Analysis of zz-www.sudokuwiki.org-0086-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=86
level: medium
position: .......78.3.8..2..48...71....7..5...9...2...3...9..6....52...81..4..1.5.12....... initial
Autosolve
position: .....2.7873.8..2..482..71....7..58..9..72.5.3...9..6.7..52...81..4..1.5212....... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B5: 6 => CTR => B5: 1,4 * PRF # A8: 3,6 => SOL * DIS # E7: 3,6 => CTR => E7: 4,7,9 * DIS # E7: 3,6 => CTR => E7: 4,7,9 * DIS # E8: 3,6 => CTR => E8: 7,8,9 * PRF # A8: 3,6 => SOL * DIS # D1: 3,6 => CTR => D1: 1,4 * PRF # D4: 3,6 => SOL * CNT 8 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B5: 6 => CTR => B5: 1,4 * PRF B5: 1,4 # A8: 3,6 => SOL * STA B5: 1,4 + A8: 3,6 * CNT 2 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .......78.3.8..2..48...71....7..5...9...2...3...9..6....52...81..4..1.5.12....... | initial |
| .....2.7873.8..2..482..71....7..58..9..72.5.3...9..6.7..52...81..4..1.5212....... | autosolve |
| 569142378731896245482537169217365894946728513853914627695273481374681952128459736 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) A1: 5,6 I4: 4,9 H5: 1,4 A7: 3,6 D8: 3,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,E2: 1.. / C2 = 1 => 10 pairs (_) / E2 = 1 => 8 pairs (_) D1,D4: 1.. / D1 = 1 => 11 pairs (_) / D4 = 1 => 6 pairs (_) A4,A6: 2.. / A4 = 2 => 9 pairs (_) / A6 = 2 => 9 pairs (_) H4,H6: 2.. / H4 = 2 => 9 pairs (_) / H6 = 2 => 9 pairs (_) A4,H4: 2.. / A4 = 2 => 9 pairs (_) / H4 = 2 => 9 pairs (_) A6,H6: 2.. / A6 = 2 => 9 pairs (_) / H6 = 2 => 9 pairs (_) G1,H3: 3.. / G1 = 3 => 0 pairs (*) / H3 = 3 => 0 pairs (X) C6,C9: 3.. / C6 = 3 => 11 pairs (_) / C9 = 3 => 12 pairs (_) H3,H9: 3.. / H3 = 3 => 7 pairs (_) / H9 = 3 => 0 pairs (*) A1,B1: 5.. / A1 = 5 => 4 pairs (_) / B1 = 5 => 0 pairs (X) I2,I3: 5.. / I2 = 5 => 6 pairs (_) / I3 = 5 => 13 pairs (_) A6,B6: 5.. / A6 = 5 => 0 pairs (X) / B6 = 5 => 4 pairs (_) D9,E9: 5.. / D9 = 5 => 8 pairs (_) / E9 = 5 => 8 pairs (_) E2,I2: 5.. / E2 = 5 => 13 pairs (_) / I2 = 5 => 6 pairs (_) A1,A6: 5.. / A1 = 5 => 4 pairs (_) / A6 = 5 => 0 pairs (X) B1,B6: 5.. / B1 = 5 => 0 pairs (X) / B6 = 5 => 4 pairs (_) D3,D9: 5.. / D3 = 5 => 8 pairs (_) / D9 = 5 => 8 pairs (_) H9,I9: 6.. / H9 = 6 => 12 pairs (_) / I9 = 6 => 6 pairs (_) B7,B8: 7.. / B7 = 7 => 6 pairs (_) / B8 = 7 => 7 pairs (_) E9,G9: 7.. / E9 = 7 => 8 pairs (_) / G9 = 7 => 6 pairs (_) A8,C9: 8.. / A8 = 8 => 6 pairs (_) / C9 = 8 => 0 pairs (*) C5,F5: 8.. / C5 = 8 => 9 pairs (_) / F5 = 8 => 13 pairs (_) A8,E8: 8.. / A8 = 8 => 6 pairs (_) / E8 = 8 => 0 pairs (*) A6,A8: 8.. / A6 = 8 => 0 pairs (*) / A8 = 8 => 0 pairs (X) H4,I4: 9.. / H4 = 9 => 14 pairs (_) / I4 = 9 => 7 pairs (_) * DURATION: 0:00:34.936317 START: 