Analysis of zz-menneske-no-06900300-base.sdk
Contents
Original Sudoku
level: medium
position: .5.7....8...2....7....1..9...7..6..5.2.....8.4.....9....5.3....8...9.2..1....7.49 initial
Autosolve
position: .5.7....8...2....7....1..9...7..6..552.....8.4.....9....5.3....8...9.2..1....7.49 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G5: 4,7 => CTR => G5: 1,3,6 * DIS # B8: 3,6 => CTR => B8: 4,7 * PRF # C9: 3,6 => SOL * DIS # G9: 3,6 => CTR => G9: 5,8 * DIS # G7: 1,6 => CTR => G7: 7,8 * DIS # H8: 1,6 => CTR => H8: 3,5,7 * DIS # I8: 1,6 => CTR => I8: 3 * DIS # D7: 1,6 => CTR => D7: 4,8 * DIS # I5: 1,6 => CTR => I5: 3,4 * CNT 9 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G5: 4,7 => CTR => G5: 1,3,6 * PRF G5: 1,3,6 # C9: 3,6 => SOL * STA G5: 1,3,6 + C9: 3,6 * CNT 2 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5.7....8...2....7....1..9...7..6..5.2.....8.4.....9....5.3....8...9.2..1....7.49 | initial |
| .5.7....8...2....7....1..9...7..6..552.....8.4.....9....5.3....8...9.2..1....7.49 | autosolve |
| 352769418619284537748315692987146325526973184431852976295438761874691253163527849 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) E1: 4,6 A4: 3,9 E5: 4,7 B9: 3,6 I7: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,I3: 2.. / H1 = 2 => 0 pairs (X) / I3 = 2 => 15 pairs (_) A7,C9: 2.. / A7 = 2 => 0 pairs (*) / C9 = 2 => 0 pairs (X) F7,E9: 2.. / F7 = 2 => 5 pairs (_) / E9 = 2 => 0 pairs (*) E4,H4: 2.. / E4 = 2 => 6 pairs (_) / H4 = 2 => 15 pairs (_) A7,F7: 2.. / A7 = 2 => 0 pairs (*) / F7 = 2 => 0 pairs (X) C9,E9: 2.. / C9 = 2 => 5 pairs (_) / E9 = 2 => 0 pairs (*) F6,F7: 2.. / F6 = 2 => 0 pairs (*) / F7 = 2 => 0 pairs (X) I3,I6: 2.. / I3 = 2 => 15 pairs (_) / I6 = 2 => 0 pairs (X) I3,I5: 4.. / I3 = 4 => 0 pairs (X) / I5 = 4 => 14 pairs (_) H8,G9: 5.. / H8 = 5 => 6 pairs (_) / G9 = 5 => 0 pairs (X) H2,H8: 5.. / H2 = 5 => 0 pairs (X) / H8 = 5 => 6 pairs (_) A3,B3: 7.. / A3 = 7 => 5 pairs (_) / B3 = 7 => 0 pairs (X) E5,E6: 7.. / E5 = 7 => 11 pairs (_) / E6 = 7 => 0 pairs (X) G5,H6: 7.. / G5 = 7 => 0 pairs (X) / H6 = 7 => 11 pairs (_) E5,G5: 7.. / E5 = 7 => 11 pairs (_) / G5 = 7 => 0 pairs (X) E6,H6: 7.. / E6 = 7 => 0 pairs (X) / H6 = 7 => 11 pairs (_) B8,H8: 7.. / B8 = 7 => 5 pairs (_) / H8 = 7 => 0 pairs (X) A3,A7: 7.. / A3 = 7 => 5 pairs (_) / A7 = 7 => 0 pairs (X) G5,G7: 7.. / G5 = 7 => 0 pairs (X) / G7 = 7 => 11 pairs (_) G7,G9: 8.. / G7 = 8 => 0 pairs (X) / G9 = 8 => 11 pairs (_) F1,F2: 9.. / F1 = 9 => 5 pairs (_) / F2 = 9 => 7 pairs (_) D4,D5: 9.. / D4 = 9 => 8 pairs (_) / D5 = 9 => 6 pairs (_) A7,B7: 9.. / A7 = 9 => 0 pairs (X) / B7 = 9 => 6 pairs (_) C5,D5: 9.. / C5 = 9 => 8 pairs (_) / D5 = 9 => 6 pairs (_) * DURATION: 0:00:27.616662 START: 06:33:30.731420 END: 06:33:58.348082 2017-05-01 * CP COUNT: (24) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B9,E1,E5,I7) * .5.7....8...2....7....1..9...7..6..552.....8.4.....9....5.3....8...9.2..1....7.49 * PAIR E1: 4,6 BLK 2 E2: 4,6,5,8 # reduction candidate for 4,6 E2: 4,6 # 16 pairs D3: 4,6,3,5,8 # reduction candidate for 4,6 D3: 4,6 # 9 pairs * PAIR E1: 4,6 ROW 1 C1: 4,6,1,2,3,9 # reduction candidate for 4,6 C1: 4,6 # 8 pairs G1: 4,6,1,3 # reduction candidate for 4,6 G1: 4,6 # 7 pairs * PAIR A4: 3,9 BLK 4 B4: 3,9,1,8 # reduction candidate for 3,9 B4: 3,9 # 10 pairs C5: 3,9,1,6 # reduction candidate for 3,9 C5: 3,9 # 7 pairs * PAIR A4: 3,9 ROW 4 D4: 3,9,1,4,8 # reduction candidate for 3,9 D4: 3,9 # 9 pairs D4: 1,4,8 # 6 pairs * PAIR A4: 3,9 COL A A1: 3,9,2,6 # reduction candidate for 3,9 A1: 3,9 # 9 pairs A2: 3,9,6 # reduction candidate for 3,9 A2: 3,9 # 8 pairs * PAIR E5: 4,7 ROW 5 G5: 4,7,1,3,6 # reduction candidate for 4,7 G5: 4,7 => CTR * .5.7...28...2...5727..1..94..7.264.552..4..8.4.....9.27954328..8...9.27.1.2..7549 G5: 1,3,6 # 11 pairs * PAIR B9: 3,6 BLK 7 B8: 3,6,4,7 # reduction candidate for 3,6 B8: 3,6 => CTR * .5.7....8...2...57....1..9...7..6..552....78.4.....9....5.3....8...9.27.1....7549 B8: 4,7 # 6 pairs C8: 3,6,4 # reduction candidate for 3,6 C8: 3,6 # 8 pairs C9: 3,6,2 # reduction candidate for 3,6 C9: 3,6 => SOLVED * 352769418619284537748315692987146325526973184431852976295438761874691253163527849 C9: 2 # 5 pairs * PAIR B9: 3,6 ROW 9 G9: 3,6,5,8 # reduction candidate for 3,6 G9: 3,6 => CTR * .5.76...8...2....77...1..94..7..64.552..4.78.4...7.9.2..5.3287.87..9.25.1.2..7.49 G9: 5,8 # 7 pairs * PAIR B9: 3,6 COL B B2: 3,6,1,4,8,9 # reduction candidate for 3,6 B2: 3,6 # 10 pairs B3: 3,6,4,7,8 # reduction candidate for 3,6 B3: 3,6 # 10 pairs B6: 3,6,1,8 # reduction candidate for 3,6 B6: 3,6 # 7 pairs * PAIR I7: 1,6 BLK 9 G7: 1,6,7,8 # reduction candidate for 1,6 G7: 1,6 => CTR * .5.76...8...2....7....1..94..7..64.552..4.78.4...7.9.2..5.32.7.87..9.2531.2.57849 G7: 7,8 # 6 pairs H7: 1,6,7 # reduction candidate for 1,6 H7: 1,6 # 11 pairs H8: 1,6,3,5,7 # reduction candidate for 1,6 H8: 1,6 => CTR * .5.7....8...2...577...1..9...7..6..552.....8.4...5.97...5.3....87..9.2..1....7549 H8: 3,5,7 # 5 pairs I8: 1,6,3 # reduction candidate for 1,6 I8: 1,6 => CTR * .5.7....8...2....77...1..9...7..6..55269417834...7.962..5.3287.87..9.2..1.2..7.49 I8: 3 # 6 pairs * PAIR I7: 1,6 ROW 7 D7: 1,6,4,8 # reduction candidate for 1,6 D7: 1,6 => CTR * .5.76...86..2....77...1..94..7..64.552..4.78.4...7.9.2..5.3287.87.49.2..1.2..7.49 D7: 4,8 # 6 pairs * PAIR I7: 1,6 COL I I5: 1,6,3,4 # reduction candidate for 1,6 I5: 1,6 => CTR * .5.7...28...2...5727..1..94..7.264.552....78.4.....9.27954328..8...9.273132..7549 I5: 3,4 # 6 pairs I6: 1,6,2,3 # reduction candidate for 1,6 I6: 1,6 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-menneske-no-06900300-base-pr-000.dot * REASONING * DIS # G5: 4,7 => CTR => G5: 1,3,6 * DIS # B8: 3,6 => CTR => B8: 4,7 * PRF # C9: 3,6 => SOL * DIS # G9: 3,6 => CTR => G9: 5,8 * DIS # G7: 1,6 => CTR => G7: 7,8 * DIS # H8: 1,6 => CTR => H8: 3,5,7 * DIS # I8: 1,6 => CTR => I8: 3 * DIS # D7: 1,6 => CTR => D7: 4,8 * DIS # I5: 1,6 => CTR => I5: 3,4 * CNT 9 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B9,E1,E5,I7) * .5.7....8...2....7....1..9...7..6..552.....8.4.....9....5.3....8...9.2..1....7.49 * PAIR E1: 4,6 BLK 2 E2: 4,6,5,8 # reduction candidate for 4,6 E2: 4,6 # 16 pairs D3: 4,6,3,5,8 # reduction candidate for 4,6 D3: 4,6 # 9 pairs * PAIR E1: 4,6 ROW 1 C1: 4,6,1,2,3,9 # reduction candidate for 4,6 C1: 4,6 # 8 pairs G1: 4,6,1,3 # reduction candidate for 4,6 G1: 4,6 # 7 pairs * PAIR A4: 3,9 BLK 4 B4: 3,9,1,8 # reduction candidate for 3,9 B4: 3,9 # 10 pairs C5: 3,9,1,6 # reduction candidate for 3,9 C5: 3,9 # 7 pairs * PAIR A4: 3,9 ROW 4 D4: 3,9,1,4,8 # reduction candidate for 3,9 D4: 3,9 # 9 pairs D4: 1,4,8 # 6 pairs * PAIR A4: 3,9 COL A A1: 3,9,2,6 # reduction candidate for 3,9 A1: 3,9 # 9 pairs A2: 3,9,6 # reduction candidate for 3,9 A2: 3,9 # 8 pairs * PAIR E5: 4,7 ROW 5 G5: 4,7,1,3,6 # reduction candidate for 4,7 G5: 4,7 => CTR * .5.7...28...2...5727..1..94..7.264.552..4..8.4.....9.27954328..8...9.27.1.2..7549 * PAIR RESTART * PAIR B9: 3,6 BLK 7 C9: 3,6,2 # reduction candidate for 3,6 C9: 3,6 => SOLVED * 352769418619284537748315692987146325526973184431852976295438761874691253163527849 * DURATION: 0:00:09.389368 START: 06:34:17.948123 END: 06:34:27.337491 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-menneske-no-06900300-base-pr-001.dot * REASONING * DIS # G5: 4,7 => CTR => G5: 1,3,6 * PRF G5: 1,3,6 # C9: 3,6 => SOL * STA G5: 1,3,6 + C9: 3,6 * CNT 2 HDP CHAINS / 12 HYP OPENED
