Analysis of zz-menneske-no-06902995-base.sdk
Contents
Original Sudoku
level: medium
position: 1..8.6...........2.5......6..2..74.........7..7..3....8..5..61.4......8...39....5 initial
Autosolve
position: 1..8.6...........2.5......6..2..74.........7..7..3....8..5..61.4.5....8...39....5 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 4,9 => CTR => B1: 2,3 * DIS # E1: 4,9 => CTR => E1: 2,5 * DIS # H1: 4,9 => CTR => H1: 3,5 * PRF # I1: 4,9 => SOL * DIS # I1: 3,7 => CTR => I1: 4,9 * DIS # E4: 1,6 => CTR => E4: 5,8,9 * PRF # B8: 2,9 => SOL * DIS # B1: 2,9 => CTR => B1: 3,4 * DIS # I7: 7,9 => CTR => I7: 3,4 * DIS # C2: 7,9 => CTR => C2: 4,6,8 * DIS # C3: 7,9 => CTR => C3: 4,8 * DIS # G8: 2,7 => CTR => G8: 3,9 * DIS # A9: 2,7 => CTR => A9: 6 * PRF # A9: 6 => SOL * PRF # E9: 2,7 => SOL * DIS # E9: 2,4 => CTR => E9: 1,6,7,8 * DIS # F9: 2,4 => CTR => F9: 1,8 * CNT 17 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 4,9 => CTR => B1: 2,3 * DIS B1: 2,3 # E1: 4,9 => CTR => E1: 2,5 * DIS B1: 2,3 + E1: 2,5 # H1: 4,9 => CTR => H1: 3,5 * PRF B1: 2,3 + E1: 2,5 + H1: 3,5 # I1: 4,9 => SOL * STA B1: 2,3 + E1: 2,5 + H1: 3,5 + I1: 4,9 * CNT 4 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1..8.6...........2.5......6..2..74.........7..7..3....8..5..61.4......8...39....5 | initial |
| 1..8.6...........2.5......6..2..74.........7..7..3....8..5..61.4.5....8...39....5 | autosolve |
| 139826754768495132254713896382157469546289371971634528897542613425361987613978245 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) C1: 4,9 G2: 1,8 G3: 1,8 D4: 1,6 B7: 2,9 C7: 7,9 G9: 2,7 H9: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,G3: 1.. / G2 = 1 => 7 pairs (_) / G3 = 1 => 6 pairs (_) C5,C6: 1.. / C5 = 1 => 8 pairs (_) / C6 = 1 => 9 pairs (_) B8,B9: 1.. / B8 = 1 => 0 pairs (X) / B9 = 1 => 8 pairs (_) B1,A3: 2.. / B1 = 2 => 0 pairs (X) / A3 = 2 => 10 pairs (_) B1,E1: 2.. / B1 = 2 => 0 pairs (X) / E1 = 2 => 10 pairs (_) A3,A9: 2.. / A3 = 2 => 10 pairs (_) / A9 = 2 => 0 pairs (X) H6,H9: 2.. / H6 = 2 => 0 pairs (*) / H9 = 2 => 0 pairs (X) F7,I7: 3.. / F7 = 3 => 9 pairs (_) / I7 = 3 => 0 pairs (*) I7,H9: 4.. / I7 = 4 => 0 pairs (X) / H9 = 4 => 0 pairs (_) I1,I7: 4.. / I1 = 4 => 0 pairs (*) / I7 = 4 => 0 pairs (X) H4,H6: 6.. / H4 = 6 => 7 pairs (_) / H6 = 6 => 0 pairs (X) G1,I1: 7.. / G1 = 7 => 0 pairs (*) / I1 = 7 => 0 pairs (X) C7,A9: 7.. / C7 = 7 => 9 pairs (_) / A9 = 7 => 0 pairs (X) G2,G3: 8.. / G2 = 8 => 6 pairs (_) / G3 = 8 => 7 pairs (_) E9,F9: 8.. / E9 = 8 => 8 pairs (_) / F9 = 8 => 8 pairs (_) C3,G3: 8.. / C3 = 8 => 6 pairs (_) / G3 = 8 => 7 pairs (_) * DURATION: 0:00:20.245619 START: 06:37:41.639118 END: 06:38:01.884737 2017-05-01 * CP COUNT: (16) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,C1,C7,D4,G2,G3,G9,H9) * 