Analysis of zz-www.sudokuwiki.org-0112-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=112
level: medium
position: .5.........61.8....3.6.7..1.1....36.6.......9.48....2.7..9.1.8....2.54.........9. initial
Autosolve
position: .5.........61.8....3.6.7..1.1....36.6.......9.48....2.7..9.1.8....2.54.........9. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E1: 3,4 => CTR => E1: 2,9 * DIS # F1: 3,4 => CTR => F1: 2,9 * DIS # I1: 3,4 => CTR => I1: 2,6,7,8 * DIS # D5: 3,4 => CTR => D5: 5,7,8 * DIS # D9: 3,4 => CTR => D9: 7,8 * DIS # I2: 4,5 => CTR => I2: 2,3,7 * DIS # E3: 2,9 => CTR => E3: 4,5 * DIS # H5: 4,5 => CTR => H5: 1,7 * DIS # C5: 2,7 => CTR => C5: 3,5 * PRF # E5: 2,7 => SOL * PRF # B2: 2,7 => SOL * DIS # B2: 9 => CTR => B2: 2,7 * DIS # I4: 5,7 => CTR => I4: 4,8 * DIS # G5: 5,7 => CTR => G5: 1,8 * DIS # H5: 5,7 => CTR => H5: 1,4 * DIS # D6: 5,7 => CTR => D6: 3 * DIS # B9: 2,6 => CTR => B9: 8 * CNT 17 HDP CHAINS / 41 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E1: 3,4 => CTR => E1: 2,9 * DIS E1: 2,9 # F1: 3,4 => CTR => F1: 2,9 * DIS E1: 2,9 + F1: 2,9 # E2: 5 => CTR => E2: 3,4 * DIS E1: 2,9 + F1: 2,9 + E2: 3,4 # D5: 3,4 => CTR => D5: 5,7 * DIS E1: 2,9 + F1: 2,9 + E2: 3,4 + D5: 5,7 # D9: 3,4 => CTR => D9: 7,8 * PRF E1: 2,9 + F1: 2,9 + E2: 3,4 + D5: 5,7 + D9: 7,8 => SOL * STA E1: 2,9 + F1: 2,9 + E2: 3,4 + D5: 5,7 + D9: 7,8 * CNT 6 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5.........61.8....3.6.7..1.1....36.6.......9.48....2.7..9.1.8....2.54.........9. | initial |
| .5.........61.8....3.6.7..1.1....36.6.......9.48....2.7..9.1.8....2.54.........9. | autosolve |
| 157492638426138957839657241215879364673524819948316725762941583391285476584763192 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) D1: 3,4 H3: 4,5 B5: 2,7 I6: 5,7 B7: 2,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,C1: 1.. / A1 = 1 => 8 pairs (_) / C1 = 1 => 0 pairs (X) E5,E6: 1.. / E5 = 1 => 0 pairs (X) / E6 = 1 => 17 pairs (_) H8,G9: 1.. / H8 = 1 => 0 pairs (X) / G9 = 1 => 20 pairs (_) E6,G6: 1.. / E6 = 1 => 17 pairs (_) / G6 = 1 => 0 pairs (X) H5,H8: 1.. / H5 = 1 => 20 pairs (_) / H8 = 1 => 0 pairs (X) C5,A6: 3.. / C5 = 3 => 8 pairs (_) / A6 = 3 => 0 pairs (X) I4,H5: 4.. / I4 = 4 => 7 pairs (_) / H5 = 4 => 0 pairs (X) C7,E7: 4.. / C7 = 4 => 7 pairs (_) / E7 = 4 => 7 pairs (_) E2,E3: 5.. / E2 = 5 => 6 pairs (_) / E3 = 5 => 9 pairs (_) G1,I1: 6.. / G1 = 6 => 6 pairs (_) / I1 = 6 => 0 pairs (X) E6,F6: 6.. / E6 = 6 => 0 pairs (X) / F6 = 6 => 6 pairs (_) F6,F9: 6.. / F6 = 6 => 6 pairs (_) / F9 = 6 => 0 pairs (X) C1,B2: 7.. / C1 = 7 => 28 pairs (_) / B2 = 7 => 0 pairs (X) B2,B5: 7.. / B2 = 7 => 0 pairs (X) / B5 = 7 => 28 pairs (_) A1,A3: 8.. / A1 = 8 => 0 pairs (X) / A3 = 8 => 7 pairs (_) I4,G5: 