Analysis of xx-top500-222-base.sdk
Contents
Original Sudoku
level: medium
position: ....3..824.1..................4.65...8.....3....7........5..7..6.....4...3..2.... initial
Autosolve
position: ...1346824.18..3.........4....4.6578786.5..34.4.7832.6...54.7636..3..42..346278.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A6: 5,9 => CTR => A6: 1 * PRF # A6: 1 => SOL * PRF # A9: 5,9 => SOL * DIS # A9: 1 => CTR => A9: 5,9 * DIS # F3: 2,9 => CTR => F3: 5 * DIS # I2: 5,9 => CTR => I2: 7 * DIS # I3: 5,9 => CTR => I3: 1,7 * DIS # F2: 2 => CTR => F2: 5,9 * DIS # H9: 5,9 => CTR => H9: 1 * PRF # H9: 1 => SOL * PRF # I3: 1,9 => SOL * DIS # I3: 5,7 => CTR => I3: 1,9 * DIS # A6: 5 => CTR => A6: 1,9 * DIS # A6: 5,9 => CTR => A6: 1 * PRF # A6: 1 => SOL * DIS # F5: 1,9 => CTR => F5: 2 * PRF # F5: 2 => SOL * PRF # F5: 2,9 => SOL * DIS # F5: 1 => CTR => F5: 2,9 * DIS # F5: 1,9 => CTR => F5: 2 * PRF # F5: 2 => SOL * DIS # A6: 5 => CTR => A6: 1,9 * DIS # H9: 5 => CTR => H9: 1,9 * PRF # C7: 9 => SOL * PRF # A9: 5 => SOL * PRF # F7: 8 => SOL * PRF # C8: 8,9 => SOL * PRF # F8: 1,9 => SOL * PRF # I8: 5 => SOL * CNT 29 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A6: 5,9 => CTR => A6: 1 * PRF A6: 1 => SOL * STA A6: 1 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....3..824.1..................4.65...8.....3....7........5..7..6.....4...3..2.... | initial |
| ...1346824.18..3.........4....4.6578786.5..34.4.7832.6...54.7636..3..42..346278.. | autosolve |
| 957134682421869357863275941392416578786952134145783296219548763678391425534627819 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (23) A1: 5,9 B1: 5,7 B2: 2,6 A3: 3,8 B3: 2,6 C3: 3,8 E2: 6,7 D3: 2,9 E3: 6,7 H2: 5,9 G3: 1,9 A4: 2,3 B4: 1,9 C4: 2,3 C6: 5,9 E4: 1,9 D5: 2,9 G5: 1,9 H6: 1,9 A7: 2,8 B7: 1,9 B8: 5,7 E8: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G3,I3: 1.. / G3 = 1 => 0 pairs (X) / I3 = 1 => 0 pairs (_) B4,A6: 1.. / B4 = 1 => 0 pairs (X) / A6 = 1 => 0 pairs (_) E4,F5: 1.. / E4 = 1 => 0 pairs (*) / F5 = 1 => 0 pairs (X) G5,H6: 1.. / G5 = 1 => 0 pairs (*) / H6 = 1 => 0 pairs (X) B7,A9: 1.. / B7 = 1 => 0 pairs (*) / A9 = 1 => 0 pairs (X) B4,E4: 1.. / B4 = 1 => 0 pairs (X) / E4 = 1 => 0 pairs (_) F5,G5: 1.. / F5 = 1 => 0 pairs (X) / G5 = 1 => 0 pairs (_) A6,H6: 1.. / A6 = 1 => 0 pairs (*) / H6 = 1 => 0 pairs (X) B7,F7: 1.. / B7 = 1 => 0 pairs (*) / F7 = 1 => 0 pairs (X) A6,A9: 1.. / A6 = 1 => 0 pairs (*) / A9 = 1 => 0 pairs (X) B4,B7: 1.. / B4 = 1 => 0 pairs (X) / B7 = 1 => 0 pairs (_) E4,E8: 1.. / E4 = 1 => 0 pairs (*) / E8 = 1 => 0 pairs (X) G3,G5: 1.. / G3 = 1 => 0 pairs (X) / G5 = 1 => 0 pairs (_) H6,H9: 1.. / H6 = 1 => 0 pairs (X) / H9 = 1 => 0 pairs (_) B2,B3: 2.. / B2 = 2 => 20 pairs (_) / B3 = 2 => 0 pairs (X) A4,C4: 2.. / A4 = 2 => 19 pairs (_) / C4 = 2 => 19 pairs (_) D5,F5: 2.. / D5 = 2 => 0 pairs (X) / F5 = 2 => 0 pairs (_) A7,C7: 2.. / A7 = 2 => 19 pairs (_) / C7 = 2 => 19 pairs (_) B2,F2: 2.. / B2 = 2 => 20 pairs (_) / F2 = 2 => 0 pairs (X) A4,A7: 2.. / A4 = 2 => 19 pairs (_) / A7 = 2 => 19 pairs (_) C4,C7: 2.. / C4 = 2 => 19 pairs (_) / C7 = 2 => 19 pairs (_) D3,D5: 2.. / D3 = 2 => 0 pairs (*) / D5 = 2 => 0 pairs (X) A3,C3: 3.. / A3 = 3 => 19 pairs (_) / C3 = 3 => 19 pairs (_) A4,C4: 3.. / A4 = 3 => 19 pairs (_) / C4 = 3 => 19 pairs (_) A3,A4: 3.. / A3 = 3 => 19 pairs (_) / A4 = 3 => 19 pairs (_) C3,C4: 3.. / C3 = 3 => 19 pairs (_) / C4 = 3 => 19 pairs (_) F2,F3: 5.. / F2 = 5 => 0 pairs (X) / F3 = 5 => 24 pairs (_) A6,C6: 5.. / A6 = 5 => 0 pairs (X) / C6 = 5 => 24 pairs (_) F3,I3: 5.. / F3 = 5 => 24 pairs (_) / I3 = 5 => 0 pairs (X) B1,B8: 5.. / B1 = 5 => 23 pairs (_) / B8 = 5 => 26 pairs (_) H2,H9: 5.. / H2 = 5 => 25 pairs (_) / H9 = 5 => 0 pairs (X) B2,B3: 6.. / B2 = 6 => 0 pairs (X) / B3 = 6 => 20 pairs (_) E2,E3: 6.. / E2 = 6 => 20 pairs (_) / E3 = 6 => 0 pairs (X) B2,E2: 6.. / B2 = 6 => 0 pairs (X) / E2 = 6 => 20 pairs (_) B3,E3: 6.. / B3 = 6 => 20 pairs (_) / E3 = 6 => 0 pairs (X) B1,C1: 7.. / B1 = 7 => 26 pairs (_) / C1 = 7 => 23 pairs (_) E2,E3: 7.. / E2 = 7 => 0 pairs (X) / E3 = 7 => 20 pairs (_) I2,I3: 7.. / I2 = 7 => 20 pairs (_) / I3 = 7 => 0 pairs (X) B8,C8: 7.. / B8 = 7 => 23 pairs (_) / C8 = 7 => 26 pairs (_) E2,I2: 7.. / E2 = 7 => 0 pairs (X) / I2 = 7 => 20 pairs (_) E3,I3: 7.. / E3 = 7 => 20 pairs (_) / I3 = 7 => 0 pairs (X) B1,B8: 7.. / B1 = 7 => 26 pairs (_) / B8 = 7 => 23 pairs (_) C1,C8: 7.. / C1 = 7 => 23 pairs (_) / C8 = 7 => 26 pairs (_) A3,C3: 8.. / A3 = 8 => 19 pairs (_) / C3 = 8 => 19 pairs (_) F7,F8: 8.. / F7 = 8 => 0 pairs (*) / F8 = 8 => 0 pairs (X) C8,F8: 8.. / C8 = 8 => 0 pairs (*) / F8 = 8 => 0 pairs (X) A3,A7: 8.. / A3 = 8 => 19 pairs (_) / A7 = 8 => 19 pairs (_) A1,C1: 9.. / A1 = 9 => 26 pairs (_) / C1 = 9 => 24 pairs (_) G5,H6: 9.. / G5 = 9 => 0 pairs (X) / H6 = 9 => 0 pairs (_) B4,E4: 9.. / B4 = 9 => 0 pairs (*) / E4 = 9 => 0 pairs (X) B4,B7: 9.. / B4 = 9 => 0 pairs (*) / B7 = 9 => 0 pairs (X) D3,D5: 9.. / D3 = 9 => 0 pairs (X) / D5 = 9 => 0 pairs (_) E4,E8: 9.. / E4 = 9 => 0 pairs (X) / E8 = 9 => 0 pairs (_) G3,G5: 9.. / G3 = 9 => 0 pairs (*) / G5 = 9 => 0 pairs (X) * DURATION: 0:02:02.018847 START: 10:22:12.342715 END: 10:24:14.361562 2017-05-04 * CP COUNT: (54) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A4,A7,B1,B2,B3,B4,B7,B8,C3,C4,C6,D3,D5,E2,E3,E4,E8,G3,G5,H2,H6) * ...1346824.18..3.........4....4.6578786.5..34.4.7832.6...54.7636..3..42..346278.. * PAIR A1: 5,9 BLK 1 C1: 5,9,7 # reduction candidate for 5,9 C1: 5,9 # 26 pairs C1: 7 # 23 pairs * PAIR A1: 5,9 COL A A6: 5,9,1 # reduction candidate for 5,9 A6: 5,9 => CTR * ...1346824.18..3.........4..1.496578786251934.4.783216.9.5487636.8319425.346278.. A6: 1 => SOLVED * 957134682421869357863275941392416578786952134145783296219548763678391425534627819 A9: 5,9,1 # reduction candidate for 5,9 A9: 5,9 => SOLVED * 957134682421869357863275941392416578786952134145783296219548763678391425534627819 