1..8.6...........2.5......6..2..74.........7..7..3....8..5..61.4.5....8...39....5 * PAIR C1: 4,9 BLK 1 B1: 4,9,2,3 # reduction candidate for 4,9 B1: 4,9 => CTR * 1..826...........225......6..2..74.........7..7..3....8..5736144.5....8.7.39...25 B1: 2,3 # 9 pairs B2: 4,9,3,6,8 # reduction candidate for 4,9 B2: 4,9 # 11 pairs C2: 4,9,6,7,8 # reduction candidate for 4,9 C2: 4,9 # 15 pairs C3: 4,9,7,8 # reduction candidate for 4,9 C3: 4,9 # 10 pairs * PAIR C1: 4,9 ROW 1 E1: 4,9,2,5 # reduction candidate for 4,9 E1: 4,9 => CTR * 12.8.6...........2.5......6..2..74.........7..7..3....8975..61.4.5....8.2.39..745 E1: 2,5 # 9 pairs H1: 4,9,3,5 # reduction candidate for 4,9 H1: 4,9 => CTR * 13.8265.77.......225......6..2..74.........7..7..3....82.5.36144.5....8...39..725 H1: 3,5 # 9 pairs I1: 4,9,3,7 # reduction candidate for 4,9 I1: 4,9 => SOLVED * 139826754768495132254713896382157469546289371971634528897542613425361987613978245 I1: 3,7 => CTR * 1..826..77.......225......6..2..74.........7..7..3....82.5.36144.5....8...39..725 * PAIR C1: 4,9 COL C C5: 4,9,1,6,8 # reduction candidate for 4,9 C5: 4,9 # 10 pairs C6: 4,9,1,6,8 # reduction candidate for 4,9 C6: 4,9 # 9 pairs * PAIR D4: 1,6 BLK 5 E4: 1,6,5,8,9 # reduction candidate for 1,6 E4: 1,6 => CTR * 1..826..77.......225......6..2..74.........7..7..3..6.8.75..6144.5....8...39..725 E4: 5,8,9 # 8 pairs D5: 1,6,2,4 # reduction candidate for 1,6 D5: 1,6 # 10 pairs E5: 1,6,2,4,5,8,9 # reduction candidate for 1,6 E5: 1,6 # 11 pairs D6: 1,6,2,4 # reduction candidate for 1,6 D6: 1,6 # 11 pairs * PAIR D4: 1,6 COL D D8: 1,6,2,3,7 # reduction candidate for 1,6 D8: 1,6 # 13 pairs D8: 2,3,7 # 8 pairs * PAIR B7: 2,9 BLK 7 B8: 2,9,1,6 # reduction candidate for 2,9 B8: 2,9 => SOLVED * 139826754768495132254713896382157469546289371971634528897542613425361987613978245 B8: 1,6 # 9 pairs * PAIR B7: 2,9 COL B B1: 2,9,3,4 # reduction candidate for 2,9 B1: 2,9 => CTR * 1.98.6734.......52.5.....96..21.746........7..7..3..2.8975..61.4.5....8...39...45 B1: 3,4 # 11 pairs * PAIR C7: 7,9 ROW 7 I7: 7,9,3,4 # reduction candidate for 7,9 I7: 7,9 => CTR * 1398267547..3...9225.7...36.821.74633...8..71.71634.288275436194952..387613978245 I7: 3,4 # 9 pairs * PAIR C7: 7,9 COL C C2: 7,9,4,6,8 # reduction candidate for 7,9 C2: 7,9 => CTR * 1.4826..7769...8.2258...1.6.82..74...4.....7..7..3....8..5.36144.5....8...39..725 C2: 4,6,8 # 8 pairs C3: 7,9,4,8 # reduction candidate for 7,9 C3: 7,9 => CTR * 1.4826..77.....1.2259...8.6..2..74...4.....7..7..3....8..5.36144.5....8...39..725 C3: 4,8 # 9 pairs * PAIR G9: 2,7 BLK 9 G8: 2,7,3,9 # reduction candidate for 2,7 G8: 2,7 => CTR * 1..8.6...........2.5......6..2..74.........7..7..3....8..5..61.4.5....8...39....5 G8: 3,9 # 12 