8.. / I4 = 8 => 0 pairs (X) / G5 = 8 => 6 pairs (_) B8,B9: 8.. / B8 = 8 => 0 pairs (X) / B9 = 8 => 6 pairs (_) A3,G3: 8.. / A3 = 8 => 7 pairs (_) / G3 = 8 => 0 pairs (X) B8,E8: 8.. / B8 = 8 => 0 pairs (X) / E8 = 8 => 6 pairs (_) I1,I4: 8.. / I1 = 8 => 6 pairs (_) / I4 = 8 => 0 pairs (X) B2,B8: 9.. / B2 = 9 => 0 pairs (X) / B8 = 9 => 0 pairs (_) * DURATION: 0:00:27.007991 START: 05:31:34.032934 END: 05:32:01.040925 2017-05-01 * CP COUNT: (21) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,B7,D1,H3,I6) * .5.........61.8....3.6.7..1.1....36.6.......9.48....2.7..9.1.8....2.54.........9. * PAIR D1: 3,4 BLK 2 E1: 3,4,2,9 # reduction candidate for 3,4 E1: 3,4 => CTR * .5.....7..761.8....3.6.7..1.1....36.62......9.48....2.76.9.1.8..9.2854.........9. E1: 2,9 # 6 pairs F1: 3,4,2,9 # reduction candidate for 3,4 F1: 3,4 => CTR * .5.....7..761.8....3.6.7..1.1....36.62......9.48....2.76.9.1.8..9.2854.........9. F1: 2,9 # 6 pairs E2: 3,4,2,5,9 # reduction candidate for 3,4 E2: 3,4 # 15 pairs * PAIR D1: 3,4 ROW 1 H1: 3,4,7 # reduction candidate for 3,4 H1: 3,4 # 28 pairs I1: 3,4,2,6,7,8 # reduction candidate for 3,4 I1: 3,4 => CTR * 851...67..761.8932.3.6.7851.1....36862...3.49348....2.76.9.1.8.98.2.541........9. I1: 2,6,7,8 # 5 pairs * PAIR D1: 3,4 COL D D5: 3,4,5,7,8 # reduction candidate for 3,4 D5: 3,4 => CTR * 157...638.96138.7.83.657941.1....36467.3148593485..1277.4961.839.32.541...1...79. D5: 5,7,8 # 5 pairs D9: 3,4,7,8 # reduction candidate for 3,4 D9: 3,4 => CTR * 157....3..96138.7.83.657941.1....36467..14..9.48...12.7..9.1.8....2.541...1...79. D9: 7,8 # 6 pairs * PAIR H3: 4,5 BLK 3 H2: 4,5,3,7 # reduction candidate for 4,5 H2: 4,5 # 13 pairs I2: 4,5,2,3,7 # reduction candidate for 4,5 I2: 4,5 => CTR * 1574..63849613827583265794121.789364673...859.48...1277..9.1.83...275416..1...792 I2: 2,3,7 # 8 pairs * PAIR H3: 4,5 ROW 3 E3: 4,5,2,9 # reduction candidate for 4,5 E3: 2,9 => CTR * .5.....7..76158....3.6.7..1.1....36.62......9.48....2.76.9.1.8..9.2854.........9. E3: 4,5 # 7 pairs * PAIR H3: 4,5 COL H H5: 4,5,1,7 # reduction candidate for 4,5 H5: 4,5 => CTR * 1574..638496138.7.83265794121.789364673...859.48...1277..9.1.83...275416..1...79. H5: 1,7 # 11 pairs * PAIR B5: 2,7 BLK 4 C4: 2,7,5,9 # reduction candidate for 2,7 C4: 2,7 # 10 pairs C5: 2,7,3,5 # reduction candidate for 2,7 C5: 2,7 => CTR * .57....3..96138.7..34657..1519...36.672.1...9348...12.7..9.1.8.9.32.541........9. C5: 3,5 # 6 pairs * PAIR B5: 2,7 ROW 5 E5: 2,7,1,3,4,8 # reduction candidate for 2,7 E5: 2,7 => SOLVED * 157492638426138957839657241215879364673524819948316725762941583391285476584763192 E5: 1,3,4,8 # 5 pairs * PAIR B5: 2,7 COL B B2: 2,7,9 # reduction candidate for 2,7 B2: 2,7 => SOLVED * 