Analysis of zz-menneske-no-06911017-base.sdk
Contents
Original Sudoku
level: medium
position: ..2...7.....1..3.......6.29.......17..8..4...56.....3.14.6.......5..7..3...3..59. initial
Autosolve
position: ..2...7.....1..3.......6.29.......17..8..4...56.....3.1436...7...5..7..3...3..59. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I1: 5,6 => CTR => I1: 1,4 * DIS # C3: 7 => CTR => C3: 1,4 * DIS # G8: 6 => CTR => G8: 1,4 * PRF # C6: 4,9 => SOL * PRF # G4: 4,9 => SOL * DIS # I5: 5,6 => CTR => I5: 2 * DIS # E4: 5,9 => CTR => E4: 2,3,6,8 * DIS # F4: 5,9 => CTR => F4: 2,3,8 * PRF # G6: 2,8 => SOL * DIS # I6: 2,8 => CTR => I6: 4 * DIS # G8: 4,6 => CTR => G8: 1 * PRF # G8: 1 => SOL * PRF # I9: 4,6 => SOL * DIS # I9: 1 => CTR => I9: 4,6 * CNT 14 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 # I1: 5,6 => CTR => I1: 1,4 * DIS I1: 1,4 # A4: 4,9 => CTR => A4: 2,3 * PRF I1: 1,4 + A4: 2,3 # C6: 4,9 => SOL * STA I1: 1,4 + A4: 2,3 + C6: 4,9 * CNT 3 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..2...7.....1..3.......6.29.......17..8..4...56.....3.14.6.......5..7..3...3..59. | initial |
| ..2...7.....1..3.......6.29.......17..8..4...56.....3.1436...7...5..7..3...3..59. | autosolve |
| 982453761476129385351876429234568917718934652569712834143695278695287143827341596 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) G3: 1,4 C4: 4,9 H5: 5,6 C9: 6,7 E7: 5,9 F7: 5,9 G7: 2,8 I7: 2,8 H8: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I1,G3: 1.. / I1 = 1 => 0 pairs (*) / G3 = 1 => 0 pairs (X) B5,C6: 1.. / B5 = 1 => 0 pairs (*) / C6 = 1 => 0 pairs (X) G8,I9: 1.. / G8 = 1 => 0 pairs (*) / I9 = 1 => 0 pairs (X) B1,I1: 1.. / B1 = 1 => 0 pairs (X) / I1 = 1 => 0 pairs (_) B5,E5: 1.. / B5 = 1 => 0 pairs (*) / E5 = 1 => 0 pairs (X) E8,G8: 1.. / E8 = 1 => 0 pairs (X) / G8 = 1 => 0 pairs (_) C3,C6: 1.. / C3 = 1 => 0 pairs (*) / C6 = 1 => 0 pairs (X) F6,F9: 1.. / F6 = 1 => 0 pairs (X) / F9 = 1 => 0 pairs (_) G3,G8: 1.. / G3 = 1 => 0 pairs (X) / G8 = 1 => 0 pairs (_) I1,I9: 1.. / I1 = 1 => 0 pairs (*) / I9 = 1 => 0 pairs (X) E2,F2: 2.. / E2 = 2 => 11 pairs (_) / F2 = 2 => 10 pairs (_) G7,I7: 2.. / G7 = 2 => 9 pairs (_) / I7 = 2 => 0 pairs (X) F1,F4: 3.. / F1 = 3 => 0 pairs (*) / F4 = 3 => 0 pairs (X) E9,I9: 4.. / E9 = 4 => 11 pairs (_) / I9 = 4 => 0 pairs (X) H5,I5: 5.. / H5 = 5 => 9 pairs (_) / I5 = 5 => 0 pairs (X) E7,F7: 5.. / E7 = 5 => 7 pairs (_) / F7 = 5 => 7 pairs (_) E4,E5: 6.. / E4 = 6 => 9 pairs (_) / E5 = 6 => 0 pairs (X) E4,G4: 6.. / E4 = 6 => 9 pairs (_) / G4 = 6 => 0 pairs (X) C2,C9: 6.. / C2 = 6 => 15 pairs (_) / C9 = 6 => 9 pairs (_) H1,H2: 8.. / H1 = 8 => 9 pairs (_) / H2 = 8 => 9 pairs (_) G7,I7: 8.. / G7 = 8 => 0 pairs (X) / I7 = 8 => 9 pairs (_) I6,I7: 8.. / I6 = 8 => 0 pairs (X) / I7 = 8 => 9 pairs (_) A8,B8: 9.. / A8 = 9 => 11 pairs (_) / B8 = 9 => 10 pairs (_) E7,F7: 9.. / E7 = 9 => 7 pairs (_) / F7 = 9 => 7 pairs (_) * DURATION: 0:00:33.770869 START: 06:49:43.629780 END: 06:50:17.400649 2017-05-01 * CP COUNT: (24) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C4,C9,E7,F7,G3,G7,H5,H8,I7) * ..2...7.....1..3.......6.29.......17..8..4...56.....3.1436...7...5..7..3...3..59. * PAIR G3: 1,4 BLK 3 I1: 1,4,5,6 # reduction candidate for 1,4 I1: 5,6 => CTR * .12...7.....1..3.......6129.......17..8.14...561....3.1436...7...5..7..3...3.159. I1: 1,4 # 14 pairs * PAIR G3: 