Analysis of xx-top500-274-base.sdk
Contents
Original Sudoku
level: medium
position: ...6.7.....24......3....8...5..3..2.6.......4....1....7.....3..4..7............5. initial
Autosolve
position: .4.6572.3.6248357.537.2.846.54.3672.62.57..3437.2146.57.5.4236.4.3765..22.639.457 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 1,9 => CTR => A1: 8 * DIS # A4: 8 => CTR => A4: 1,9 * DIS # A1: 1,9 => CTR => A1: 8 * PRF # H8: 1,9 => SOL * DIS # H8: 8 => CTR => H8: 1,9 * PRF # I4: 1,9 => SOL * DIS # I4: 8 => CTR => I4: 1,9 * DIS # I7: 1,9 => CTR => I7: 8 * PRF # I7: 8 => SOL * DIS # A4: 8,9 => CTR => A4: 1 * PRF # A4: 1 => SOL * PRF # C5: 8,9 => SOL * DIS # C5: 1 => CTR => C5: 8,9 * DIS # C1: 8,9 => CTR => C1: 1 * PRF # C1: 1 => SOL * DIS # A4: 8,9 => CTR => A4: 1 * PRF # A4: 1 => SOL * PRF # I4: 8,9 => SOL * DIS # I4: 1 => CTR => I4: 8,9 * PRF # C5: 8,9 => SOL * DIS # C5: 1 => CTR => C5: 8,9 * PRF # I4: 1,9 => SOL * DIS # I4: 8 => CTR => I4: 1,9 * DIS # C5: 1,9 => CTR => C5: 8 * PRF # C5: 8 => SOL * PRF # I4: 8,9 => SOL * DIS # I4: 1 => CTR => I4: 8,9 * DIS # H8: 8,9 => CTR => H8: 1 * PRF # H8: 1 => SOL * DIS # B7: 1,8 => CTR => B7: 9 * DIS # B7: 1,8 => CTR => B7: 9 * DIS # I7: 1,9 => CTR => I7: 8 * PRF # I7: 8 => SOL * PRF # H8: 1,9 => SOL * DIS # H8: 8 => CTR => H8: 1,9 * DIS # B8: 1,9 => CTR => B8: 8 * PRF # B8: 8 => SOL * CNT 37 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 1,9 => CTR => A1: 8 * PRF A1: 8 # H8: 1,9 => SOL * STA A1: 8 + H8: 1,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...6.7.....24......3....8...5..3..2.6.......4....1....7.....3..4..7............5. | initial |
| .4.6572.3.6248357.537.2.846.54.3672.62.57..3437.2146.57.5.4236.4.3765..22.639.457 | autosolve |
| 841657293962483571537921846154836729628579134379214685795142368483765912216398457 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) A2: 1,9 D3: 1,9 F3: 1,9 H1: 1,9 I2: 1,9 C6: 8,9 D4: 8,9 F5: 8,9 G5: 1,9 H6: 8,9 B9: 1,8 D7: 1,8 F9: 1,8 G8: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D3,F3: 1.. / D3 = 1 => 0 pairs (X) / F3 = 1 => 0 pairs (_) H1,I2: 1.. / H1 = 1 => 0 pairs (X) / I2 = 1 => 0 pairs (_) A4,C5: 1.. / A4 = 1 => 0 pairs (*) / C5 = 1 => 0 pairs (X) I4,G5: 1.. / I4 = 1 => 0 pairs (X) / G5 = 1 => 0 pairs (_) D7,F9: 1.. / D7 = 1 => 0 pairs (*) / F9 = 1 => 0 pairs (X) A2,I2: 1.. / A2 = 1 => 0 pairs (X) / I2 = 1 => 0 pairs (_) A4,I4: 1.. / A4 = 1 => 0 pairs (*) / I4 = 1 => 0 pairs (X) C5,G5: 1.. / C5 = 1 => 0 pairs (X) / G5 = 1 => 0 pairs (_) B9,F9: 1.. / B9 = 1 => 0 pairs (*) / F9 = 1 => 0 pairs (X) C1,C5: 1.. / C1 = 1 => 0 pairs (*) / C5 = 1 => 0 pairs (X) D3,D7: 1.. / D3 = 1 => 0 pairs (X) / D7 = 1 => 0 pairs (_) F3,F9: 1.. / F3 = 1 => 0 pairs (*) / F9 = 1 => 0 pairs (X) G5,G8: 1.. / G5 = 1 => 0 pairs (*) / G8 = 1 => 0 pairs (X) H1,H8: 1.. / H1 = 1 => 0 pairs (X) / H8 = 1 => 0 pairs (_) A1,C1: 8.. / A1 = 8 => 16 pairs (_) / C1 = 8 => 0 pairs (X) D4,F5: 8.. / D4 = 8 => 0 pairs (*) / F5 = 8 => 0 pairs (X) I4,H6: 8.. / I4 = 8 => 0 pairs (X) / H6 = 8 => 0 pairs (_) D7,F9: 8.. / D7 = 8 => 0 pairs (X) / F9 = 8 => 0 pairs (_) I7,H8: 8.. / I7 = 8 => 0 pairs (*) / H8 = 8 => 0 pairs (X) C5,F5: 8.. / C5 = 8 => 0 pairs (*) / F5 = 8 => 0 pairs (X) C6,H6: 8.. / C6 = 8 => 0 pairs (X) / H6 = 8 => 0 pairs (_) B8,H8: 8.. / B8 = 8 => 0 pairs (*) / H8 = 8 => 0 pairs (X) B9,F9: 8.. / B9 = 8 => 0 pairs (X) / F9 = 8 => 0 pairs (_) A1,A4: 8.. / A1 = 8 => 16 pairs (_) / A4 = 8 => 0 pairs (X) D4,D7: 8.. / D4 = 8 => 0 pairs (*) / D7 = 8 => 0 pairs (X) F5,F9: 8.. / F5 = 8 => 0 pairs (X) / F9 = 8 => 0 pairs (_) H6,H8: 8.. / H6 = 8 => 0 pairs (*) / H8 = 8 => 0 pairs (X) I4,I7: 8.. / I4 = 8 => 0 pairs (X) / I7 = 8 => 0 pairs (_) D3,F3: 9.. / D3 = 9 => 0 pairs (*) / F3 = 9 => 0 pairs (X) H1,I2: 9.. / H1 = 9 => 0 pairs (*) / I2 = 9 => 0 pairs (X) D4,F5: 9.. / D4 = 9 => 0 pairs (X) / F5 = 9 => 0 pairs (_) B7,B8: 9.. / B7 = 9 => 16 pairs (_) / B8 = 9 => 0 pairs (X) A2,I2: 9.. / A2 = 9 => 0 pairs (*) / I2 = 9 => 0 pairs (X) C6,H6: 9.. / C6 = 9 => 0 pairs (*) / H6 = 9 => 0 pairs (X) B7,I7: 9.. / B7 = 9 => 16 pairs (_) / I7 = 9 => 0 pairs (X) D3,D4: 9.. / D3 = 9 => 0 pairs (*) / D4 = 9 => 0 pairs (X) F3,F5: 9.. / F3 = 9 => 0 pairs (X) / F5 = 9 => 0 pairs (_) G5,G8: 9.. / G5 = 9 => 0 pairs (X) / G8 = 9 => 0 pairs (_) * DURATION: 0:01:19.568454 START: 12:17:00.178331 END: 12:18:19.746785 2017-05-04 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B9,C6,D3,D4,D7,F3,F5,F9,G5,G8,H1,H6,I2) * .4.6572.3.6248357.537.2.846.54.3672.62.57..3437.2146.57.5.4236.4.3765..22.639.457 * PAIR A2: 1,9 BLK 1 A1: 1,9,8 # reduction candidate for 1,9 A1: 1,9 => CTR * .486572.3.6248357.537.2.8468549367216215789343792146857.58423694.3765..22.639.457 A1: 8 # 16 pairs C1: 1,9,8 # reduction candidate for 1,9 C1: 1,9 # 16 pairs * PAIR A2: 1,9 COL A A4: 1,9,8 # reduction candidate for 1,9 A4: 8 => CTR * .4.6572.3.6248357.537.2.8468549367216215789343792146857.58423694.3765..22.639.457 A4: 1,9 # 16 pairs * PAIR H1: 1,9 ROW 1 A1: 1,9,8 # reduction candidate for 1,9 A1: 1,9 => CTR * .486572.3.6248357.537.2.8468549367216215789343792146857.58423694.3765..22.639.457 A1: 8 # 16 pairs C1: 1,9,8 # reduction candidate for 1,9 C1: 1,9 # 16 pairs * PAIR H1: 1,9 COL H H8: 1,9,8 # reduction candidate for 1,9 H8: 1,9 => SOLVED * 841657293962483571537921846154836729628579134379214685795142368483765912216398457 