Analysis of zz-www.sudokuwiki.org-0036-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=36
level: medium
position: ..4..8.578..........945.2.....8...4..28.3.76..9...6.....3.825..........398.1..6.. initial
Autosolve
position: ..4..8.5785.........945.2.....8...4..28.3.76..9...6.....3.825..........39851.36.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F2: 1,7 => CTR => F2: 9 * DIS # C4: 1,7 => CTR => C4: 6 * DIS # A6: 1,7 => CTR => A6: 3,4,5 * DIS # F5: 5,9 => CTR => F5: 1,4 * DIS # E8: 4,7 => CTR => E8: 6,9 * PRF # F8: 4,7 => SOL * CNT 6 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F2: 1,7 => CTR => F2: 9 * PRF F2: 9 # F4: 5 => SOL * STA F2: 9 + F4: 5 * CNT 2 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..4..8.578..........945.2.....8...4..28.3.76..9...6.....3.825..........398.1..6.. | initial |
| ..4..8.5785.........945.2.....8...4..28.3.76..9...6.....3.825..........39851.36.. | autosolve |
| 214368957857219436639457218376825149428931765591746382743682591162594873985173624 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) F3: 1,7 C6: 1,7 D5: 5,9 E9: 4,7 H9: 2,7 I9: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,C2: 2.. / A1 = 2 => 6 pairs (_) / C2 = 2 => 9 pairs (_) A8,C8: 2.. / A8 = 2 => 9 pairs (_) / C8 = 2 => 6 pairs (_) H9,I9: 2.. / H9 = 2 => 8 pairs (_) / I9 = 2 => 0 pairs (X) E4,I4: 2.. / E4 = 2 => 9 pairs (_) / I4 = 2 => 9 pairs (_) A1,A8: 2.. / A1 = 2 => 6 pairs (_) / A8 = 2 => 9 pairs (_) C2,C8: 2.. / C2 = 2 => 9 pairs (_) / C8 = 2 => 6 pairs (_) H6,H9: 2.. / H6 = 2 => 0 pairs (X) / H9 = 2 => 8 pairs (_) D1,D2: 3.. / D1 = 3 => 9 pairs (_) / D2 = 3 => 7 pairs (_) G2,I2: 4.. / G2 = 4 => 6 pairs (_) / I2 = 4 => 0 pairs (X) A5,A6: 4.. / A5 = 4 => 0 pairs (*) / A6 = 4 => 0 pairs (X) F5,E6: 4.. / F5 = 4 => 8 pairs (_) / E6 = 4 => 0 pairs (*) B7,B8: 4.. / B7 = 4 => 7 pairs (_) / B8 = 4 => 0 pairs (X) A5,F5: 4.. / A5 = 4 => 0 pairs (*) / F5 = 4 => 0 pairs (X) A6,E6: 4.. / A6 = 4 => 8 pairs (_) / E6 = 4 => 0 pairs (*) B7,I7: 4.. / B7 = 4 => 7 pairs (_) / I7 = 4 => 0 pairs (X) E9,I9: 4.. / E9 = 4 => 0 pairs (X) / I9 = 4 => 8 pairs (_) F5,F8: 4.. / F5 = 4 => 8 pairs (_) / F8 = 4 => 0 pairs (*) G2,G8: 4.. / G2 = 4 => 6 pairs (_) / G8 = 4 => 0 pairs (X) D8,F8: 5.. / D8 = 5 => 8 pairs (_) / F8 = 5 => 8 pairs (_) I2,I3: 6.. / I2 = 6 => 8 pairs (_) / I3 = 6 => 9 pairs (_) E9,H9: 7.. / E9 = 7 => 8 pairs (_) / H9 = 7 => 0 pairs (X) H3,I3: 8.. / H3 = 8 => 9 pairs (_) / I3 = 8 => 8 pairs (_) G8,H8: 8.. / G8 = 8 => 7 pairs (_) / H8 = 8 => 9 