairs * PAIR A4: 1,7 ROW 4 D4: 1,7,2,4,5,9 # reduction candidate for 1,7 D4: 1,7 => CTR * 9......534356.9....2135.9.6.59.628342.85...79..3....253....57......2.5..59...1... D4: 2,4,5,9 # 5 pairs H4: 1,7,3,4 # reduction candidate for 1,7 H4: 1,7 # 13 pairs I4: 1,7,4 # reduction candidate for 1,7 I4: 1,7 # 7 pairs * PAIR A4: 1,7 COL A A8: 1,7,6,8 # reduction candidate for 1,7 A8: 6,8 # 6 pairs A8: 1,7 # 6 pairs * PAIR C6: 3,9 BLK 4 C4: 3,9,5 # reduction candidate for 3,9 C4: 5 => CTR * 9....6.534.3..9....2135.9.6..59628..2.85....9..9....253...957......2359.59...1... C4: 3,9 # 18 pairs * PAIR C6: 3,9 ROW 6 E6: 3,9,1,4,7,8 # reduction candidate for 3,9 E6: 1,4,7,8 => CTR * 9....6.53463..9....513.29.6..5.6.8..2.8.....9.......253...957......2359.59...1... E6: 3,9 # 6 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-menneske-no-06903546-base-pr-000.dot * REASONING * DIS # B2: 2,6,7,8 => CTR => B2: 3,5 * DIS # C4: 3,5 => CTR => C4: 9 * DIS # B2: 7,8 => CTR => B2: 2,3,5,6 * DIS # B3: 7,8 => CTR => B3: 2,5 * DIS # E3: 7,8 => CTR => E3: 4,5 * DIS # F3: 7,8 => CTR => F3: 2,4 * DIS # D2: 1,2 => CTR => D2: 5,6,7,8 * DIS # B4: 1,7 => CTR => B4: 3,4,5 * DIS # A6: 1,7 => CTR => A6: 6 * DIS # D4: 1,7 => CTR => D4: 2,4,5,9 * DIS # C4: 5 => CTR => C4: 3,9 * DIS # E6: 1,4,7,8 => CTR => E6: 3,9 * CNT 12 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,C2,C6,G2) * 9......534....9.....13..9.6....6.8..2.8.....9.......253....57......2.5..59...1... * PAIR C2: 3,5 BLK 1 B2: 3,5,2,6,7,8 # reduction candidate for 3,5 B2: 2,6,7,8 => CTR * 9......534.3..9....513.29.6..5.6.8..2.8.....9.......253....57......2.5..59...1... * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A3,A8,B1,B7,B8,C1,C7,C8,C9,E1,E2,H3,H4,H9,I2,I4,I7,I8) * 9..1.24534356.921..213549.61592638..2485173696734981253..84579....92653.59.7316.. * PAIR C9: 2,4 ROW 9 I9: 2,4,8 # reduction candidate for 2,4 I9: 2,4 => SOLVED * 967182453435679218821354976159263847248517369673498125316845792784926531592731684 * DURATION: 0:00:05.371250 START: 06:39:46.006128 END: 06:39:51.377378 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-menneske-no-06903546-base-pr-001.dot * REASONING * DIS # B2: 2,6,7,8 => CTR => B2: 3,5 * PRF B2: 3,5 # I9: 2,4 => SOL * STA B2: 3,5 + I9: 2,4 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.menneske.no/sudoku/utskrift.html?number=6903546 umulig --------------------------------------------------
Solution
position: 967182453435679218821354976159263847248517369673498125316845792784926531592731684 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 # B2: 3,5 => UNS * DIS # B2: 2,6,7,8 => CTR => B2: 3,5 * DIS # C4: 3,5 => CTR => C4: 9 * INC # C4: 9 => UNS * INC # B1: 7,8 => UNS * DIS # B2: 7,8 => CTR => B2: 2,3,5,6 * INC # B2: 2,3,5,6 => UNS * DIS # B3: 7,8 => CTR => B3: 2,5 * INC # B3: 2,5 => UNS * DIS # E3: 7,8 => CTR => E3: 4,5 * INC # E3: 4,5 => UNS * DIS # F3: 7,8 => CTR => F3: 2,4 * INC # F3: 2,4 => UNS * INC # H3: 7,8 => UNS * INC # A8: 7,8 => UNS * INC # A8: 1,6 => UNS * INC # G1: 1,2 => UNS * INC # I2: 1,2 => UNS * DIS # D2: 1,2 => CTR => D2: 5,6,7,8 * INC # D2: 5,6,7,8 => UNS * DIS # B4: 1,7 => CTR => B4: 3,4,5 * INC # B4: 3,4,5 => UNS * INC # B5: 1,7 => UNS * DIS # A6: 1,7 => CTR => A6: 6 * INC # A6: 6 => UNS * INC # B6: 1,7 => UNS * DIS # D4: 1,7 => CTR => D4: 2,4,5,9 * INC # D4: 2,4,5,9 => UNS * INC # H4: 1,7 => UNS * INC # I4: 1,7 => UNS * INC # A8: 1,7 => UNS * INC # A8: 6,8 => UNS * INC # C4: 3,9 => UNS * DIS # C4: 5 => CTR => C4: 3,9 * INC # E6: 3,9 => UNS * DIS # E6: 1,4,7,8 => CTR => E6: 3,9 * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 3,5 => UNS * DIS # B2: 2,6,7,8 => CTR => B2: 3,5 * PRF B2: 3,5 # I9: 2,4 => SOL * STA B2: 3,5 + I9: 2,4 * CNT 3 HDP CHAINS / 3 HYP OPENED