04:58:20.308242 END: 04:58:55.244559 2017-05-01 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A7,D8,H5,I4) * .....2.7873.8..2..482..71....7..58..9..72.5.3...9..6.7..52...81..4..1.5212....... * PAIR A1: 5,6 BLK 1 B1: 5,6,1,9 # reduction candidate for 5,6 B1: 5,6 # 14 pairs B1: 1,9 # 6 pairs * PAIR I4: 4,9 BLK 6 H4: 4,9,1,2 # reduction candidate for 4,9 H4: 4,9 # 13 pairs H4: 1,2 # 8 pairs * PAIR I4: 4,9 COL I I2: 4,9,5,6 # reduction candidate for 4,9 I2: 4,9 # 14 pairs I9: 4,9,6 # reduction candidate for 4,9 I9: 4,9 # 12 pairs * PAIR H5: 1,4 BLK 6 H4: 1,4,2,9 # reduction candidate for 1,4 H4: 1,4 # 12 pairs H6: 1,4,2 # reduction candidate for 1,4 H6: 1,4 # 9 pairs * PAIR H5: 1,4 ROW 5 B5: 1,4,6 # reduction candidate for 1,4 B5: 6 => CTR * 5164.2.78739816245482..71.6.4716582996.72.5.325.9..6.7..52...818.46.1.5212.....64 B5: 1,4 # 8 pairs * PAIR A7: 3,6 BLK 7 A8: 3,6,8 # reduction candidate for 3,6 A8: 3,6 => SOLVED * 569142378731896245482537169217365894946728513853914627695273481374681952128459736 A8: 8 # 6 pairs * PAIR A7: 3,6 ROW 7 E7: 3,6,4,7,9 # reduction candidate for 3,6 E7: 3,6 => CTR * 5..3.2.7873.8..2..4825971363.71.58299..72.5.325.9.36.76.523..818946713521234..... E7: 4,7,9 # 5 pairs F7: 3,6,4,9 # reduction candidate for 3,6 F7: 3,6 # 8 pairs * PAIR A7: 3,6 COL A A4: 3,6,2 # reduction candidate for 3,6 A4: 3,6 # 9 pairs A4: 2 # 9 pairs * PAIR D8: 3,6 BLK 8 E7: 3,6,4,7,9 # reduction candidate for 3,6 E7: 3,6 => CTR * 5..3.2.7873.8..2..4825971363.71.58299..72.5.325.9.36.76.523..818946713521234..... E7: 4,7,9 # 5 pairs F7: 3,6,4,9 # reduction candidate for 3,6 F7: 3,6 # 8 pairs E8: 3,6,7,8,9 # reduction candidate for 3,6 E8: 3,6 => CTR * 5...32.7873185.2..4826971353.7..58299..7265.325.9836476.52..3818.4361.52123578... E8: 7,8,9 # 5 pairs * PAIR D8: 3,6 ROW 8 A8: 3,6,8 # reduction candidate for 3,6 A8: 3,6 => SOLVED * 569142378731896245482537169217365894946728513853914627695273481374681952128459736 A8: 8 # 6 pairs * PAIR D8: 3,6 COL D D1: 3,6,1,4 # reduction candidate for 3,6 D1: 3,6 => CTR * ...34297873.81.2454825.71..267135894948726513...984627..52..4818.4..1.5212.4587.. D1: 1,4 # 6 pairs D3: 3,6,5 # reduction candidate for 3,6 D3: 3,6 # 8 pairs D4: 3,6,1,4 # reduction candidate for 3,6 D4: 3,6 => SOLVED * 569142378731896245482537169217365894946728513853914627695273481374681952128459736 D4: 1,4 # 6 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0086-base-pr-000.dot * REASONING * DIS # B5: 6 => CTR => B5: 1,4 * PRF # A8: 3,6 => SOL * DIS # E7: 3,6 => CTR => E7: 4,7,9 * DIS # E7: 3,6 => CTR => E7: 4,7,9 * DIS # E8: 3,6 => CTR => E8: 7,8,9 * PRF # A8: 3,6 => SOL * DIS # D1: 3,6 => CTR => D1: 1,4 * PRF # D4: 3,6 => SOL * CNT 8 HDP CHAINS / 29 