Analysis of zz-sudoku-de-777320-base.sdk
Contents
Original Sudoku
level: medium
position: 1.3.7.8.9............3..521...91...59..6.8..72...54...687..2............4.2.8.7.6 initial
Autosolve
position: 1.32758.952.8.1.73...3.6521...9132.59..628.172.1754.986871329543..467182412589736 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 9 => CTR => C2: 4,6 * PRF # B4: 4,6 => SOL * DIS # C2: 4,9 => CTR => C2: 6 * PRF # C2: 6 => SOL * PRF # C3: 4,9 => SOL * DIS # C2: 9 => CTR => C2: 4,6 * PRF # B5: 4,5 => SOL * DIS # B5: 3 => CTR => B5: 4,5 * PRF # B4: 4,6 => SOL * PRF # B5: 5 => SOL * CNT 10 HDP CHAINS / 18 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 9 => CTR => C2: 4,6 * PRF C2: 4,6 # B4: 4,6 => SOL * STA C2: 4,6 + B4: 4,6 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.3.7.8.9............3..521...91...59..6.8..72...54...687..2............4.2.8.7.6 | initial |
| 1.32758.952.8.1.73...3.6521...9132.59..628.172.1754.986871329543..467182412589736 | autosolve |
| 143275869526891473879346521768913245954628317231754698687132954395467182412589736 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) B1: 4,6 A3: 7,8 E2: 4,9 E3: 4,9 H1: 4,6 G2: 4,6 A4: 7,8 C5: 4,5 B6: 3,6 H4: 4,6 G5: 3,4 G6: 3,6 B8: 5,9 C8: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B5,B6: 3.. / B5 = 3 => 0 pairs (X) / B6 = 3 => 0 pairs (_) G5,G6: 3.. / G5 = 3 => 0 pairs (*) / G6 = 3 => 0 pairs (X) B5,G5: 3.. / B5 = 3 => 0 pairs (X) / G5 = 3 => 0 pairs (_) B6,G6: 3.. / B6 = 3 => 0 pairs (*) / G6 = 3 => 0 pairs (X) E2,E3: 4.. / E2 = 4 => 0 pairs (X) / E3 = 4 => 15 pairs (_) H1,G2: 4.. / H1 = 4 => 0 pairs (X) / G2 = 4 => 0 pairs (_) H4,G5: 4.. / H4 = 4 => 0 pairs (*) / G5 = 4 => 0 pairs (X) B1,H1: 4.. / B1 = 4 => 0 pairs (*) / H1 = 4 => 0 pairs (X) G2,G5: 4.. / G2 = 4 => 0 pairs (*) / G5 = 4 => 0 pairs (X) H1,H4: 4.. / H1 = 4 => 0 pairs (X) / H4 = 4 => 0 pairs (_) B5,C5: 5.. / B5 = 5 => 0 pairs (*) / C5 = 5 => 0 pairs (X) B8,C8: 5.. / B8 = 5 => 10 pairs (_) / C8 = 5 => 0 pairs (*) B5,B8: 5.. / B5 = 5 => 0 pairs (*) / B8 = 5 => 0 pairs (X) C5,C8: 5.. / C5 = 5 => 10 pairs (_) / C8 = 5 => 0 pairs (*) B1,C2: 6.. / B1 = 6 => 0 pairs (X) / C2 = 6 => 0 pairs (_) H1,G2: 6.. / H1 = 6 => 0 pairs (*) / G2 = 6 => 0 pairs (X) H4,G6: 6.. / H4 = 6 => 0 pairs (X) / G6 = 6 => 0 pairs (_) B1,H1: 6.. / B1 = 6 => 0 pairs (X) / H1 = 6 => 0 pairs (_) C2,G2: 6.. / C2 = 6 => 0 pairs (*) / G2 = 6 => 0 pairs (X) B6,G6: 6.. / B6 = 6 => 0 pairs (X) / G6 = 6 => 0 pairs (_) C2,C4: 6.. / C2 = 6 => 0 pairs (*) / C4 = 6 => 0 pairs (X) G2,G6: 6.. / G2 = 6 => 0 pairs (X) / G6 = 6 => 0 pairs (_) H1,H4: 6.. / H1 = 6 => 0 pairs (*) / H4 = 6 => 0 pairs (X) A3,B3: 7.. / A3 = 7 => 14 pairs (_) / B3 = 7 => 0 pairs (*) A4,B4: 7.. / A4 = 7 => 0 pairs (*) / B4 = 7 => 0 pairs (X) A3,A4: 7.. / A3 = 7 => 14 pairs (_) / A4 = 7 => 0 pairs (*) B3,B4: 7.. / B3 = 7 => 0 pairs (*) / B4 = 7 => 0 pairs (X) A3,C3: 8.. / A3 = 8 => 0 pairs (*) / C3 = 8 => 0 pairs (X) A4,C4: 8.. / A4 = 8 => 14 pairs (_) / C4 = 8 => 0 pairs (*) A3,A4: 8.. / A3 = 8 => 0 pairs (*) / A4 = 8 => 0 pairs (X) C3,C4: 8.. / C3 = 8 => 14 pairs (_) / C4 = 8 => 0 pairs (*) E2,E3: 9.. / E2 = 9 => 15 pairs (_) / E3 = 9 => 0 pairs (X) B8,C8: 9.. / B8 = 9 => 0 pairs (*) / C8 = 9 => 0 pairs (X) C2,E2: 9.. / C2 = 9 => 0 pairs (X) / E2 = 9 => 15 pairs (_) B3,B8: 9.. / B3 = 9 => 10 pairs (_) / B8 = 9 => 0 pairs (*) * DURATION: 0:00:57.584393 START: 08:46:46.094411 END: 08:47:43.678804 2017-05-01 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B1,B6,B8,C5,C8,E2,E3,G2,G5,G6,H1,H4) * 1.32758.952.8.1.73...3.6521...9132.59..628.172.1754.986871329543..467182412589736 * PAIR B1: 4,6 BLK 1 C2: 4,6,9 # reduction candidate for 4,6 C2: 9 => CTR * 163275849529841673...396521..69132.59..628.172.1754.986871329543..467182412589736 C2: 4,6 # 15 pairs * PAIR B1: 4,6 COL B B4: 4,6,7 # reduction candidate for 4,6 B4: 4,6 => SOLVED * 143275869526891473879346521768913245954628317231754698687132954395467182412589736 B4: 7 # 14 pairs * PAIR E2: 4,9 ROW 2 C2: 4,9,6 # reduction candidate for 4,9 C2: 4,9 => CTR * 16327584952.8.1673...3.6521..69132.59..628.172.1754.986871329543..467182412589736 C2: 6 => SOLVED * 143275869526891473879346521768913245954628317231754698687132954395467182412589736 * PAIR E3: 4,9 ROW 3 B3: 4,9,7 # reduction candidate for 4,9 B3: 4,9 # 14 pairs C3: 4,9,8 # reduction candidate for 4,9 C3: 4,9 => SOLVED * 143275869526891473879346521768913245954628317231754698687132954395467182412589736 C3: 8 # 14 pairs * PAIR G2: 4,6 ROW 2 C2: 4,6,9 # reduction candidate for 4,6 C2: 9 => CTR * 163275849529841673...396521..69132.59..628.172.1754.986871329543..467182412589736 C2: 4,6 # 15 pairs * PAIR C5: 4,5 BLK 4 B5: 4,5,3 # reduction candidate for 4,5 B5: 4,5 => SOLVED * 143275869526891473879346521768913245954628317231754698687132954395467182412589736 B5: 3 => CTR * 1.32758.952.8.1.73...3.6521...9132.5935628417261754398687132954359467182412589736 * PAIR H4: 4,6 ROW 4 B4: 4,6,7 # reduction candidate for 4,6 B4: 4,6 => SOLVED * 143275869526891473879346521768913245954628317231754698687132954395467182412589736 B4: 7 # 14 pairs C4: 4,6,8 # reduction candidate for 4,6 C4: 4,6 # 14 pairs * PAIR G5: 3,4 ROW 5 B5: 3,4,5 # reduction candidate for 3,4 B5: 5 => SOLVED * 143275869526891473879346521768913245954628317231754698687132954395467182412589736 B5: 3,4 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-777320-base-pr-000.dot * REASONING * DIS # C2: 9 => CTR => C2: 4,6 * PRF # B4: 4,6 => SOL * DIS # C2: 4,9 => CTR => C2: 6 * PRF # C2: 6 => SOL * PRF # C3: 4,9 => SOL * DIS # C2: 9 => CTR => C2: 4,6 * PRF # B5: 4,5 => SOL * DIS # B5: 3 => CTR => B5: 4,5 * PRF # B4: 4,6 => SOL * PRF # B5: 5 => SOL * CNT 10 HDP CHAINS / 18 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B1,B6,B8,C5,C8,E2,E3,G2,G5,G6,H1,H4) * 1.32758.952.8.1.73...3.6521...9132.59..628.172.1754.986871329543..467182412589736 * PAIR B1: 4,6 BLK 1 C2: 4,6,9 # reduction candidate for 4,6 C2: 9 => CTR * 163275849529841673...396521..69132.59..628.172.1754.986871329543..467182412589736 * PAIR B1: 4,6 COL B B4: 4,6,7 # reduction candidate for 4,6 B4: 4,6 => SOLVED * 143275869526891473879346521768913245954628317231754698687132954395467182412589736 * DURATION: 0:00:03.793796 START: 08:48:03.510579 END: 08:48:07.304375 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-777320-base-pr-001.dot * REASONING * DIS # C2: 9 => CTR => C2: 4,6 * PRF C2: 4,6 # B4: 4,6 => SOL * STA C2: 4,6 + B4: 4,6 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokus.de/777320.html sehr schwierig * STABLE PAIRS (10p + 71s = 81c) # zz-sudoku-de-777320-base.sdk position: I25vdGU6IFBhaXIgUmVkdWN0aW9uIEFuYWx5c2lzICogU1RBQkxFIFBBSVJTICgxMHAgKyA3MXMgPSA4MWMpCgojZGlhZ29uYWxzOiAwCgojZGlzYWJsZWQ6IEIvNS81CjEuMzI3NTguOTUyLjg5MS43Mzc5ODM0NjUyMTg3LjkxMzIuNTkuNTYyOC4xNzIuMTc1NC45ODY4NzEzMjk1NDM1OTQ2NzE4MjQxMjU4OTczNg== -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 1.32758.952.8.1.73...3.6521...9132.59..628.172.1754.986871329543..467182412589736 B1: 4,6 C2: 4,6,9 # reduction candidate for 4,6 C2: 9 => CTR * 163275849529841673...396521..69132.59..628.172.1754.986871329543..467182412589736 B4: 4,6,7 # reduction candidate for 4,6 B4: 4,6 => SOLVED * 143275869526891473879346521768913245954628317231754698687132954395467182412589736 * SOLVED! -------------------------------------------------- |:step:| 00 -------------------------------------------------- * DISABLE VALUE:: B5 != 3 |:step:| 01 --------------------------------------------------
Solution
position: 143275869526891473879346521768913245954628317231754698687132954395467182412589736 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 # C2: 4,6 => UNS * DIS # C2: 9 => CTR => C2: 4,6 * PRF # B4: 4,6 => SOL * INC # B4: 7 => UNS * DIS # C2: 4,9 => CTR => C2: 6 * PRF # C2: 6 => SOL * INC # B3: 4,9 => UNS * PRF # C3: 4,9 => SOL * INC # C3: 8 => UNS * INC # C2: 4,6 => UNS * DIS # C2: 9 => CTR => C2: 4,6 * PRF # B5: 4,5 => SOL * DIS # B5: 3 => CTR => B5: 4,5 * PRF # B4: 4,6 => SOL * INC # B4: 7 => UNS * INC # C4: 4,6 => UNS * INC # B5: 3,4 => UNS * PRF # B5: 5 => SOL * CNT 18 HDP CHAINS / 18 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 4,6 => UNS * DIS # C2: 9 => CTR => C2: 4,6 * PRF C2: 4,6 # B4: 4,6 => SOL * STA C2: 4,6 + B4: 4,6 * CNT 3 HDP CHAINS / 3 HYP OPENED