Analysis of zz-www.sudokuwiki.org-0030-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=30
level: medium
position: .3.....1...91.24......7.9..9..82....85.....94....96..5..3.8......83.97...1.....3. initial
Autosolve
position: .3.9...1...91.24..1...7.9..9..8253..85.7...943..496.85.93.8......83.97...1....839 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H3: 5,6 => CTR => H3: 2 * DIS # H3: 5,6 => CTR => H3: 2 * DIS # A1: 5,6 => CTR => A1: 2,4,7 * PRF # G7: 1 => SOL * PRF # C4: 4,6 => SOL * PRF # C6: 1 => SOL * PRF # I4: 1 => SOL * DIS # C6: 7 => CTR => C6: 1,2 * CNT 8 HDP CHAINS / 37 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H3: 5,6 => CTR => H3: 2 * DIS H3: 2 # D9: 5,6 => CTR => D9: 2 * PRF H3: 2 + D9: 2 # E2: 5,6 => SOL * STA H3: 2 + D9: 2 + E2: 5,6 * CNT 3 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .3.....1...91.24......7.9..9..82....85.....94....96..5..3.8......83.97...1.....3. | initial |
| .3.9...1...91.24..1...7.9..9..8253..85.7...943..496.85.93.8......83.97...1....839 | autosolve |
| 236948517789152463145673928964825371852731694371496285693587142428319756517264839 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) F1: 4,8 D3: 5,6 G1: 5,6 B4: 4,6 C5: 2,6 B6: 2,7 E5: 1,3 F5: 1,3 H4: 6,7 G5: 2,6 G6: 1,2 F9: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C4,C6: 1.. / C4 = 1 => 12 pairs (_) / C6 = 1 => 0 pairs (*) E5,F5: 1.. / E5 = 1 => 14 pairs (_) / F5 = 1 => 16 pairs (_) I4,G6: 1.. / I4 = 1 => 0 pairs (*) / G6 = 1 => 0 pairs (X) F7,E8: 1.. / F7 = 1 => 14 pairs (_) / E8 = 1 => 16 pairs (_) C4,I4: 1.. / C4 = 1 => 12 pairs (_) / I4 = 1 => 0 pairs (*) C6,G6: 1.. / C6 = 1 => 0 pairs (*) / G6 = 1 => 0 pairs (X) E8,I8: 1.. / E8 = 1 => 16 pairs (_) / I8 = 1 => 14 pairs (_) E5,E8: 1.. / E5 = 1 => 14 pairs (_) / E8 = 1 => 16 pairs (_) F5,F7: 1.. / F5 = 1 => 16 pairs (_) / F7 = 1 => 14 pairs (_) G6,G7: 1.. / G6 = 1 => 12 pairs (_) / G7 = 1 => 0 pairs (*) G5,G6: 2.. / G5 = 2 => 12 pairs (_) / G6 = 2 => 0 pairs (*) D7,D9: 2.. / D7 = 2 => 17 pairs (_) / D9 = 2 => 13 pairs (_) C5,G5: 2.. / C5 = 2 => 0 pairs (*) / G5 = 2 => 0 pairs (X) E2,F3: 3.. / E2 = 3 => 14 pairs (_) / F3 = 3 => 16 pairs (_) I2,I3: 3.. / I2 = 3 => 16 pairs (_) / I3 = 3 => 14 pairs (_) E5,F5: 3.. / E5 = 3 => 16 pairs (_) / F5 = 3 => 14 pairs (_) E2,I2: 3.. / E2 = 3 => 14 pairs (_) / I2 = 3 => 16 pairs (_) F3,I3: 3.. / F3 = 3 => 16 pairs (_) / I3 = 3 => 14 pairs (_) E2,E5: 3.. / E2 = 3 => 14 pairs (_) / E5 = 3 => 16 pairs (_) F3,F5: 3.. / F3 = 3 => 16 pairs (_) / F5 = 3 => 14 pairs (_) B4,C4: 4.. / B4 = 4 => 13 pairs (_) / C4 = 4 => 0 pairs (*) H7,H8: 4.. / H7 = 4 => 13 pairs (_) / H8 = 4 => 18 pairs (_) G1,G7: 5.. / G1 = 5 => 16 pairs (_) / G7 = 5 => 14 pairs (_) C5,G5: 6.. / C5 = 6 => 12 pairs (_) / G5 = 6 => 0 pairs (*) B6,C6: 7.. / B6 = 7 => 13 pairs (_) / C6 = 7 => 0 pairs (X) H4,I4: 7.. / H4 = 7 => 15 pairs (_) / I4 = 7 => 12 pairs (_) F7,F9: 7.. / F7 = 7 => 14 pairs (_) / F9 = 7 => 13 pairs (_) A7,F7: 7.. / A7 = 7 => 13 pairs (_) / F7 = 7 => 14 pairs (_) B2,B6: 7.. / B2 = 7 => 0 pairs (X) / B6 = 7 => 13 pairs (_) H2,H4: 7.. / H2 = 7 => 12 pairs (_) / H4 = 7 => 15 pairs (_) B2,B3: 8.. / B2 = 8 => 15 pairs (_) / B3 = 8 => 16 pairs (_) F1,F3: 8.. / F1 = 8 => 14 pairs (_) / F3 = 8 => 0 pairs (X) F1,I1: 8.. / F1 = 8 => 14 pairs (_) / I1 = 8 => 0 pairs (X) B2,I2: 8.. / B2 = 8 => 15 pairs (_) / I2 = 8 => 16 pairs (_) * DURATION: 0:00:56.926482 START: 03:58:03.754512 END: 03:59:00.680994 2017-05-01 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B6,C5,D3,E5,F1,F5,F9,G1,G5,G6,H4) * .3.9...1...91.24..1...7.9..9..8253..85.7...943..496.85.93.8......83.97...1....839 * PAIR F1: 4,8 BLK 2 F3: 4,8,3 # reduction candidate for 4,8 F3: 3 # 16 pairs F3: 4,8 # 14 pairs * PAIR D3: 5,6 BLK 2 E1: 5,6,4 # reduction candidate for 5,6 E1: 5,6 # 14 pairs E2: 5,6,3 # reduction candidate for 5,6 E2: 5,6 # 16 pairs * PAIR D3: 5,6 ROW 3 C3: 5,6,2,4 # reduction candidate for 5,6 C3: 5,6 # 15 pairs H3: 5,6,2 # reduction candidate for 5,6 H3: 5,6 => CTR * .359..61.6891524731.4673958941825367856731294372496185.9328.5....83.97...1.5..839 H3: 2 # 12 pairs * PAIR D3: 5,6 COL D D7: 5,6,2 # reduction candidate for 5,6 D7: 5,6 # 13 pairs D9: 5,6,2 # reduction candidate for 5,6 D9: 5,6 # 17 pairs * PAIR G1: 5,6 BLK 3 H2: 5,6,7 # reduction candidate for 5,6 H2: 5,6 # 15 pairs H3: 5,6,2 # reduction candidate for 5,6 H3: 5,6 => CTR * .359..61.6891524731.4673958941825367856731294372496185.9328.5....83.97...1.5..839 H3: 2 # 12 pairs * PAIR G1: 5,6 ROW 1 A1: 5,6,2,4,7 # reduction candidate for 5,6 A1: 5,6 => CTR * .32948.1...91.24..1.4.739.894.8253..85.731.943..496.85.93.8.....683197.2.15.6.839 A1: 2,4,7 # 12 pairs C1: 5,6,2,4,7 # reduction candidate for 5,6 C1: 5,6 # 18 pairs E1: 5,6,4 # reduction candidate for 5,6 E1: 5,6 # 14 pairs * PAIR G1: 5,6 COL G G7: 5,6,1 # reduction candidate for 5,6 G7: 1 => SOLVED * 236948517789152463145673928964825371852731694371496285693587142428319756517264839 G7: 5,6 # 12 pairs * PAIR B4: 4,6 BLK 4 C4: 4,6,1 # reduction candidate for 4,6 C4: 4,6 => SOLVED * 236948517789152463145673928964825371852731694371496285693587142428319756517264839 C4: 1 # 12 pairs * PAIR B4: 4,6 COL B B3: 4,6,2,8 # reduction candidate for 4,6 B3: 4,6 # 17 pairs B8: 4,6,2 # reduction candidate for 4,6 B8: 4,6 # 15 pairs * PAIR C5: 2,6 COL C C1: 2,6,4,5,7 # reduction candidate for 2,6 C1: 2,6 # 16 pairs C3: 2,6,4,5 # reduction candidate for 2,6 C3: 2,6 # 17 pairs C9: 2,6,4,5,7 # reduction candidate for 2,6 C9: 2,6 # 20 pairs * PAIR B6: 2,7 BLK 4 C6: 2,7,1 # reduction candidate for 2,7 C6: 1 => SOLVED * 236948517789152463145673928964825371852731694371496285693587142428319756517264839 C6: 2,7 # 12 pairs * PAIR H4: 6,7 BLK 6 I4: 6,7,1 # reduction candidate for 6,7 I4: 1 => SOLVED * 236948517789152463145673928964825371852731694371496285693587142428319756517264839 I4: 6,7 # 12 pairs * PAIR H4: 6,7 COL H H2: 6,7,5 # reduction candidate for 6,7 H2: 5 # 20 pairs H2: 6,7 # 14 pairs * PAIR G6: 1,2 ROW 6 C6: 1,2,7 # reduction candidate for 1,2 C6: 7 => CTR * .329.8.17.791324.818.674923941825376856713294327496185793581642268349751.14267839 C6: 1,2 # 13 pairs * PAIR F9: 4,7 BLK 8 F7: 4,7,1 # reduction candidate for 4,7 F7: 4,7 # 16 pairs F7: 1 # 14 pairs * PAIR F9: 4,7 ROW 9 A9: 4,7,2,5,6 # reduction candidate for 4,7 A9: 4,7 # 16 pairs C9: 4,7,2,5,6 # reduction candidate for 4,7 C9: 4,7 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0030-base-pr-000.dot * REASONING * DIS # H3: 5,6 => CTR => H3: 2 * DIS # H3: 5,6 => CTR => H3: 2 * DIS # A1: 5,6 => CTR => A1: 2,4,7 * PRF # G7: 1 => SOL * PRF # C4: 4,6 => SOL * PRF # C6: 1 => SOL * PRF # I4: 1 => SOL * DIS # C6: 7 => CTR => C6: 1,2 * CNT 8 HDP CHAINS / 37 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B6,C5,D3,E5,F1,F5,F9,G1,G5,G6,H4) * .3.9...1...91.24..1...7.9..9..8253..85.7...943..496.85.93.8......83.97...1....839 * PAIR F1: 4,8 BLK 2 F3: 4,8,3 # reduction candidate for 4,8 F3: 3 # 16 pairs F3: 4,8 # 14 pairs * PAIR D3: 5,6 BLK 2 E1: 5,6,4 # reduction candidate for 5,6 E1: 5,6 # 14 pairs E2: 5,6,3 # reduction candidate for 5,6 E2: 5,6 # 16 pairs * PAIR D3: 5,6 ROW 3 C3: 5,6,2,4 # reduction candidate for 5,6 C3: 5,6 # 15 pairs H3: 5,6,2 # reduction candidate for 5,6 H3: 5,6 => CTR * .359..61.6891524731.4673958941825367856731294372496185.9328.5....83.97...1.5..839 * RESTART * PAIR D3: 5,6 ROW 3 C3: 5,6,4 # reduction candidate for 5,6 C3: 4 # 19 pairs C3: 5,6 # 15 pairs * PAIR D3: 5,6 COL D D7: 5,6,2 # reduction candidate for 5,6 D7: 5,6 # 13 pairs D9: 5,6,2 # reduction candidate for 5,6 D9: 5,6 => CTR * .3.9...1..791.24.818..7.9239.18253768567...94327496185.9328...1..83197.2.1....839 * RESTART * PAIR RESTART * PAIR D3: 5,6 BLK 2 E1: 5,6,4 # reduction candidate for 5,6 E1: 5,6 # 20 pairs E2: 5,6,3 # reduction candidate for 5,6 E2: 5,6 => SOLVED * 236948517789152463145673928964825371852731694371496285693587142428319756517264839 * DURATION: 0:00:11.847511 START: 03:59:33.802965 END: 03:59:45.650476 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0030-base-pr-001.dot * REASONING * DIS # H3: 5,6 => CTR => H3: 2 * DIS H3: 2 # D9: 5,6 => CTR => D9: 2 * PRF H3: 2 + D9: 2 # E2: 5,6 => SOL * STA H3: 2 + D9: 2 + E2: 5,6 * CNT 3 HDP CHAINS / 12 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=30
Solution
position: 236948517789152463145673928964825371852731694371496285693587142428319756517264839 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 # F3: 4,8 => UNS * INC # F3: 3 => UNS * INC # E1: 5,6 => UNS * INC # E2: 5,6 => UNS * INC # C3: 5,6 => UNS * DIS # H3: 5,6 => CTR => H3: 2 * INC # H3: 2 => UNS * INC # D7: 5,6 => UNS * INC # D9: 5,6 => UNS * INC # H2: 5,6 => UNS * DIS # H3: 5,6 => CTR => H3: 2 * INC # H3: 2 => UNS * DIS # A1: 5,6 => CTR => A1: 2,4,7 * INC # A1: 2,4,7 => UNS * INC # C1: 5,6 => UNS * INC # E1: 5,6 => UNS * INC # G7: 5,6 => UNS * PRF # G7: 1 => SOL * PRF # C4: 4,6 => SOL * INC # C4: 1 => UNS * INC # B3: 4,6 => UNS * INC # B8: 4,6 => UNS * INC # C1: 2,6 => UNS * INC # C3: 2,6 => UNS * INC # C9: 2,6 => UNS * INC # C6: 2,7 => UNS * PRF # C6: 1 => SOL * INC # I4: 6,7 => UNS * PRF # I4: 1 => SOL * INC # H2: 6,7 => UNS * INC # H2: 5 => UNS * INC # C6: 1,2 => UNS * DIS # C6: 7 => CTR => C6: 1,2 * INC # F7: 4,7 => UNS * INC # F7: 1 => UNS * INC # A9: 4,7 => UNS * INC # C9: 4,7 => UNS * CNT 37 HDP CHAINS / 37 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F3: 4,8 => UNS * INC # F3: 3 => UNS * INC # E1: 5,6 => UNS * INC # E2: 5,6 => UNS * INC # C3: 5,6 => UNS * DIS # H3: 5,6 => CTR => H3: 2 * INC H3: 2 # C3: 5,6 => UNS * INC H3: 2 # C3: 4 => UNS * INC H3: 2 # D7: 5,6 => UNS * DIS H3: 2 # D9: 5,6 => CTR => D9: 2 * INC H3: 2 + D9: 2 # E1: 5,6 => UNS * PRF H3: 2 + D9: 2 # E2: 5,6 => SOL * STA H3: 2 + D9: 2 + E2: 5,6 * CNT 12 HDP CHAINS / 12 HYP OPENED