Analysis of zz-www.sudokuwiki.org-0103-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=103
level: medium
position: ..92....862.........74.61.......7.4.1.8...7.9.7.8.......21.39.........517....83.. initial
Autosolve
position: ..92....862..8......74.61......1784.1.8...7.9.7.8...1...21.3987.......517....83.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G1: 4,5 => CTR => G1: 6 * DIS # B9: 4,5 => CTR => B9: 1,6,9 * DIS # A6: 4,5 => CTR => A6: 2,3,9 * CNT 3 HDP CHAINS / 24 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G1: 4,5 => CTR => G1: 6 * DIS G1: 6 # I2: 3 => CTR => I2: 4,5 * DIS G1: 6 + I2: 4,5 # B7: 4,5 => CTR => B7: 6 * DIS G1: 6 + I2: 4,5 + B7: 6 # B9: 4,5 => CTR => B9: 1,9 * PRF G1: 6 + I2: 4,5 + B7: 6 + B9: 1,9 # C9: 4,5 => SOL * STA G1: 6 + I2: 4,5 + B7: 6 + B9: 1,9 + C9: 4,5 * CNT 5 HDP CHAINS / 11 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..92....862.........74.61.......7.4.1.8...7.9.7.8.......21.39.........517....83.. | initial |
| ..92....862..8......74.61......1784.1.8...7.9.7.8...1...21.3987.......517....83.. | autosolve |
| 459231678621789534387456192236917845148325769975864213562143987893672451714598326 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) F1: 1,5 G2: 4,5 A7: 4,5 H9: 2,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,C2: 1.. / B1 = 1 => 10 pairs (_) / C2 = 1 => 10 pairs (_) F1,F2: 1.. / F1 = 1 => 10 pairs (_) / F2 = 1 => 10 pairs (_) B9,C9: 1.. / B9 = 1 => 10 pairs (_) / C9 = 1 => 10 pairs (_) B1,F1: 1.. / B1 = 1 => 10 pairs (_) / F1 = 1 => 10 pairs (_) C2,F2: 1.. / C2 = 1 => 10 pairs (_) / F2 = 1 => 10 pairs (_) B1,B9: 1.. / B1 = 1 => 10 pairs (_) / B9 = 1 => 10 pairs (_) C2,C9: 1.. / C2 = 1 => 10 pairs (_) / C9 = 1 => 10 pairs (_) H3,I3: 2.. / H3 = 2 => 0 pairs (X) / I3 = 2 => 6 pairs (_) A4,A6: 2.. / A4 = 2 => 4 pairs (_) / A6 = 2 => 0 pairs (X) A4,I4: 2.. / A4 = 2 => 4 pairs (_) / I4 = 2 => 0 pairs (X) G6,G8: 2.. / G6 = 2 => 8 pairs (_) / G8 = 2 => 8 pairs (_) G8,I9: 4.. / G8 = 4 => 12 pairs (_) / I9 = 4 => 8 pairs (_) I2,I9: 4.. / I2 = 4 => 12 pairs (_) / I9 = 4 => 8 pairs (_) G1,H1: 6.. / G1 = 6 => 8 pairs (_) / H1 = 6 => 0 pairs (X) B7,E7: 6.. / B7 = 6 => 6 pairs (_) / E7 = 6 => 9 pairs (_) E1,D2: 7.. / E1 = 7 => 7 pairs (_) / D2 = 7 => 10 pairs (_) H1,H2: 7.. / H1 = 7 => 10 pairs (_) / H2 = 7 => 7 pairs (_) D8,E8: 7.. / D8 = 7 => 7 pairs (_) / E8 = 7 => 10 pairs (_) E1,H1: 7.. / E1 = 7 => 7 pairs (_) / H1 = 7 => 10 pairs (_) D2,H2: 7.. / D2 = 7 => 10 pairs (_) / H2 = 7 => 7 pairs (_) D2,D8: 7.. / D2 = 7 => 10 pairs (_) / D8 = 7 => 7 pairs (_) E1,E8: 7.. / E1 = 7 => 7 pairs (_) / E8 = 7 => 10 pairs (_) A3,B3: 8.. / A3 = 8 => 5 pairs (_) / B3 = 8 => 7 pairs (_) A8,B8: 8.. / A8 = 8 => 7 pairs (_) / B8 = 8 => 5 pairs (_) A3,A8: 8.. / A3 = 8 => 5 pairs (_) / A8 = 8 => 7 pairs (_) B3,B8: 8.. / B3 = 8 => 7 pairs (_) / B8 = 8 => 5 pairs (_) H2,H3: 9.. / H2 = 9 => 13 pairs (_) / H3 = 9 => 7 pairs (_) E3,H3: 9.. / E3 = 9 => 13 pairs (_) / H3 = 9 => 7 pairs (_) * DURATION: 0:00:33.138706 START: 05:18:30.366505 END: 05:19:03.505211 2017-05-01 * CP COUNT: (28) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,F1,G2,H9) * ..92....862..8......74.61......1784.1.8...7.9.7.8...1...21.3987.......517....83.. * PAIR F1: 1,5 BLK 2 F2: 1,5,9 # reduction candidate for 1,5 F2: 9 # 13 pairs F2: 1,5 # 10 pairs * PAIR F1: 1,5 ROW 1 B1: 1,5,3,4 # reduction candidate for 1,5 B1: 3,4 # 11 pairs B1: 1,5 # 8 pairs * PAIR G2: 4,5 BLK 3 G1: 4,5,6 # reduction candidate for 4,5 G1: 4,5 => CTR * 439271568621.8.4738574361922953178461.8...7393748..21.5421639879837..651716..8324 G1: 6 # 8 pairs I2: 4,5,3 # reduction candidate for 4,5 I2: 4,5 # 12 pairs * PAIR G2: 4,5 ROW 2 C2: 4,5,1,3 # reduction candidate for 4,5 C2: 4,5 # 21 pairs C2: 1,3 # 6 pairs * PAIR A7: 4,5 BLK 7 B7: 4,5,6 # reduction candidate for 4,5 B7: 4,5 # 9 pairs B9: 4,5,1,6,9 # reduction candidate for 4,5 B9: 4,5 => CTR * .192.5..862..81..3..74.61.....31784.148..273937.849.1.4621.3987..3....517.1..83.4 B9: 1,6,9 # 4 pairs C9: 4,5,1,6 # reduction candidate for 4,5 C9: 4,5 # 12 pairs * PAIR A7: 4,5 ROW 7 E7: 4,5,6 # reduction candidate for 4,5 E7: 6 # 9 pairs E7: 4,5 # 6 pairs * PAIR A7: 4,5 COL A A1: 4,5,3 # reduction candidate for 4,5 A1: 4,5 # 6 pairs A6: 4,5,2,3,9 # reduction candidate for 4,5 A6: 4,5 => CTR * 3492.1678621789.3.85743619229.31784.138..57.9.7.892513562143987983....517....83.. A6: 2,3,9 # 4 pairs * PAIR H9: 2,6 BLK 9 G8: 2,6,4 # reduction candidate for 2,6 G8: 2,6 # 8 pairs I9: 2,6,4 # reduction candidate for 2,6 I9: 2,6 # 12 pairs * PAIR H9: 2,6 ROW 9 E9: 2,6,4,5,9 # reduction candidate for 2,6 E9: 2,6 # 11 pairs E9: 4,5,9 # 8 pairs * PAIR H9: 2,6 COL H H5: 2,6,3 # reduction candidate for 2,6 H5: 2,6 # 14 pairs H5: 3 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0103-base-pr-000.dot * REASONING * DIS # G1: 4,5 => CTR => G1: 6 * DIS # B9: 4,5 => CTR => B9: 1,6,9 * DIS # A6: 4,5 => CTR => A6: 2,3,9 * CNT 3 HDP CHAINS / 24 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,F1,G2,H9) * ..92....862..8......74.61......1784.1.8...7.9.7.8...1...21.3987.......517....83.. * PAIR F1: 1,5 BLK 2 F2: 1,5,9 # reduction candidate for 1,5 F2: 9 # 13 pairs F2: 1,5 # 10 pairs * PAIR F1: 1,5 ROW 1 B1: 1,5,3,4 # reduction candidate for 1,5 B1: 3,4 # 11 pairs B1: 