1,4 ROW 3 C3: 1,4,7 # reduction candidate for 1,4 C3: 7 => CTR * ..2...7.1...1723...17..6429.......17..8.14...5617...3.1436...7...5..7163..63.1594 C3: 1,4 # 10 pairs * PAIR G3: 1,4 COL G G8: 1,4,6 # reduction candidate for 1,4 G8: 6 => CTR * ..2...7.....1..3.......6129.......17..8..4...561....3.1436...7...5.17643...34.591 G8: 1,4 # 13 pairs * PAIR C4: 4,9 BLK 4 A4: 4,9,2,3 # reduction candidate for 4,9 A4: 4,9 # 12 pairs C6: 4,9,1,7 # reduction candidate for 4,9 C6: 4,9 => SOLVED * 982453761476129385351876429234568917718934652569712834143695278695287143827341596 C6: 1,7 # 10 pairs * PAIR C4: 4,9 ROW 4 G4: 4,9,2,6,8 # reduction candidate for 4,9 G4: 4,9 => SOLVED * 982453761476129385351876429234568917718934652569712834143695278695287143827341596 G4: 2,6,8 # 9 pairs * PAIR C4: 4,9 COL C C2: 4,9,6,7 # reduction candidate for 4,9 C2: 6,7 # 15 pairs C2: 4,9 # 12 pairs * PAIR H5: 5,6 BLK 6 I5: 5,6,2 # reduction candidate for 5,6 I5: 5,6 => CTR * .12...7.....1..3.......6129....6..17..8.14...561...43.1436...7...5..7643...34.591 I5: 2 # 13 pairs * PAIR H5: 5,6 COL H H1: 5,6,4,8 # reduction candidate for 5,6 H1: 5,6 # 12 pairs H2: 5,6,4,8 # reduction candidate for 5,6 H2: 5,6 # 12 pairs * PAIR C9: 6,7 BLK 7 A9: 6,7,2,8 # reduction candidate for 6,7 A9: 6,7 # 12 pairs A9: 2,8 # 10 pairs * PAIR C9: 6,7 COL C C2: 6,7,4,9 # reduction candidate for 6,7 C2: 6,7 # 15 pairs C2: 4,9 # 12 pairs * PAIR E7: 5,9 COL E E1: 5,9,3,4,8 # reduction candidate for 5,9 E1: 5,9 # 10 pairs E2: 5,9,2,4,7,8 # reduction candidate for 5,9 E2: 5,9 # 13 pairs E4: 5,9,2,3,6,8 # reduction candidate for 5,9 E4: 5,9 => CTR * ..2...7.1...1..3.5..1..6429...853617318764952567...834143695278..52.7143..634.59. E4: 2,3,6,8 # 9 pairs * PAIR F7: 5,9 COL F F1: 5,9,3,8 # reduction candidate for 5,9 F1: 5,9 # 16 pairs F2: 5,9,2,8 # reduction candidate for 5,9 F2: 5,9 # 13 pairs F4: 5,9,2,3,8 # reduction candidate for 5,9 F4: 5,9 => CTR * ..24.37614.619.3.5..1..6429..4....17.18..4.52569.1.8341436..278695..7143..7341596 F4: 2,3,8 # 9 pairs * PAIR G7: 2,8 COL G G4: 2,8,4,6,9 # reduction candidate for 2,8 G4: 2,8 # 12 pairs G6: 2,8,4,9 # reduction candidate for 2,8 G6: 2,8 => SOLVED * 982453761476129385351876429234568917718934652569712834143695278695287143827341596 G6: 4,9 # 10 pairs * PAIR I7: 2,8 COL I I6: 2,8,4 # reduction candidate for 2,8 I6: 2,8 => CTR * ..2...7.....1..3.......6129.......17..8..4...561...43.1436...7...5.17643...34.591 I6: 4 # 13 pairs * PAIR H8: 4,6 BLK 9 G8: 4,6,1 # reduction candidate for 4,6 G8: 4,6 => CTR * ..2...7.....1..3.......6129.......17..8..4...561....3.1436...7...5.17..3...3..591 G8: 1 => SOLVED * 982453761476129385351876429234568917718934652569712834143695278695287143827341596 I9: 4,6,1 # reduction candidate for 4,6 I9: 4,6 => SOLVED * 982453761476129385351876429234568917718934652569712834143695278695287143827341596 I9: 1 => CTR * .12...7.....1..3.......6129.......17..8.14...561....3.1436...7...5..7..3...34.591 * PAIR H8: 4,6 COL H H1: 4,6,5,8 # reduction candidate for 4,6 H1: 4,6 # 10 pairs H2: 4,6,5,8 # reduction candidate for 4,6 H2: 4,6 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-menneske-no-06911017-base-pr-000.dot * REASONING * DIS # I1: 5,6 => CTR => I1: 1,4 * DIS # C3: 7 => CTR => C3: 1,4 * DIS # G8: 6 => CTR => G8: 1,4 * PRF # C6: 4,9 => SOL * PRF # G4: 4,9 => SOL * DIS # I5: 5,6 => CTR => I5: 2 * DIS # E4: 5,9 => CTR => E4: 2,3,6,8 * DIS # F4: 5,9 => CTR => F4: 2,3,8 * PRF # G6: 2,8 => SOL * DIS # I6: 2,8 => CTR => I6: 4 * DIS # G8: 4,6 => CTR => G8: 1 * PRF # G8: 1 => SOL * PRF # I9: 4,6 => SOL * DIS # I9: 1 => CTR => I9: 4,6 * CNT 14 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C4,C9,E7,F7,G3,G7,H5,H8,I7) * ..2...7.....1..3.......6.29.......17..8..4...56.....3.1436...7...5..7..3...3..59. * PAIR G3: 1,4 BLK 3 I1: 1,4,5,6 # reduction candidate for 1,4 I1: 5,6 => CTR * .12...7.....1..3.......6129.......17..8.14...561....3.1436...7...5..7..3...3.159. * PAIR C4: 4,9 BLK 4 A4: 4,9,2,3 # reduction candidate for 4,9 A4: 4,9 => CTR * .12...7.4...1..3....74.6129.......17..8.14...561...43.1436...7...5..7643..634.591 C6: 4,9,1,7 # reduction candidate for 4,9 C6: 4,9 => SOLVED * 982453761476129385351876429234568917718934652569712834143695278695287143827341596 * DURATION: 0:00:05.033629 START: 06:50:49.474129 END: 06:50:54.507758 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-menneske-no-06911017-base-pr-001.dot * REASONING * DIS # I1: 5,6 => CTR => I1: 1,4 * DIS I1: 1,4 # A4: 4,9 => CTR => A4: 2,3 * PRF I1: 1,4 + A4: 2,3 # C6: 4,9 => SOL * STA I1: 1,4 + A4: 2,3 + C6: 4,9 * CNT 3 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.menneske.no/sudoku/utskrift.html?number=6911017 umulig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: ..2...7.....1..3.......6.29.......17..8..4...56.....3.1436...7...5..7..3...3..59. G3: 1,4 I1: 1,4,5,6 # reduction candidate for 1,4 I1: 5,6 => CTR * .12...7.....1..3.......6129.......17..8.14...561....3.1436...7...5..7..3...3.159. C4: 4,9 A4: 2,3,4,9 # reduction candidate for 4,9 A4: 4,9 => CTR * .12...7.4...1..3....74.6129.......17..8.14...561...43.1436...7...5..7643..634.591 C6: 1,4,7,9 # reduction candidate for 4,9 C6: 4,9 => SOLVED * 982453761476129385351876429234568917718934652569712834143695278695287143827341596 * SOLVED!
Solution
position: 982453761476129385351876429234568917718934652569712834143695278695287143827341596 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 # I1: 1,4 => UNS * DIS # I1: 5,6 => CTR => I1: 1,4 * INC # C3: 1,4 => UNS * DIS # C3: 7 => CTR => C3: 1,4 * INC # G8: 1,4 => UNS * DIS # G8: 6 => CTR => G8: 1,4 * INC # A4: 4,9 => UNS * PRF # C6: 4,9 => SOL * INC # C6: 1,7 => UNS * PRF # G4: 4,9 => SOL * INC # G4: 2,6,8 => UNS * INC # C2: 4,9 => UNS * INC # C2: 6,7 => UNS * DIS # I5: 5,6 => CTR => I5: 2 * INC # I5: 2 => UNS * INC # H1: 5,6 => UNS * INC # H2: 5,6 => UNS * INC # A9: 6,7 => UNS * INC # A9: 2,8 => UNS * INC # C2: 6,7 => UNS * INC # C2: 4,9 => UNS * INC # E1: 5,9 => UNS * INC # E2: 5,9 => UNS * DIS # E4: 5,9 => CTR => E4: 2,3,6,8 * INC # E4: 2,3,6,8 => UNS * INC # F1: 5,9 => UNS * INC # F2: 5,9 => UNS * DIS # F4: 5,9 => CTR => F4: 2,3,8 * INC # F4: 2,3,8 => UNS * INC # G4: 2,8 => UNS * PRF # G6: 2,8 => SOL * INC # G6: 4,9 => UNS * DIS # I6: 2,8 => CTR => I6: 4 * INC # I6: 4 => UNS * DIS # G8: 4,6 => CTR => G8: 1 * PRF # G8: 1 => SOL * PRF # I9: 4,6 => SOL * DIS # I9: 1 => CTR => I9: 4,6 * INC # H1: 4,6 => UNS * INC # H2: 4,6 => UNS * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # I1: 1,4 => UNS * DIS # I1: 5,6 => CTR => I1: 1,4 * DIS I1: 1,4 # A4: 4,9 => CTR => A4: 2,3 * PRF I1: 1,4 + A4: 2,3 # C6: 4,9 => SOL * STA I1: 1,4 + A4: 2,3 + C6: 4,9 * CNT 4 HDP CHAINS / 4 HYP OPENED