H8: 8 => CTR * .4.657213162483579537.2.846.54.3672162157893437.2146.57.5.4236.4.3765..22.639.457 * PAIR I2: 1,9 COL I I4: 1,9,8 # reduction candidate for 1,9 I4: 1,9 => SOLVED * 841657293962483571537921846154836729628579134379214685795142368483765912216398457 I4: 8 => CTR * .4.6572.3.6248357.537.2.84615493672862.5781343782146957.584236.4.3765982286391457 I7: 1,9,8 # reduction candidate for 1,9 I7: 1,9 => CTR * 84.6572.3.6248357.537.2.846.54.3672862.5781343782146957.584236.4.3765982286391457 I7: 8 => SOLVED * 841657293962483571537921846154836729628579134379214685795142368483765912216398457 * PAIR C6: 8,9 BLK 4 A4: 8,9,1 # reduction candidate for 8,9 A4: 8,9 => CTR * .4.6572.3.6248357.537.2.846.54.367216215789343792146857.58423694.3765..22.639.457 A4: 1 => SOLVED * 841657293962483571537921846154836729628579134379214685795142368483765912216398457 C5: 8,9,1 # reduction candidate for 8,9 C5: 8,9 => SOLVED * 841657293962483571537921846154836729628579134379214685795142368483765912216398457 C5: 1 => CTR * .4.6572.3.6248357.537.2.846.54.3672.6215789343792146857.584236.4837651922.639.457 * PAIR C6: 8,9 COL C C1: 8,9,1 # reduction candidate for 8,9 C1: 8,9 => CTR * .4.6572.3.6248357.537.2.846.54.3672.6215789343792146857.584236.4837651922.639.457 C1: 1 => SOLVED * 841657293962483571537921846154836729628579134379214685795142368483765912216398457 * PAIR D4: 8,9 ROW 4 A4: 8,9,1 # reduction candidate for 8,9 A4: 8,9 => CTR * .4.6572.3.6248357.537.2.846.54.367216215789343792146857.58423694.3765..22.639.457 A4: 1 => SOLVED * 841657293962483571537921846154836729628579134379214685795142368483765912216398457 I4: 8,9,1 # reduction candidate for 8,9 I4: 8,9 => SOLVED * 841657293962483571537921846154836729628579134379214685795142368483765912216398457 I4: 1 => CTR * .4.6572.3.6248357.537.2.846.54.367216215789343792146857.58423694.3765..22.639.457 * PAIR F5: 8,9 ROW 5 C5: 8,9,1 # reduction candidate for 8,9 C5: 8,9 => SOLVED * 841657293962483571537921846154836729628579134379214685795142368483765912216398457 C5: 1 => CTR * .4.6572.3.6248357.537.2.846.54.3672.6215789343792146857.584236.4837651922.639.457 * PAIR G5: 1,9 BLK 6 I4: 1,9,8 # reduction candidate for 1,9 I4: 1,9 => SOLVED * 841657293962483571537921846154836729628579134379214685795142368483765912216398457 I4: 8 => CTR * .4.6572.3.6248357.537.2.84615493672862.5781343782146957.584236.4.3765982286391457 * PAIR G5: 1,9 ROW 5 C5: 1,9,8 # reduction candidate for 1,9 C5: 1,9 => CTR * .4.657213162483579537.2.846.54.3672.62.578.3437.2146.57.584236.4.3765.82286391457 C5: 8 => SOLVED * 841657293962483571537921846154836729628579134379214685795142368483765912216398457 * PAIR H6: 8,9 BLK 6 I4: 8,9,1 # reduction candidate for 8,9 I4: 8,9 => SOLVED * 841657293962483571537921846154836729628579134379214685795142368483765912216398457 I4: 1 => CTR * .4.6572.3.6248357.537.2.846.54.367216215789343792146857.58423694.3765..22.639.457 * PAIR H6: 8,9 COL H H8: 8,9,1 # reduction candidate for 8,9 H8: 8,9 => CTR * .4.657213162483579537.2.846.54.36721621578934379214685795.4236.4.3765..22.639.457 H8: 1 => SOLVED * 841657293962483571537921846154836729628579134379214685795142368483765912216398457 * PAIR B9: 1,8 BLK 7 B7: 1,8,9 # reduction candidate for 1,8 B7: 1,8 => CTR * .4.6572.3.6248357.537.2.846.54.3672.62.57..3437.2146.57.5.423694937651822.639.457 B7: 9 # 16 pairs B8: 1,8,9 # reduction candidate for 1,8 B8: 1,8 # 16 pairs * PAIR D7: 1,8 ROW 7 B7: 1,8,9 # reduction candidate for 1,8 B7: 1,8 => CTR * .4.6572.3.6248357.537.2.846.54.3672.62.57..3437.2146.57.5.423694937651822.639.457 B7: 9 # 16 pairs I7: 1,8,9 # reduction candidate for 1,8 I7: 1,8 # 16 pairs * PAIR G8: 1,9 BLK 9 I7: 1,9,8 # reduction candidate for 1,9 I7: 1,9 => CTR * 84.6572.3.6248357.537.2.846.54.3672862.5781343782146957.584236.4.3765982286391457 I7: 8 => SOLVED * 841657293962483571537921846154836729628579134379214685795142368483765912216398457 H8: 1,9,8 # reduction candidate for 1,9 H8: 1,9 => SOLVED * 841657293962483571537921846154836729628579134379214685795142368483765912216398457 H8: 8 => CTR * .4.657213162483579537.2.846.54.3672162157893437.2146.57.5.4236.4.3765..22.639.457 * PAIR G8: 1,9 ROW 8 B8: 1,9,8 # reduction candidate for 1,9 B8: 1,9 => CTR * .4.657213162483579537.2.846.54.3672.62.57..3437.2146.57.5.4236.4.3765.822.639.457 B8: 8 => SOLVED * 841657293962483571537921846154836729628579134379214685795142368483765912216398457 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-274-base-pr-000.dot * REASONING * DIS # A1: 1,9 => CTR => A1: 8 * DIS # A4: 8 => CTR => A4: 1,9 * DIS # A1: 1,9 => CTR => A1: 8 * PRF # H8: 1,9 => SOL * DIS # H8: 8 => CTR => H8: 1,9 * PRF # I4: 1,9 => SOL * DIS # I4: 8 => CTR => I4: 1,9 * DIS # I7: 1,9 => CTR => I7: 8 * PRF # I7: 8 => SOL * DIS # A4: 8,9 => CTR => A4: 1 * PRF # A4: 1 => SOL * PRF # C5: 8,9 => SOL * DIS # C5: 1 => CTR => C5: 8,9 * DIS # C1: 8,9 => CTR => C1: 1 * PRF # C1: 1 => SOL * DIS # A4: 8,9 => CTR => A4: 1 * PRF # A4: 1 => SOL * PRF # I4: 8,9 => SOL * DIS # I4: 1 => CTR => I4: 8,9 * PRF # C5: 8,9 => SOL * DIS # C5: 1 => CTR => C5: 8,9 * PRF # I4: 1,9 => SOL * DIS # I4: 8 => CTR => I4: 1,9 * DIS # C5: 1,9 => CTR => C5: 8 * PRF # C5: 8 => SOL * PRF # I4: 8,9 => SOL * DIS # I4: 1 => CTR => I4: 8,9 * DIS # H8: 8,9 => CTR => H8: 1 * PRF # H8: 1 => SOL * DIS # B7: 1,8 => CTR => B7: 9 * DIS # B7: 1,8 => CTR => B7: 