Header Info
http://www.menneske.no/sudoku/utskrift.html?number=6900300 umulig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: .5.7....8...2....7....1..9...7..6..552.....8.4.....9....5.3....8...9.2..1....7.49 E1: 4,6 E2: 4,5,6,8 # reduction candidate for 4,6 D3: 3,4,5,6,8 # reduction candidate for 4,6 C1: 1,2,3,4,6,9 # reduction candidate for 4,6 G1: 1,3,4,6 # reduction candidate for 4,6 A4: 3,9 B4: 1,3,8,9 # reduction candidate for 3,9 C5: 1,3,6,9 # reduction candidate for 3,9 D4: 1,3,4,8,9 # reduction candidate for 3,9 A1: 2,3,6,9 # reduction candidate for 3,9 A2: 3,6,9 # reduction candidate for 3,9 E5: 4,7 G5: 1,3,4,6,7 # reduction candidate for 4,7 G5: 4,7 => CTR * .5.7...28...2...5727..1..94..7.264.552..4..8.4.....9.27954328..8...9.27.1.2..7549 B9: 3,6 C9: 2,3,6 # reduction candidate for 3,6 C9: 3,6 => SOLVED * 352769418619284537748315692987146325526973184431852976295438761874691253163527849 * SOLVED!
Solution
position: 352769418619284537748315692987146325526973184431852976295438761874691253163527849 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 # E2: 4,6 => UNS * INC # D3: 4,6 => UNS * INC # C1: 4,6 => UNS * INC # G1: 4,6 => UNS * INC # B4: 3,9 => UNS * INC # C5: 3,9 => UNS * INC # D4: 3,9 => UNS * INC # D4: 1,4,8 => UNS * INC # A1: 3,9 => UNS * INC # A2: 3,9 => UNS * DIS # G5: 4,7 => CTR => G5: 1,3,6 * INC # G5: 1,3,6 => UNS * DIS # B8: 3,6 => CTR => B8: 4,7 * INC # B8: 4,7 => UNS * INC # C8: 3,6 => UNS * PRF # C9: 3,6 => SOL * INC # C9: 2 => UNS * DIS # G9: 3,6 => CTR => G9: 5,8 * INC # G9: 5,8 => UNS * INC # B2: 3,6 => UNS * INC # B3: 3,6 => UNS * INC # B6: 3,6 => UNS * DIS # G7: 1,6 => CTR => G7: 7,8 * INC # G7: 7,8 => UNS * INC # H7: 1,6 => UNS * DIS # H8: 1,6 => CTR => H8: 3,5,7 * INC # H8: 3,5,7 => UNS * DIS # I8: 1,6 => CTR => I8: 3 * INC # I8: 3 => UNS * DIS # D7: 1,6 => CTR => D7: 4,8 * INC # D7: 4,8 => UNS * DIS # I5: 1,6 => CTR => I5: 3,4 * INC # I5: 3,4 => UNS * INC # I6: 1,6 => UNS * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E2: 4,6 => UNS * INC # D3: 4,6 => UNS * INC # C1: 4,6 => UNS * INC # G1: 4,6 => UNS * INC # B4: 3,9 => UNS * INC # C5: 3,9 => UNS * INC # D4: 3,9 => UNS * INC # D4: 1,4,8 => UNS * INC # A1: 3,9 => UNS * INC # A2: 3,9 => UNS * DIS # G5: 4,7 => CTR => G5: 1,3,6 * PRF G5: 1,3,6 # C9: 3,6 => SOL * STA G5: 1,3,6 + C9: 3,6 * CNT 12 HDP CHAINS / 12 HYP OPENED