Analysis of xx-top500-230-base.sdk
Contents
Original Sudoku
level: medium
position: ...8...5.7.....3.....2.....1.....7.4.2.13..........6..6....4....1.....2.....7.... initial
Autosolve
position: 9438672517.241.36..612.347.1.6..2734427136..5.3.74.61267..241.33146...272..371.46 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B9: 5,8 => CTR => B9: 9 * PRF # F8: 5,9 => SOL * PRF # E4: 5,9 => SOL * DIS # C6: 5,8 => CTR => C6: 9 * DIS # F6: 9 => CTR => F6: 5,8 * PRF # E4: 5,9 => SOL * PRF # B4: 8 => SOL * PRF # G9: 5 => SOL * PRF # F8: 5,9 => SOL * PRF # G9: 5 => SOL * PRF # C7: 5 => SOL * PRF # F8: 5,9 => SOL * CNT 12 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B9: 5,8 => CTR => B9: 9 * PRF B9: 9 # F8: 5,9 => SOL * STA B9: 9 + F8: 5,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...8...5.7.....3.....2.....1.....7.4.2.13..........6..6....4....1.....2.....7.... | initial |
| 9438672517.241.36..612.347.1.6..2734427136..5.3.74.61267..241.33146...272..371.46 | autosolve |
| 943867251752419368861253479186592734427136895539748612675924183314685927298371546 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) B2: 5,8 A3: 5,8 F2: 5,9 E3: 5,9 I2: 8,9 I3: 8,9 A6: 5,8 D4: 5,9 G5: 8,9 H5: 8,9 D7: 5,9 H7: 8,9 G8: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,A3: 5.. / B2 = 5 => 0 pairs (*) / A3 = 5 => 0 pairs (X) F2,E3: 5.. / F2 = 5 => 0 pairs (X) / E3 = 5 => 0 pairs (_) G8,G9: 5.. / G8 = 5 => 12 pairs (_) / G9 = 5 => 0 pairs (*) B2,F2: 5.. / B2 = 5 => 0 pairs (*) / F2 = 5 => 0 pairs (X) A3,E3: 5.. / A3 = 5 => 0 pairs (X) / E3 = 5 => 0 pairs (_) C7,D7: 5.. / C7 = 5 => 0 pairs (*) / D7 = 5 => 0 pairs (X) A3,A6: 5.. / A3 = 5 => 0 pairs (X) / A6 = 5 => 0 pairs (_) D4,D7: 5.. / D4 = 5 => 0 pairs (*) / D7 = 5 => 0 pairs (X) B2,A3: 8.. / B2 = 8 => 0 pairs (X) / A3 = 8 => 0 pairs (_) I2,I3: 8.. / I2 = 8 => 0 pairs (*) / I3 = 8 => 0 pairs (X) E4,F6: 8.. / E4 = 8 => 16 pairs (_) / F6 = 8 => 0 pairs (*) G5,H5: 8.. / G5 = 8 => 12 pairs (_) / H5 = 8 => 12 pairs (_) E8,F8: 8.. / E8 = 8 => 0 pairs (*) / F8 = 8 => 0 pairs (X) H7,G9: 8.. / H7 = 8 => 12 pairs (_) / G9 = 8 => 12 pairs (_) B2,I2: 8.. / B2 = 8 => 0 pairs (X) / I2 = 8 => 0 pairs (_) A3,I3: 8.. / A3 = 8 => 0 pairs (*) / I3 = 8 => 0 pairs (X) B4,E4: 8.. / B4 = 8 => 0 pairs (*) / E4 = 8 => 0 pairs (X) C7,H7: 8.. / C7 = 8 => 12 pairs (_) / H7 = 8 => 12 pairs (_) A3,A6: 8.. / A3 = 8 => 0 pairs (*) / A6 = 8 => 0 pairs (X) E4,E8: 8.. / E4 = 8 => 16 pairs (_) / E8 = 8 => 0 pairs (*) F6,F8: 8.. / F6 = 8 => 0 pairs (*) / F8 = 8 => 0 pairs (X) G5,G9: 8.. / G5 = 8 => 12 pairs (_) / G9 = 8 => 12 pairs (_) H5,H7: 8.. / H5 = 8 => 12 pairs (_) / H7 = 8 => 12 pairs (_) F2,E3: 9.. / F2 = 9 => 0 pairs (*) / E3 = 9 => 0 pairs (X) I2,I3: 9.. / I2 = 9 => 0 pairs (X) / I3 = 9 => 0 pairs (_) B4,C6: 9.. / B4 = 9 => 0 pairs (X) / C6 = 9 => 18 pairs (_) G5,H5: 9.. / G5 = 9 => 12 pairs (_) / H5 = 9 => 12 pairs (_) F2,I2: 9.. / F2 = 9 => 0 pairs (*) / I2 = 9 => 0 pairs (X) E3,I3: 9.. / E3 = 9 => 0 pairs (X) / I3 = 9 => 0 pairs (_) C6,F6: 9.. / C6 = 9 => 18 pairs (_) / F6 = 9 => 0 pairs (X) B4,B9: 9.. / B4 = 9 => 0 pairs (X) / B9 = 9 => 18 pairs (_) D4,D7: 9.. / D4 = 9 => 12 pairs (_) / D7 = 9 => 0 pairs (*) H5,H7: 9.. / H5 = 9 => 12 pairs (_) / H7 = 9 => 12 pairs (_) * DURATION: 0:00:55.682199 START: 10:42:03.488967 END: 10:42:59.171166 2017-05-04 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A6,B2,D4,D7,E3,F2,G5,G8,H5,H7,I2,I3) * 9438672517.241.36..612.347.1.6..2734427136..5.3.74.61267..241.33146...272..371.46 * PAIR B2: 5,8 COL B B4: 5,8,9 # reduction candidate for 5,8 B4: 5,8 # 18 pairs B9: 5,8,9 # reduction candidate for 5,8 B9: 5,8 => CTR * 9438672517.241.36..612.347.196582734427136..5.3.749612675924183314658927289371546 B9: 9 # 18 pairs * PAIR F2: 5,9 COL F F6: 5,9,8 # reduction candidate for 5,9 F6: 5,9 # 16 pairs F8: 5,9,8 # reduction candidate for 5,9 F8: 5,9 => SOLVED * 943867251752419368861253479186592734427136895539748612675924183314685927298371546 F8: 8 # 16 pairs * PAIR E3: 5,9 COL E E4: 5,9,8 # reduction candidate for 5,9 E4: 5,9 => SOLVED * 943867251752419368861253479186592734427136895539748612675924183314685927298371546 E4: 8 # 16 pairs E8: 5,9,8 # reduction candidate for 5,9 E8: 5,9 # 16 pairs * PAIR A6: 5,8 BLK 4 B4: 5,8,9 # reduction candidate for 5,8 B4: 5,8 # 18 pairs C6: 5,8,9 # reduction candidate for 5,8 C6: 5,8 => CTR * 9438672517.241.36..612.347.196582734427136..5.3.749612675924183314658927289371546 C6: 9 # 18 pairs * PAIR A6: 5,8 ROW 6 F6: 5,8,9 # reduction candidate for 5,8 F6: 9 => CTR * 9438672517.24153695612934781.6.82734427136..5.3.74961267.9241833146589272.9371546 F6: 5,8 # 18 pairs * PAIR D4: 5,9 BLK 5 E4: 5,9,8 # reduction candidate for 5,9 E4: 5,9 => SOLVED * 943867251752419368861253479186592734427136895539748612675924183314685927298371546 E4: 8 # 16 pairs F6: 5,9,8 # reduction candidate for 5,9 F6: 5,9 # 16 pairs * PAIR D4: 5,9 ROW 4 B4: 5,9,8 # reduction candidate for 5,9 B4: 8 => SOLVED * 943867251752419368861253479186592734427136895539748612675924183314685927298371546 B4: 5,9 # 16 pairs * PAIR G5: 8,9 COL G G9: 8,9,5 # reduction candidate for 8,9 G9: 5 => SOLVED * 943867251752419368861253479186592734427136895539748612675924183314685927298371546 G9: 8,9 # 12 pairs * PAIR D7: 5,9 BLK 8 E8: 5,9,8 # reduction candidate for 5,9 E8: 5,9 # 16 pairs F8: 5,9,8 # reduction candidate for 5,9 F8: 5,9 => SOLVED * 943867251752419368861253479186592734427136895539748612675924183314685927298371546 F8: 8 # 16 pairs * PAIR D7: 5,9 ROW 7 C7: 5,9,8 # reduction candidate for 5,9 C7: 8 # 12 pairs C7: 5,9 # 12 pairs * PAIR H7: 8,9 BLK 9 G9: 8,9,5 # reduction candidate for 8,9 G9: 5 => SOLVED * 943867251752419368861253479186592734427136895539748612675924183314685927298371546 G9: 8,9 # 12 pairs * PAIR H7: 8,9 ROW 7 C7: 8,9,5 # reduction candidate for 8,9 C7: 5 => SOLVED * 943867251752419368861253479186592734427136895539748612675924183314685927298371546 