pairs (_) G6,G8: 8.. / G6 = 8 => 9 pairs (_) / G8 = 8 => 7 pairs (_) I3,I6: 8.. / I3 = 8 => 8 pairs (_) / I6 = 8 => 9 pairs (_) * DURATION: 0:00:32.887512 START: 04:07:52.426475 END: 04:08:25.313987 2017-05-01 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C6,D5,E9,F3,H9,I9) * ..4..8.5785.........945.2.....8...4..28.3.76..9...6.....3.825..........39851.36.. * PAIR F3: 1,7 BLK 2 E2: 1,7,2,6,9 # reduction candidate for 1,7 E2: 1,7 # 13 pairs F2: 1,7,9 # reduction candidate for 1,7 F2: 1,7 => CTR * ..4.68.5785..9.4.6..945.2.8...81.942.28934761491726..5.436825.9...549..3985173624 F2: 9 # 11 pairs * PAIR F3: 1,7 ROW 3 A3: 1,7,3,6 # reduction candidate for 1,7 A3: 1,7 # 10 pairs B3: 1,7,3,6 # reduction candidate for 1,7 B3: 1,7 # 10 pairs * PAIR F3: 1,7 COL F F4: 1,7,5,9 # reduction candidate for 1,7 F4: 1,7 # 15 pairs F4: 5,9 # 9 pairs * PAIR C6: 1,7 BLK 4 A4: 1,7,3,5,6 # reduction candidate for 1,7 A4: 1,7 # 11 pairs B4: 1,7,3,6 # reduction candidate for 1,7 B4: 1,7 # 9 pairs C4: 1,7,6 # reduction candidate for 1,7 C4: 1,7 => CTR * ..4..8.5785.........9451238...8..349.28.3.76139..46825..3.825.........839851.36.. C4: 6 # 6 pairs A6: 1,7,3,4,5 # reduction candidate for 1,7 A6: 1,7 => CTR * ..4..8.5785.7.94....945.2..5368.7.4.428.35761.9.246..5.43.825.9...594..3985173624 A6: 3,4,5 # 6 pairs * PAIR C6: 1,7 ROW 6 E6: 1,7,2,4 # reduction candidate for 1,7 E6: 1,7 # 11 pairs E6: 2,4 # 7 pairs * PAIR C6: 1,7 COL C C2: 1,7,2,6 # reduction candidate for 1,7 C2: 1,7 # 7 pairs C8: 1,7,2,6 # reduction candidate for 1,7 C8: 1,7 # 10 pairs * PAIR D5: 5,9 BLK 5 F4: 5,9,1,7 # reduction candidate for 5,9 F4: 5,9 # 9 pairs F5: 5,9,1,4 # reduction candidate for 5,9 F5: 5,9 => CTR * ..4..8.5785....496..945.2.8...8..94.42893.761.9..46....43.825.9...594..3985173624 F5: 1,4 # 7 pairs * PAIR D5: 5,9 ROW 5 I5: 5,9,1 # reduction candidate for 5,9 I5: 1 # 11 pairs I5: 5,9 # 9 pairs * PAIR D5: 5,9 COL D D8: 5,9,6,7 # reduction candidate for 5,9 D8: 6,7 # 9 pairs D8: 5,9 # 9 pairs * PAIR E9: 4,7 BLK 8 E8: 4,7,6,9 # reduction candidate for 4,7 E8: 4,7 => CTR * 2.4.6895785....4.6..945.2.8...8..14.128534769497216385..3.825.1..1..58.39851.3624 E8: 6,9 # 7 pairs F8: 4,7,5,9 # reduction candidate for 4,7 F8: 4,7 => SOLVED * 214368957857219436639457218376825149428931765591746382743682591162594873985173624 F8: 5,9 # 9 pairs * PAIR E9: 4,7 COL E E6: 4,7,1,2 # reduction candidate for 4,7 E6: 1,2 # 9 pairs E6: 4,7 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0036-base-pr-000.dot * REASONING * DIS # F2: 1,7 => CTR => F2: 9 * DIS # C4: 1,7 => CTR => C4: 6 * DIS # A6: 1,7 => CTR => A6: 3,4,5 * DIS # F5: 5,9 => CTR => F5: 1,4 * DIS # E8: 4,7 => CTR => E8: 6,9 * PRF # F8: 4,7 => SOL * CNT 6 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C6,D5,E9,F3,H9,I9) * ..4..8.5785.........945.2.....8...4..28.3.76..9...6.....3.825..........39851.36.. * PAIR F3: 1,7 BLK 2 E2: 1,7,2,6,9 # reduction candidate for 1,7 E2: 1,7 # 13 pairs F2: 1,7,9 # reduction candidate for 1,7 F2: 1,7 => CTR * ..4.68.5785..9.4.6..945.2.8...81.942.28934761491726..5.436825.9...549..3985173624 * RESTART * PAIR F3: 1,7 BLK 2 E2: 1,7,2,6 # reduction candidate for 1,7 E2: 1,7 # 13 pairs E2: 2,6 # 12 pairs * PAIR F3: 1,7 ROW 3 A3: 1,7,3,6 # reduction candidate for 1,7 A3: 1,7 # 15 pairs B3: 1,7,3,6 # reduction candidate for 1,7 B3: 1,7 # 15 pairs * PAIR F3: 1,7 COL F F4: 1,7,5 # reduction candidate for 1,7 F4: 5 => SOLVED * 214368957857219436639457218376825149428931765591746382743682591162594873985173624 * DURATION: 0:00:07.556125 START: 04:08:45.474970 END: 04:08:53.031095 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0036-base-pr-001.dot * REASONING * DIS # F2: 1,7 => CTR => F2: 9 * PRF F2: 9 # F4: 5 => SOL * STA F2: 9 + F4: 5 * CNT 2 HDP CHAINS / 8 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=36
Solution
position: 214368957857219436639457218376825149428931765591746382743682591162594873985173624 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: 1,7 => UNS * DIS # F2: 1,7 => CTR => F2: 9 * INC # F2: 9 => UNS * INC # A3: 1,7 => UNS * INC # B3: 1,7 => UNS * INC # F4: 1,7 => UNS * INC # F4: 5,9 => UNS * INC # A4: 1,7 => UNS * INC # B4: 1,7 => UNS * DIS # C4: 1,7 => CTR => C4: 6 * INC # C4: 6 => UNS * DIS # A6: 1,7 => CTR => A6: 3,4,5 * INC # A6: 3,4,5 => UNS * INC # E6: 1,7 => UNS * INC # E6: 2,4 => UNS * INC # C2: 1,7 => UNS * INC # C8: 1,7 => UNS * INC # F4: 5,9 => UNS * DIS # F5: 5,9 => CTR => F5: 1,4 * INC # F5: 1,4 => UNS * INC # I5: 5,9 => UNS * INC # I5: 1 => UNS * INC # D8: 5,9 => UNS * INC # D8: 6,7 => UNS * DIS # E8: 4,7 => CTR => E8: 6,9 * INC # E8: 6,9 => UNS * PRF # F8: 4,7 => SOL * INC # F8: 5,9 => UNS * INC # E6: 4,7 => UNS * INC # E6: 1,2 => UNS * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E2: 1,7 => UNS * DIS # F2: 1,7 => CTR => F2: 9 * INC F2: 9 # E2: 1,7 => UNS * INC F2: 9 # E2: 2,6 => UNS * INC F2: 9 # A3: 1,7 => UNS * INC F2: 9 # B3: 1,7 => UNS * INC F2: 9 # F4: 1,7 => UNS * PRF F2: 9 # F4: 5 => SOL * STA F2: 9 + F4: 5 * CNT 8 HDP CHAINS / 8 HYP OPENED