Analysis of zz-www.sudokuwiki.org-0045-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=45
level: medium
position: 1..3.......2...4...7..45.2.3..8....7....9....8....1..9.1.58..9...6...5....3..6..1 initial
Autosolve
position: 1..3......32...4...7..45.2.3..8....7....9....8....1..9.1.58..9...6...5....3..6..1 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 6,9 => CTR => B1: 4,5 * DIS # C1: 8,9 => CTR => C1: 4,5 * DIS # F7: 2,4 => CTR => F7: 3,7 * DIS # F8: 2,4 => CTR => F8: 3,7,9 * DIS # A9: 4,7 => CTR => A9: 2,5,9 * DIS # C5: 4,7 => CTR => C5: 1,5 * DIS # E8: 2,7 => CTR => E8: 1,3 * DIS # F8: 2,7 => CTR => F8: 3,4,9 * DIS # D9: 2,7 => CTR => D9: 4,9 * DIS # A9: 2,7 => CTR => A9: 4,5,9 * DIS # E6: 2,7 => CTR => E6: 3,5,6 * CNT 11 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 # B1: 6,9 => CTR => B1: 4,5 * DIS B1: 4,5 # A2: 5 => CTR => A2: 6,9 * DIS B1: 4,5 + A2: 6,9 # F5: 2,4 => CTR => F5: 3,7 * DIS B1: 4,5 + A2: 6,9 + F5: 3,7 # F7: 2,4 => CTR => F7: 3,7 * DIS B1: 4,5 + A2: 6,9 + F5: 3,7 + F7: 3,7 # F8: 2,4 => CTR => F8: 9 * PRF B1: 4,5 + A2: 6,9 + F5: 3,7 + F7: 3,7 + F8: 9 # A7: 4,7 => SOL * STA B1: 4,5 + A2: 6,9 + F5: 3,7 + F7: 3,7 + F8: 9 + A7: 4,7 * CNT 6 HDP CHAINS / 14 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1..3.......2...4...7..45.2.3..8....7....9....8....1..9.1.58..9...6...5....3..6..1 | initial |
| 1..3......32...4...7..45.2.3..8....7....9....8....1..9.1.58..9...6...5....3..6..1 | autosolve |
| 145362978632978415978145326329854167461297853857631249714583692286719534593426781 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) A3: 6,9 C3: 8,9 F4: 2,4 C7: 4,7 E9: 2,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H2,G3: 1.. / H2 = 1 => 10 pairs (_) / G3 = 1 => 14 pairs (_) C4,C5: 1.. / C4 = 1 => 0 pairs (X) / C5 = 1 => 5 pairs (_) D8,E8: 1.. / D8 = 1 => 14 pairs (_) / E8 = 1 => 8 pairs (_) D3,G3: 1.. / D3 = 1 => 10 pairs (_) / G3 = 1 => 14 pairs (_) E2,E8: 1.. / E2 = 1 => 14 pairs (_) / E8 = 1 => 8 pairs (_) E1,F1: 2.. / E1 = 2 => 9 pairs (_) / F1 = 2 => 10 pairs (_) G3,I3: 3.. / G3 = 3 => 0 pairs (*) / I3 = 3 => 0 pairs (X) F5,E6: 3.. / F5 = 3 => 0 pairs (X) / E6 = 3 => 7 pairs (_) E6,E8: 3.. / E6 = 3 => 7 pairs (_) / E8 = 3 => 0 pairs (X) B1,C1: 4.. / B1 = 4 => 5 pairs (_) / C1 = 4 => 0 pairs (X) E4,E6: 5.. / E4 = 5 => 5 pairs (_) / E6 = 5 => 0 pairs (X) A9,B9: 5.. / A9 = 5 => 12 pairs (_) / B9 = 5 => 0 pairs (X) G7,I7: 6.. / G7 = 6 => 7 pairs (_) / I7 = 6 => 9 pairs (_) C1,C3: 8.. / C1 = 8 => 0 pairs (X) / C3 = 8 => 5 pairs (_) F1,F2: 8.. / F1 = 8 => 11 pairs (_) / F2 = 8 => 6 pairs (_) B8,B9: 8.. / B8 = 8 => 5 pairs (_) / B9 = 8 => 0 pairs (X) G1,G3: 9.. / G1 = 9 => 6 pairs (_) / G3 = 9 => 9 pairs (_) B4,C4: 9.. / B4 = 9 => 0 pairs (X) / C4 = 9 => 6 pairs (_) * DURATION: 0:00:21.500649 START: 04:18:57.768126 END: 04:19:19.268775 2017-05-01 * CP COUNT: (18) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,C3,C7,E9,F4) * 1..3......32...4...7..45.2.3..8....7....9....8....1..9.1.58..9...6...5....3..6..1 * PAIR A3: 6,9 BLK 1 B1: 6,9,4,5 # reduction candidate for 6,9 B1: 6,9 => CTR * 1943.....5329..41.6781459233.985.1.77.169....8.5731..9.1758..9..86.195...53..6..1 B1: 4,5 # 6 pairs A2: 6,9,5 # reduction candidate for 6,9 A2: 6,9 # 12 pairs * PAIR A3: 6,9 ROW 3 D3: 6,9,1 # reduction candidate for 6,9 D3: 6,9 # 14 pairs G3: 6,9,1,3,8 # reduction candidate for 6,9 G3: 6,9 # 10 pairs * PAIR C3: 8,9 BLK 1 C1: 8,9,4,5 # reduction candidate for 8,9 C1: 8,9 => CTR * 149328...532.6.418678145923394852167721694...86..312.9.1.58..9..86.1.5...53.76841 C1: 4,5 # 6 pairs * PAIR C3: 8,9 ROW 3 G3: 8,9,1,3,6 # reduction candidate for 8,9 G3: 8,9 # 11 pairs G3: 1,3,6 # 6 pairs * PAIR F4: 2,4 BLK 5 D5: 2,4,6,7 # reduction candidate for 2,4 D5: 2,4 # 9 pairs F5: 2,4,3,7 # reduction candidate for 2,4 F5: 2,4 # 21 pairs D6: 2,4,6,7 # reduction candidate for 2,4 D6: 2,4 # 9 pairs * PAIR F4: 2,4 ROW 4 B4: 2,4,5,6,9 # reduction candidate for 2,4 B4: 2,4 # 9 pairs B4: 5,6,9 # 5 pairs * PAIR F4: 2,4 COL F F7: 2,4,3,7 # reduction candidate for 2,4 F7: 2,4 => CTR * 1..32.76..32.6.41.6781459233..85..47....97.328.7.3165971458.396.86.1357...3.76..1 F7: 3,7 # 6 pairs F8: 2,4,3,7,9 # reduction candidate for 2,4 F8: 2,4 => CTR * 14.32.....3276.41.67.145.2.3..854.674...97...8.7.312.9.14583.9...6.1.5.4..3476.81 F8: 3,7,9 # 5 pairs * PAIR C7: 4,7 BLK 7 A7: 4,7,2 # reduction candidate for 4,7 A7: 4,7 # 10 pairs A8: 4,7,2,9 # reduction candidate for 4,7 A8: 4,7 # 9 pairs A9: 4,7,2,5,9 # reduction candidate for 4,7 A9: 4,7 => CTR * 1..328...5327694186781459233..85...77...9.8328...3165921758..9.986.1.5...53976281 A9: 2,5,9 # 5 pairs * PAIR C7: 4,7 ROW 7 F7: 4,7,2,3 # reduction candidate for 4,7 F7: 4,7 # 12 pairs F7: 2,3 # 6 pairs * PAIR C7: 4,7 COL C C5: 4,7,1,5 # reduction candidate for 4,7 C5: 4,7 => CTR * 14.3.....532...41.67.145.2.39185...7....9.1..8.5.31249.1.58..9..86.1.5...53..6..1 C5: 1,5 # 6 pairs C6: 4,7,5 # reduction candidate for 4,7 C6: 4,7 # 9 pairs * PAIR E9: 2,7 BLK 8 F7: 2,7,3,4 # reduction candidate for 2,7 F7: 2,7 # 16 pairs D8: 2,7,1,4,9 # reduction candidate for 2,7 D8: 2,7 # 11 pairs E8: 2,7,1,3 # reduction candidate for 2,7 E8: 2,7 => CTR * 1..362978.32.184..6789451233.9854.17..1.97...8.7.31..9.14583.9...61.9534.934.6.81 E8: 1,3 # 6 pairs F8: 2,7,3,4,9 # reduction candidate for 2,7 F8: 2,7 => CTR * 14.32.....3276.41.67.145.2.3..854.674...97...8.7.31249.14583.92..6.125.4253.76..1 