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A7,D8,H5,I4) * .....2.7873.8..2..482..71....7..58..9..72.5.3...9..6.7..52...81..4..1.5212....... * PAIR A1: 5,6 BLK 1 B1: 5,6,1,9 # reduction candidate for 5,6 B1: 5,6 # 14 pairs B1: 1,9 # 6 pairs * PAIR I4: 4,9 BLK 6 H4: 4,9,1,2 # reduction candidate for 4,9 H4: 4,9 # 13 pairs H4: 1,2 # 8 pairs * PAIR I4: 4,9 COL I I2: 4,9,5,6 # reduction candidate for 4,9 I2: 4,9 # 14 pairs I9: 4,9,6 # reduction candidate for 4,9 I9: 4,9 # 12 pairs * PAIR H5: 1,4 BLK 6 H4: 1,4,2,9 # reduction candidate for 1,4 H4: 1,4 # 12 pairs H6: 1,4,2 # reduction candidate for 1,4 H6: 1,4 # 9 pairs * PAIR H5: 1,4 ROW 5 B5: 1,4,6 # reduction candidate for 1,4 B5: 6 => CTR * 5164.2.78739816245482..71.6.4716582996.72.5.325.9..6.7..52...818.46.1.5212.....64 * PAIR RESTART * PAIR H5: 1,4 BLK 6 H4: 1,4,2,9 # reduction candidate for 1,4 H4: 1,4 # 15 pairs H6: 1,4,2 # reduction candidate for 1,4 H6: 1,4 # 12 pairs * PAIR A7: 3,6 BLK 7 A8: 3,6,8 # reduction candidate for 3,6 A8: 3,6 => SOLVED * 569142378731896245482537169217365894946728513853914627695273481374681952128459736 * DURATION: 0:00:11.979601 START: 04:59:19.501337 END: 04:59:31.480938 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0086-base-pr-001.dot * REASONING * DIS # B5: 6 => CTR => B5: 1,4 * PRF B5: 1,4 # A8: 3,6 => SOL * STA B5: 1,4 + A8: 3,6 * CNT 2 HDP CHAINS / 13 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=86
Solution
position: 569142378731896245482537169217365894946728513853914627695273481374681952128459736 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 # B1: 5,6 => UNS * INC # B1: 1,9 => UNS * INC # H4: 4,9 => UNS * INC # H4: 1,2 => UNS * INC # I2: 4,9 => UNS * INC # I9: 4,9 => UNS * INC # H4: 1,4 => UNS * INC # H6: 1,4 => UNS * INC # B5: 1,4 => UNS * DIS # B5: 6 => CTR => B5: 1,4 * PRF # A8: 3,6 => SOL * INC # A8: 8 => UNS * DIS # E7: 3,6 => CTR => E7: 4,7,9 * INC # E7: 4,7,9 => UNS * INC # F7: 3,6 => UNS * INC # A4: 3,6 => UNS * INC # A4: 2 => UNS * DIS # E7: 3,6 => CTR => E7: 4,7,9 * INC # E7: 4,7,9 => UNS * INC # F7: 3,6 => UNS * DIS # E8: 3,6 => CTR => E8: 7,8,9 * INC # E8: 7,8,9 => UNS * PRF # A8: 3,6 => SOL * INC # A8: 8 => UNS * DIS # D1: 3,6 => CTR => D1: 1,4 * INC # D1: 1,4 => UNS * INC # D3: 3,6 => UNS * PRF # D4: 3,6 => SOL * INC # D4: 1,4 => UNS * CNT 29 HDP CHAINS / 29 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 5,6 => UNS * INC # B1: 1,9 => UNS * INC # H4: 4,9 => UNS * INC # H4: 1,2 => UNS * INC # I2: 4,9 => UNS * INC # I9: 4,9 => UNS * INC # H4: 1,4 => UNS * INC # H6: 1,4 => UNS * INC # B5: 1,4 => UNS * DIS # B5: 6 => CTR => B5: 1,4 * INC B5: 1,4 # H4: 1,4 => UNS * INC B5: 1,4 # H6: 1,4 => UNS * PRF B5: 1,4 # A8: 3,6 => SOL * STA B5: 1,4 + A8: 3,6 * CNT 13 HDP CHAINS / 13 HYP OPENED