C7: 8,9 # 12 pairs * PAIR G8: 5,9 BLK 9 G9: 5,9,8 # reduction candidate for 5,9 G9: 8 # 12 pairs G9: 5,9 # 12 pairs * PAIR G8: 5,9 ROW 8 E8: 5,9,8 # reduction candidate for 5,9 E8: 5,9 # 16 pairs F8: 5,9,8 # reduction candidate for 5,9 F8: 5,9 => SOLVED * 943867251752419368861253479186592734427136895539748612675924183314685927298371546 F8: 8 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-230-base-pr-000.dot * REASONING * DIS # B9: 5,8 => CTR => B9: 9 * PRF # F8: 5,9 => SOL * PRF # E4: 5,9 => SOL * DIS # C6: 5,8 => CTR => C6: 9 * DIS # F6: 9 => CTR => F6: 5,8 * PRF # E4: 5,9 => SOL * PRF # B4: 8 => SOL * PRF # G9: 5 => SOL * PRF # F8: 5,9 => SOL * PRF # G9: 5 => SOL * PRF # C7: 5 => SOL * PRF # F8: 5,9 => SOL * CNT 12 HDP CHAINS / 35 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A6,B2,D4,D7,E3,F2,G5,G8,H5,H7,I2,I3) * 9438672517.241.36..612.347.1.6..2734427136..5.3.74.61267..241.33146...272..371.46 * PAIR B2: 5,8 COL B B4: 5,8,9 # reduction candidate for 5,8 B4: 5,8 # 18 pairs B9: 5,8,9 # reduction candidate for 5,8 B9: 5,8 => CTR * 9438672517.241.36..612.347.196582734427136..5.3.749612675924183314658927289371546 * RESTART * PAIR RESTART * PAIR F2: 5,9 COL F F8: 5,9,8 # reduction candidate for 5,9 F8: 5,9 => SOLVED * 943867251752419368861253479186592734427136895539748612675924183314685927298371546 * DURATION: 0:00:04.095801 START: 10:43:35.664904 END: 10:43:39.760705 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-230-base-pr-001.dot * REASONING * DIS # B9: 5,8 => CTR => B9: 9 * PRF B9: 9 # F8: 5,9 => SOL * STA B9: 9 + F8: 5,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 230 solution: 943867251752419368861253479186592734427136895539748612675924183314685927298371546 info: 2065 FNBWXY S8.f 12064 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 943867251752419368861253479186592734427136895539748612675924183314685927298371546 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 # B4: 5,8 => UNS * DIS # B9: 5,8 => CTR => B9: 9 * INC # B9: 9 => UNS * INC # F6: 5,9 => UNS * PRF # F8: 5,9 => SOL * INC # F8: 8 => UNS * PRF # E4: 5,9 => SOL * INC # E4: 8 => UNS * INC # E8: 5,9 => UNS * INC # B4: 5,8 => UNS * DIS # C6: 5,8 => CTR => C6: 9 * INC # C6: 9 => UNS * INC # F6: 5,8 => UNS * DIS # F6: 9 => CTR => F6: 5,8 * PRF # E4: 5,9 => SOL * INC # E4: 8 => UNS * INC # F6: 5,9 => UNS * INC # B4: 5,9 => UNS * PRF # B4: 8 => SOL * INC # G9: 8,9 => UNS * PRF # G9: 5 => SOL * INC # E8: 5,9 => UNS * PRF # F8: 5,9 => SOL * INC # F8: 8 => UNS * INC # C7: 5,9 => UNS * INC # C7: 8 => UNS * INC # G9: 8,9 => UNS * PRF # G9: 5 => SOL * INC # C7: 8,9 => UNS * PRF # C7: 5 => SOL * INC # G9: 5,9 => UNS * INC # G9: 8 => UNS * INC # E8: 5,9 => UNS * PRF # F8: 5,9 => SOL * INC # F8: 8 => UNS * CNT 35 HDP CHAINS / 35 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B4: 5,8 => UNS * DIS # B9: 5,8 => CTR => B9: 9 * PRF B9: 9 # F8: 5,9 => SOL * STA B9: 9 + F8: 5,9 * CNT 3 HDP CHAINS / 3 HYP OPENED