pairs * PAIR G9: 2,7 ROW 9 A9: 2,7,6 # reduction candidate for 2,7 A9: 2,7 => CTR * 1.98.67.4........2.5......6..21.746........7..7..3..2.8975..61.4.5....8...39...45 A9: 6 => SOLVED * 139826754768495132254713896382157469546289371971634528897542613425361987613978245 E9: 2,7,1,4,6,8 # reduction candidate for 2,7 E9: 2,7 => SOLVED * 139826754768495132254713896382157469546289371971634528897542613425361987613978245 E9: 1,4,6,8 # 8 pairs * PAIR H9: 2,4 ROW 9 E9: 2,4,1,6,7,8 # reduction candidate for 2,4 E9: 2,4 => CTR * 1..826..7........225......6..2..74.........7..7..3....8.75..6144.5....8.613948725 E9: 1,6,7,8 # 8 pairs F9: 2,4,1,8 # reduction candidate for 2,4 F9: 2,4 => CTR * 1..826..7........225......6..2..74.........7..7..3....8.75..6144.5....8.613984725 F9: 1,8 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-menneske-no-06902995-base-pr-000.dot * REASONING * DIS # B1: 4,9 => CTR => B1: 2,3 * DIS # E1: 4,9 => CTR => E1: 2,5 * DIS # H1: 4,9 => CTR => H1: 3,5 * PRF # I1: 4,9 => SOL * DIS # I1: 3,7 => CTR => I1: 4,9 * DIS # E4: 1,6 => CTR => E4: 5,8,9 * PRF # B8: 2,9 => SOL * DIS # B1: 2,9 => CTR => B1: 3,4 * DIS # I7: 7,9 => CTR => I7: 3,4 * DIS # C2: 7,9 => CTR => C2: 4,6,8 * DIS # C3: 7,9 => CTR => C3: 4,8 * DIS # G8: 2,7 => CTR => G8: 3,9 * DIS # A9: 2,7 => CTR => A9: 6 * PRF # A9: 6 => SOL * PRF # E9: 2,7 => SOL * DIS # E9: 2,4 => CTR => E9: 1,6,7,8 * DIS # F9: 2,4 => CTR => F9: 1,8 * CNT 17 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,C1,C7,D4,G2,G3,G9,H9) * 1..8.6...........2.5......6..2..74.........7..7..3....8..5..61.4.5....8...39....5 * PAIR C1: 4,9 BLK 1 B1: 4,9,2,3 # reduction candidate for 4,9 B1: 4,9 => CTR * 1..826...........225......6..2..74.........7..7..3....8..5736144.5....8.7.39...25 B2: 4,9,3,6,8 # reduction candidate for 4,9 B2: 4,9 # 11 pairs C2: 4,9,6,7,8 # reduction candidate for 4,9 C2: 4,9 # 15 pairs C3: 4,9,7,8 # reduction candidate for 4,9 C3: 4,9 # 10 pairs * PAIR C1: 4,9 ROW 1 E1: 4,9,2,5 # reduction candidate for 4,9 E1: 4,9 => CTR * 12.8.6...........2.5......6..2..74.........7..7..3....8975..61.4.5....8.2.39..745 H1: 4,9,3,5 # reduction candidate for 4,9 H1: 4,9 => CTR * 13.8265.77.......225......6..2..74.........7..7..3....82.5.36144.5....8...39..725 I1: 4,9,7 # reduction candidate for 4,9 I1: 4,9 => SOLVED * 139826754768495132254713896382157469546289371971634528897542613425361987613978245 * DURATION: 0:00:07.293286 START: 06:38:31.359623 END: 06:38:38.652909 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-menneske-no-06902995-base-pr-001.dot * REASONING * DIS # B1: 4,9 => CTR => B1: 2,3 * DIS B1: 2,3 # E1: 4,9 => CTR => E1: 2,5 * DIS B1: 2,3 + E1: 2,5 # H1: 4,9 => CTR => H1: 3,5 * PRF B1: 2,3 + E1: 2,5 + H1: 3,5 # I1: 4,9 => SOL * STA B1: 