9 * DIS # I7: 1,9 => CTR => I7: 8 * PRF # I7: 8 => SOL * PRF # H8: 1,9 => SOL * DIS # H8: 8 => CTR => H8: 1,9 * DIS # B8: 1,9 => CTR => B8: 8 * PRF # B8: 8 => SOL * CNT 37 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B9,C6,D3,D4,D7,F3,F5,F9,G5,G8,H1,H6,I2) * .4.6572.3.6248357.537.2.846.54.3672.62.57..3437.2146.57.5.4236.4.3765..22.639.457 * PAIR A2: 1,9 BLK 1 A1: 1,9,8 # reduction candidate for 1,9 A1: 1,9 => CTR * .486572.3.6248357.537.2.8468549367216215789343792146857.58423694.3765..22.639.457 * RESTART * PAIR H1: 1,9 COL H H8: 1,9,8 # reduction candidate for 1,9 H8: 1,9 => SOLVED * 841657293962483571537921846154836729628579134379214685795142368483765912216398457 * DURATION: 0:00:03.717800 START: 12:19:22.347025 END: 12:19:26.064825 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-274-base-pr-001.dot * REASONING * DIS # A1: 1,9 => CTR => A1: 8 * PRF A1: 8 # H8: 1,9 => SOL * STA A1: 8 + H8: 1,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 274 solution: 841657293962483571537921846154836729628579134379214685795142368483765912216398457 info: 2203 FNBHWY S8.f 10921 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 841657293962483571537921846154836729628579134379214685795142368483765912216398457 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 # A1: 1,9 => CTR => A1: 8 * INC # A1: 8 => UNS * INC # C1: 1,9 => UNS * INC # A4: 1,9 => UNS * DIS # A4: 8 => CTR => A4: 1,9 * DIS # A1: 1,9 => CTR => A1: 8 * INC # A1: 8 => UNS * INC # C1: 1,9 => UNS * PRF # H8: 1,9 => SOL * DIS # H8: 8 => CTR => H8: 1,9 * PRF # I4: 1,9 => SOL * DIS # I4: 8 => CTR => I4: 1,9 * DIS # I7: 1,9 => CTR => I7: 8 * PRF # I7: 8 => SOL * DIS # A4: 8,9 => CTR => A4: 1 * PRF # A4: 1 => SOL * PRF # C5: 8,9 => SOL * DIS # C5: 1 => CTR => C5: 8,9 * DIS # C1: 8,9 => CTR => C1: 1 * PRF # C1: 1 => SOL * DIS # A4: 8,9 => CTR => A4: 1 * PRF # A4: 1 => SOL * PRF # I4: 8,9 => SOL * DIS # I4: 1 => CTR => I4: 8,9 * PRF # C5: 8,9 => SOL * DIS # C5: 1 => CTR => C5: 8,9 * PRF # I4: 1,9 => SOL * DIS # I4: 8 => CTR => I4: 1,9 * DIS # C5: 1,9 => CTR => C5: 8 * PRF # C5: 8 => SOL * PRF # I4: 8,9 => SOL * DIS # I4: 1 => CTR => I4: 8,9 * DIS # H8: 8,9 => CTR => H8: 1 * PRF # H8: 1 => SOL * DIS # B7: 1,8 => CTR => B7: 9 * INC # B7: 9 => UNS * INC # B8: 1,8 => UNS * DIS # B7: 1,8 => CTR => B7: 9 * INC # B7: 9 => UNS * INC # I7: 1,8 => UNS * DIS # I7: 1,9 => CTR => I7: 8 * PRF # I7: 8 => SOL * PRF # H8: 1,9 => SOL * DIS # H8: 8 => CTR => H8: 1,9 * DIS # B8: 1,9 => CTR => B8: 8 * PRF # B8: 8 => SOL * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 1,9 => CTR => A1: 8 * PRF A1: 8 # H8: 1,9 => SOL * STA A1: 8 + H8: 1,9 * CNT 2 HDP CHAINS / 2 HYP OPENED