1,5 # 8 pairs * PAIR G2: 4,5 BLK 3 G1: 4,5,6 # reduction candidate for 4,5 G1: 4,5 => CTR * 439271568621.8.4738574361922953178461.8...7393748..21.5421639879837..651716..8324 I2: 4,5,3 # reduction candidate for 4,5 I2: 4,5 # 12 pairs * RESTART * PAIR G2: 4,5 BLK 3 I2: 4,5,3 # reduction candidate for 4,5 I2: 3 => CTR * ..923.67862.78.493..7496125...31784.1.8..2739.74869512.62153987..36742517..928364 * PAIR A7: 4,5 BLK 7 B7: 4,5,6 # reduction candidate for 4,5 B7: 4,5 => CTR * 4192756386239814758574.61....5.1784.1.8.54729.748.2516542163987.86.49251791528364 B9: 4,5,1,9 # reduction candidate for 4,5 B9: 4,5 => CTR * .192.56.8623.81.....74.61......1784.1.8...7.9.7.8...1..621.3987..4...25175...83.. C9: 4,5,1 # reduction candidate for 4,5 C9: 4,5 => SOLVED * 459231678621789534387456192236917845148325769975864213562143987893672451714598326 * DURATION: 0:00:10.830818 START: 05:19:19.673560 END: 05:19:30.504378 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0103-base-pr-001.dot * REASONING * DIS # G1: 4,5 => CTR => G1: 6 * DIS G1: 6 # I2: 3 => CTR => I2: 4,5 * DIS G1: 6 + I2: 4,5 # B7: 4,5 => CTR => B7: 6 * DIS G1: 6 + I2: 4,5 + B7: 6 # B9: 4,5 => CTR => B9: 1,9 * PRF G1: 6 + I2: 4,5 + B7: 6 + B9: 1,9 # C9: 4,5 => SOL * STA G1: 6 + I2: 4,5 + B7: 6 + B9: 1,9 + C9: 4,5 * CNT 5 HDP CHAINS / 11 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=103
Solution
position: 459231678621789534387456192236917845148325769975864213562143987893672451714598326 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 # F2: 1,5 => UNS * INC # F2: 9 => UNS * INC # B1: 1,5 => UNS * INC # B1: 3,4 => UNS * DIS # G1: 4,5 => CTR => G1: 6 * INC # G1: 6 => UNS * INC # I2: 4,5 => UNS * INC # C2: 4,5 => UNS * INC # C2: 1,3 => UNS * INC # B7: 4,5 => UNS * DIS # B9: 4,5 => CTR => B9: 1,6,9 * INC # B9: 1,6,9 => UNS * INC # C9: 4,5 => UNS * INC # E7: 4,5 => UNS * INC # E7: 6 => UNS * INC # A1: 4,5 => UNS * DIS # A6: 4,5 => CTR => A6: 2,3,9 * INC # A6: 2,3,9 => UNS * INC # G8: 2,6 => UNS * INC # I9: 2,6 => UNS * INC # E9: 2,6 => UNS * INC # E9: 4,5,9 => UNS * INC # H5: 2,6 => UNS * INC # H5: 3 => UNS * CNT 24 HDP CHAINS / 24 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F2: 1,5 => UNS * INC # F2: 9 => UNS * INC # B1: 1,5 => UNS * INC # B1: 3,4 => UNS * DIS # G1: 4,5 => CTR => G1: 6 * INC G1: 6 # I2: 4,5 => UNS * INC G1: 6 # I2: 4,5 => UNS * DIS G1: 6 # I2: 3 => CTR => I2: 4,5 * DIS G1: 6 + I2: 4,5 # B7: 4,5 => CTR => B7: 6 * DIS G1: 6 + I2: 4,5 + B7: 6 # B9: 4,5 => CTR => B9: 1,9 * PRF G1: 6 + I2: 4,5 + B7: 6 + B9: 1,9 # C9: 4,5 => SOL * STA G1: 6 + I2: 4,5 + B7: 6 + B9: 1,9 + C9: 4,5 * CNT 11 HDP CHAINS / 11 HYP OPENED