2,3 + E1: 2,5 + H1: 3,5 + I1: 4,9 * CNT 4 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.menneske.no/sudoku/utskrift.html?number=6902995 umulig * PAIR REDUCTION .. * ROUND 1: 1..8.6...........2.5......6..2..74.........7..7..3....8..5..61.4.5....8...39....5 C1: 4,9 B1: 2,3,4,9 # reduction candidate for 4,9 B1: 4,9 => CTR * 1..826...........225......6..2..74.........7..7..3....8..5736144.5....8.7.39...25 B2: 3,4,6,8,9 # reduction candidate for 4,9 C2: 4,6,7,8,9 # reduction candidate for 4,9 C3: 4,7,8,9 # reduction candidate for 4,9 E1: 2,4,5,9 # reduction candidate for 4,9 E1: 4,9 => CTR * 12.8.6...........2.5......6..2..74.........7..7..3....8975..61.4.5....8.2.39..745 H1: 3,4,5,9 # reduction candidate for 4,9 H1: 4,9 => CTR * 13.8265.77.......225......6..2..74.........7..7..3....82.5.36144.5....8...39..725 I1: 4,7,9 # reduction candidate for 4,9 I1: 4,9 => SOLVED * 139826754768495132254713896382157469546289371971634528897542613425361987613978245 * SOLVED! |:step:| 00 -------------------------------------------------- I8 = 7 => SOL |:step:| 01 --------------------------------------------------
Solution
position: 139826754768495132254713896382157469546289371971634528897542613425361987613978245 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 # B1: 4,9 => CTR => B1: 2,3 * INC # B1: 2,3 => UNS * INC # B2: 4,9 => UNS * INC # C2: 4,9 => UNS * INC # C3: 4,9 => UNS * DIS # E1: 4,9 => CTR => E1: 2,5 * INC # E1: 2,5 => UNS * DIS # H1: 4,9 => CTR => H1: 3,5 * INC # H1: 3,5 => UNS * PRF # I1: 4,9 => SOL * DIS # I1: 3,7 => CTR => I1: 4,9 * INC # C5: 4,9 => UNS * INC # C6: 4,9 => UNS * DIS # E4: 1,6 => CTR => E4: 5,8,9 * INC # E4: 5,8,9 => UNS * INC # D5: 1,6 => UNS * INC # E5: 1,6 => UNS * INC # D6: 1,6 => UNS * INC # D8: 1,6 => UNS * INC # D8: 2,3,7 => UNS * PRF # B8: 2,9 => SOL * INC # B8: 1,6 => UNS * DIS # B1: 2,9 => CTR => B1: 3,4 * INC # B1: 3,4 => UNS * DIS # I7: 7,9 => CTR => I7: 3,4 * INC # I7: 3,4 => UNS * DIS # C2: 7,9 => CTR => C2: 4,6,8 * INC # C2: 4,6,8 => UNS * DIS # C3: 7,9 => CTR => C3: 4,8 * INC # C3: 4,8 => UNS * DIS # G8: 2,7 => CTR => G8: 3,9 * INC # G8: 3,9 => UNS * DIS # A9: 2,7 => CTR => A9: 6 * PRF # A9: 6 => SOL * PRF # E9: 2,7 => SOL * INC # E9: 1,4,6,8 => UNS * DIS # E9: 2,4 => CTR => E9: 1,6,7,8 * INC # E9: 1,6,7,8 => UNS * DIS # F9: 2,4 => CTR => F9: 1,8 * INC # F9: 1,8 => UNS * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B1: 4,9 => CTR => B1: 2,3 * INC B1: 2,3 # B2: 4,9 => UNS * INC B1: 2,3 # C2: 4,9 => UNS * INC B1: 2,3 # C3: 4,9 => UNS * DIS B1: 2,3 # E1: 4,9 => CTR => E1: 2,5 * DIS B1: 2,3 + E1: 2,5 # H1: 4,9 => CTR => H1: 3,5 * PRF B1: 2,3 + E1: 2,5 + H1: 3,5 # I1: 4,9 => SOL * STA B1: 2,3 + E1: 2,5 + H1: 3,5 + I1: 4,9 * CNT 7 HDP CHAINS / 7 HYP OPENED