F8: 3,4,9 # 5 pairs D9: 2,7,4,9 # reduction candidate for 2,7 D9: 2,7 => CTR * 1..3..76..32...41..7.1459233..8...577...9..848.4.51.39.1758.396.864..57...3..6841 D9: 4,9 # 6 pairs * PAIR E9: 2,7 ROW 9 A9: 2,7,4,5,9 # reduction candidate for 2,7 A9: 2,7 => CTR * 1..3.87.55327694186781459233..8....77.5.9.1848.4.31.59417582.9.986.1.572253976841 A9: 4,5,9 # 5 pairs G9: 2,7,8 # reduction candidate for 2,7 G9: 2,7 # 8 pairs * PAIR E9: 2,7 COL E E1: 2,7,6 # reduction candidate for 2,7 E1: 2,7 # 9 pairs E6: 2,7,3,5,6 # reduction candidate for 2,7 E6: 2,7 => CTR * 1..36297..32.184656789451233.9854.17..1.93.548....1.392145873967.613.5....3..6..1 E6: 3,5,6 # 5 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0045-base-pr-000.dot * REASONING * DIS # B1: 6,9 => CTR => B1: 4,5 * DIS # C1: 8,9 => CTR => C1: 4,5 * DIS # F7: 2,4 => CTR => F7: 3,7 * DIS # F8: 2,4 => CTR => F8: 3,7,9 * DIS # A9: 4,7 => CTR => A9: 2,5,9 * DIS # C5: 4,7 => CTR => C5: 1,5 * DIS # E8: 2,7 => CTR => E8: 1,3 * DIS # F8: 2,7 => CTR => F8: 3,4,9 * DIS # D9: 2,7 => CTR => D9: 4,9 * DIS # A9: 2,7 => CTR => A9: 4,5,9 * DIS # E6: 2,7 => CTR => E6: 3,5,6 * CNT 11 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,C3,C7,E9,F4) * 1..3......32...4...7..45.2.3..8....7....9....8....1..9.1.58..9...6...5....3..6..1 * PAIR A3: 6,9 BLK 1 B1: 6,9,4,5 # reduction candidate for 6,9 B1: 6,9 => CTR * 1943.....5329..41.6781459233.985.1.77.169....8.5731..9.1758..9..86.195...53..6..1 A2: 6,9,5 # reduction candidate for 6,9 A2: 6,9 # 12 pairs * RESTART * PAIR A3: 6,9 BLK 1 A2: 6,9,5 # reduction candidate for 6,9 A2: 5 => CTR * 149328...532.6.418678145923394852167721694...86..312.9.1.58..9..86.1.5...53.76841 * PAIR A3: 6,9 ROW 3 D3: 6,9,1 # reduction candidate for 6,9 D3: 6,9 # 14 pairs G3: 6,9,1,3 # reduction candidate for 6,9 G3: 6,9 # 18 pairs * PAIR F4: 2,4 BLK 5 D5: 2,4,6,7 # reduction candidate for 2,4 D5: 2,4 # 16 pairs F5: 2,4,3,7 # reduction candidate for 2,4 F5: 2,4 => CTR * 1..32.9689321684756789451233.985..174.17923..8...31..9.1.583796786.1953.593.76841 D6: 2,4,6,7 # reduction candidate for 2,4 D6: 2,4 # 16 pairs * PAIR F4: 2,4 ROW 4 B4: 2,4,5,6 # reduction candidate for 2,4 B4: 2,4 # 16 pairs B4: 5,6 # 14 pairs * PAIR F4: 2,4 COL F F7: 2,4,3,7 # reduction candidate for 2,4 F7: 2,4 => CTR * 1453297689327684156781459233.98..1.7..1.97.3.8.7.31..97145823962.6.135745.3476281 F8: 2,4,9 # reduction candidate for 2,4 F8: 2,4 => CTR * 14532.....3276.4156781459233.985.1.74.1.973..8.7.31..9.14583.9...6.1.5345.3476281 * PAIR RESTART * PAIR C7: 4,7 BLK 7 A7: 4,7,2 # reduction candidate for 4,7 A7: 4,7 => SOLVED * 145362978632978415978145326329854167461297853857631249714583692286719534593426781 * DURATION: 0:00:14.577079 START: 04:19:44.717998 END: 04:19:59.295077 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0045-base-pr-001.dot * REASONING * DIS # B1: 6,9 => CTR => B1: 4,5 * DIS B1: 4,5 # A2: 5 => CTR => A2: 6,9 * DIS B1: 4,5 + A2: 6,9 # F5: 2,4 => CTR => F5: 3,7 * DIS B1: 4,5 + A2: 6,9 + F5: 3,7 # F7: 2,4 => CTR => F7: 3,7 * DIS B1: 4,5 + A2: 6,9 + F5: 3,7 + F7: 3,7 # F8: 2,4 => CTR => F8: 9 * PRF B1: 4,5 + A2: 6,9 + F5: 3,7 + F7: 3,7 + F8: 9 # A7: 4,7 => SOL * STA B1: 4,5 + A2: 6,9 + F5: 3,7 + F7: 3,7 + F8: 9 + A7: 4,7 * CNT 6 HDP CHAINS / 14 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=45
Solution
position: 145362978632978415978145326329854167461297853857631249714583692286719534593426781 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 # B1: 6,9 => CTR => B1: 4,5 * INC # B1: 4,5 => UNS * INC # A2: 6,9 => UNS * INC # D3: 6,9 => UNS * INC # G3: 6,9 => UNS * DIS # C1: 8,9 => CTR => C1: 4,5 * INC # C1: 4,5 => UNS * INC # G3: 8,9 => UNS * INC # G3: 1,3,6 => UNS * INC # D5: 2,4 => UNS * INC # F5: 2,4 => UNS * INC # D6: 2,4 => UNS * INC # B4: 2,4 => UNS * INC # B4: 5,6,9 => UNS * DIS # F7: 2,4 => CTR => F7: 3,7 * INC # F7: 3,7 => UNS * DIS # F8: 2,4 => CTR => F8: 3,7,9 * INC # F8: 3,7,9 => UNS * INC # A7: 4,7 => UNS * INC # A8: 4,7 => UNS * DIS # A9: 4,7 => CTR => A9: 2,5,9 * INC # A9: 2,5,9 => UNS * INC # F7: 4,7 => UNS * INC # F7: 2,3 => UNS * DIS # C5: 4,7 => CTR => C5: 1,5 * INC # C5: 1,5 => UNS * INC # C6: 4,7 => UNS * INC # F7: 2,7 => UNS * INC # D8: 2,7 => UNS * DIS # E8: 2,7 => CTR => E8: 1,3 * INC # E8: 1,3 => UNS * DIS # F8: 2,7 => CTR => F8: 3,4,9 * INC # F8: 3,4,9 => UNS * DIS # D9: 2,7 => CTR => D9: 4,9 * INC # D9: 4,9 => UNS * DIS # A9: 2,7 => CTR => A9: 4,5,9 * INC # A9: 4,5,9 => UNS * INC # G9: 2,7 => UNS * INC # E1: 2,7 => UNS * DIS # E6: 2,7 => CTR => E6: 3,5,6 * INC # E6: 3,5,6 => UNS * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B1: 6,9 => CTR => B1: 4,5 * INC B1: 4,5 # A2: 6,9 => UNS * INC B1: 4,5 # A2: 6,9 => UNS * DIS B1: 4,5 # A2: 5 => CTR => A2: 6,9 * INC B1: 4,5 + A2: 6,9 # D3: 6,9 => UNS * INC B1: 4,5 + A2: 6,9 # G3: 6,9 => UNS * INC B1: 4,5 + A2: 6,9 # D5: 2,4 => UNS * DIS B1: 4,5 + A2: 6,9 # F5: 2,4 => CTR => F5: 3,7 * INC B1: 4,5 + A2: 6,9 + F5: 3,7 # D6: 2,4 => UNS * INC B1: 4,5 + A2: 6,9 + F5: 3,7 # B4: 2,4 => UNS * INC B1: 4,5 + A2: 6,9 + F5: 3,7 # B4: 5,6 => UNS * DIS B1: 4,5 + A2: 6,9 + F5: 3,7 # F7: 2,4 => CTR => F7: 3,7 * DIS B1: 4,5 + A2: 6,9 + F5: 3,7 + F7: 3,7 # F8: 2,4 => CTR => F8: 9 * PRF B1: 4,5 + A2: 6,9 + F5: 3,7 + F7: 3,7 + F8: 9 # A7: 4,7 => SOL * STA B1: 4,5 + A2: 6,9 + F5: 3,7 + F7: 3,7 + F8: 9 + A7: 4,7 * CNT 14 HDP CHAINS / 14 HYP OPENED