157492638426138957839657241215879364673524819948316725762941583391285476584763192 B2: 9 => CTR * 157.926.84961.8.7.8326.79.1215..9364673...8.9948....2.7..9.1.8.3.92.541.5.1....9. * PAIR I6: 5,7 BLK 6 I4: 5,7,4,8 # reduction candidate for 5,7 I4: 5,7 => CTR * .5....678.76158.3483.6.7.51.1....36.62..13849348...12.76.9.1.8.98.2.541........9. I4: 4,8 # 6 pairs G5: 5,7,1,8 # reduction candidate for 5,7 G5: 5,7 => CTR * .5.....7..76158.3..3.6.7.51.1....36862.813.49348...12.76.9.1.8.98.2.541........9. G5: 1,8 # 6 pairs H5: 5,7,1,4 # reduction candidate for 5,7 H5: 5,7 => CTR * 157...638496138.7.83265794121578936467341.859.485..1277..9.1.8..8.275416..18..79. H5: 1,4 # 6 pairs G6: 5,7,1 # reduction candidate for 5,7 G6: 5,7 # 17 pairs * PAIR I6: 5,7 ROW 6 D6: 5,7,3 # reduction candidate for 5,7 D6: 5,7 => CTR * 1574..6384961382758326579412157..36467..1.859.485..1277.4961.83...275416561...792 D6: 3 # 10 pairs * PAIR I6: 5,7 COL I I2: 5,7,2,3,4 # reduction candidate for 5,7 I2: 5,7 # 13 pairs I9: 5,7,2,3,6 # reduction candidate for 5,7 I9: 5,7 # 8 pairs * PAIR B7: 2,6 BLK 7 B9: 2,6,8 # reduction candidate for 2,6 B9: 2,6 => CTR * 157.926.84961.8.7.8326.79.1215..9364673...8.9948....2.7..9.1.8.3892.541.5.1....9. B9: 8 # 6 pairs * PAIR B7: 2,6 ROW 7 G7: 2,6,5 # reduction candidate for 2,6 G7: 2,6 # 8 pairs I7: 2,6,3,5 # reduction candidate for 2,6 I7: 2,6 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0112-base-pr-000.dot * REASONING * DIS # E1: 3,4 => CTR => E1: 2,9 * DIS # F1: 3,4 => CTR => F1: 2,9 * DIS # I1: 3,4 => CTR => I1: 2,6,7,8 * DIS # D5: 3,4 => CTR => D5: 5,7,8 * DIS # D9: 3,4 => CTR => D9: 7,8 * DIS # I2: 4,5 => CTR => I2: 2,3,7 * DIS # E3: 2,9 => CTR => E3: 4,5 * DIS # H5: 4,5 => CTR => H5: 1,7 * DIS # C5: 2,7 => CTR => C5: 3,5 * PRF # E5: 2,7 => SOL * PRF # B2: 2,7 => SOL * DIS # B2: 9 => CTR => B2: 2,7 * DIS # I4: 5,7 => CTR => I4: 4,8 * DIS # G5: 5,7 => CTR => G5: 1,8 * DIS # H5: 5,7 => CTR => H5: 1,4 * DIS # D6: 5,7 => CTR => D6: 3 * DIS # B9: 2,6 => CTR => B9: 8 * CNT 17 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,B7,D1,H3,I6) * .5.........61.8....3.6.7..1.1....36.6.......9.48....2.7..9.1.8....2.54.........9. * PAIR D1: 3,4 BLK 2 E1: 3,4,2,9 # reduction candidate for 3,4 E1: 3,4 => CTR * .5.....7..761.8....3.6.7..1.1....36.62......9.48....2.76.9.1.8..9.2854.........9. F1: 3,4,2,9 # reduction candidate for 3,4 F1: 3,4 => CTR * .5.....7..761.8....3.6.7..1.1....36.62......9.48....2.76.9.1.8..9.2854.........9. E2: 3,4,5 # reduction candidate for 3,4 E2: 3,4 # 15 pairs * RESTART * PAIR D1: 3,4 BLK 2 E2: 3,4,5 # reduction candidate for 3,4 E2: 5 => CTR * .5.3......96158.3..3264795121....36.67..12.49.48...12.7.49.1.8....2.541.5.1....9. * PAIR D1: 3,4 COL D D5: 3,4,5,7 # reduction candidate for 3,4 D5: 3,4 => CTR * .5..296.8.961.8...83265794151...23646...1.8.9348.9612.7..9.1.8.9.32.541........9. D9: 3,4,7,8 # reduction candidate for 3,4 D9: 3,4 => CTR * .5....678.761.89..8396572415178..3646237148599485..12776.9.158..9.2.54...8.....9. D9: 7,8 => SOLVED * 157492638426138957839657241215879364673524819948316725762941583391285476584763192 * DURATION: 0:00:06.994291 START: 05:32:29.207637 END: 05:32:36.201928 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0112-base-pr-001.dot * REASONING * DIS # E1: 3,4 => CTR => E1: 2,9 * DIS E1: 2,9 # F1: 3,4 => CTR => F1: 2,9 * DIS E1: 2,9 + F1: 2,9 # E2: 5 => CTR => E2: 3,4 * DIS E1: 2,9 + F1: 2,9 + E2: 3,4 # D5: 3,4 => CTR => D5: 5,7 * DIS E1: 2,9 + F1: 2,9 + E2: 3,4 + D5: 5,7 # D9: 3,4 => CTR => D9: 7,8 * PRF E1: 2,9 + F1: 2,9 + E2: 3,4 + D5: 5,7 + D9: 7,8 => SOL * STA E1: 2,9 + F1: 2,9 + E2: 3,4 + D5: 5,7 + D9: 7,8 * CNT 6 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=112
Solution
position: 157492638426138957839657241215879364673524819948316725762941583391285476584763192 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:
* DIS # E1: 3,4 => CTR => E1: 2,9 * INC # E1: 2,9 => UNS * DIS # F1: 3,4 => CTR => F1: 2,9 * INC # F1: 2,9 => UNS * INC # E2: 3,4 => UNS * INC # H1: 3,4 => UNS * DIS # I1: 3,4 => CTR => I1: 2,6,7,8 * INC # I1: 2,6,7,8 => UNS * DIS # D5: 3,4 => CTR => D5: 5,7,8 * INC # D5: 5,7,8 => UNS * DIS # D9: 3,4 => CTR => D9: 7,8 * INC # D9: 7,8 => UNS * INC # H2: 4,5 => UNS * DIS # I2: 4,5 => CTR => I2: 2,3,7 * INC # I2: 2,3,7 => UNS * INC # E3: 4,5 => UNS * DIS # E3: 2,9 => CTR => E3: 4,5 * DIS # H5: 4,5 => CTR => H5: 1,7 * INC # H5: 1,7 => UNS * INC # C4: 2,7 => UNS * DIS # C5: 2,7 => CTR => C5: 3,5 * INC # C5: 3,5 => UNS * PRF # E5: 2,7 => SOL * INC # E5: 1,3,4,8 => UNS * PRF # B2: 2,7 => SOL * DIS # B2: 9 => CTR => B2: 2,7 * DIS # I4: 5,7 => CTR => I4: 4,8 * INC # I4: 4,8 => UNS * DIS # G5: 5,7 => CTR => G5: 1,8 * INC # G5: 1,8 => UNS * DIS # H5: 5,7 => CTR => H5: 1,4 * INC # H5: 1,4 => UNS * INC # G6: 5,7 => UNS * DIS # D6: 5,7 => CTR => D6: 3 * INC # D6: 3 => UNS * INC # I2: 5,7 => UNS * INC # I9: 5,7 => UNS * DIS # B9: 2,6 => CTR => B9: 8 * INC # B9: 8 => UNS * INC # G7: 2,6 => UNS * INC # I7: 2,6 => UNS * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E1: 3,4 => CTR => E1: 2,9 * DIS E1: 2,9 # F1: 3,4 => CTR => F1: 2,9 * INC E1: 2,9 + F1: 2,9 # E2: 3,4 => UNS * INC E1: 2,9 + F1: 2,9 # E2: 3,4 => UNS * DIS E1: 2,9 + F1: 2,9 # E2: 5 => CTR => E2: 3,4 * DIS E1: 2,9 + F1: 2,9 + E2: 3,4 # D5: 3,4 => CTR => D5: 5,7 * DIS E1: 2,9 + F1: 2,9 + E2: 3,4 + D5: 5,7 # D9: 3,4 => CTR => D9: 7,8 * PRF E1: 2,9 + F1: 2,9 + E2: 3,4 + D5: 5,7 + D9: 7,8 => SOL * STA E1: 2,9 + F1: 2,9 + E2: 3,4 + D5: 5,7 + D9: 7,8 * CNT 8 HDP CHAINS / 7 HYP OPENED