A9: 1 => CTR * ...1346824.18..3.........4..1.496578786251934.4.783216.9.5487636.831.42.1346278.. * PAIR B1: 5,7 BLK 1 C1: 5,7,9 # reduction candidate for 5,7 C1: 5,7 # 26 pairs C1: 9 # 24 pairs * PAIR D3: 2,9 BLK 2 F2: 2,9,5 # reduction candidate for 2,9 F2: 2,9 # 24 pairs F3: 2,9,5 # reduction candidate for 2,9 F3: 2,9 => CTR * ...1346824.18.5397....7.145...4.6578786.51934.4.783216.1.54.7636..31.429934627851 F3: 5 # 24 pairs * PAIR H2: 5,9 BLK 3 I2: 5,9,7 # reduction candidate for 5,9 I2: 5,9 => CTR * ...1346824618723...2.965147...4.6578786251934.4.783216.1.54.7636..31.42..346278.1 I2: 7 # 20 pairs I3: 5,9,1,7 # reduction candidate for 5,9 I3: 5,9 => CTR * ...1346824.18..3.7....7.14....4.6578786.51934.4.783216.1.54.7636..31.42..346278.1 I3: 1,7 # 25 pairs * PAIR H2: 5,9 ROW 2 F2: 5,9,2 # reduction candidate for 5,9 F2: 2 => CTR * ...1346824.18.23...2.965147...4.6578786251934.4.783216.1.54.7636..31.42..346278.1 F2: 5,9 # 20 pairs * PAIR H2: 5,9 COL H H9: 5,9,1 # reduction candidate for 5,9 H9: 5,9 => CTR * ...1346824.18..3........14..1.496578786251934.4.783216.9.5487636.831.42.1346278.. H9: 1 => SOLVED * 957134682421869357863275941392416578786952134145783296219548763678391425534627819 * PAIR G3: 1,9 BLK 3 I3: 1,9,5,7 # reduction candidate for 1,9 I3: 1,9 => SOLVED * 957134682421869357863275941392416578786952134145783296219548763678391425534627819 I3: 5,7 => CTR * ...1346824.18..3........14....4.6578786.51934.4.783216.1.54.7636..31.42..346278.1 * PAIR B4: 1,9 BLK 4 A6: 1,9,5 # reduction candidate for 1,9 A6: 5 => CTR * ...1346824.18..3.........4..1.496578786251934549783216.9.5487636.831.42..346278.. A6: 1,9 # 24 pairs * PAIR C6: 5,9 BLK 4 A6: 5,9,1 # reduction candidate for 5,9 A6: 5,9 => CTR * ...1346824.18..3.........4..1.496578786251934.4.783216.9.5487636.8319425.346278.. A6: 1 => SOLVED * 957134682421869357863275941392416578786952134145783296219548763678391425534627819 * PAIR C6: 5,9 COL C C1: 5,9,7 # reduction candidate for 5,9 C1: 5,9 # 26 pairs C8: 5,9,7,8 # reduction candidate for 5,9 C8: 5,9 # 26 pairs * PAIR E4: 1,9 BLK 5 F5: 1,9,2 # reduction candidate for 1,9 F5: 1,9 => CTR * ...1346824.18..3.....9..14....4.6578786251934.4.783216.1.54.7636..31.42..346278.1 F5: 2 => SOLVED * 957134682421869357863275941392416578786952134145783296219548763678391425534627819 * PAIR D5: 2,9 BLK 5 F5: 2,9,1 # reduction candidate for 2,9 F5: 2,9 => SOLVED * 957134682421869357863275941392416578786952134145783296219548763678391425534627819 F5: 1 => CTR * ...1346824.18..3.........4....4.6578786251934.4.783216.1.54.7636..31.42..346278.1 * PAIR G5: 1,9 ROW 5 F5: 1,9,2 # reduction candidate for 1,9 F5: 1,9 => CTR * ...1346824.18..3.....9..14....4.6578786251934.4.783216.1.54.7636..31.42..346278.1 F5: 2 => SOLVED * 957134682421869357863275941392416578786952134145783296219548763678391425534627819 * PAIR H6: 1,9 ROW 6 A6: 1,9,5 # reduction candidate for 1,9 A6: 5 => CTR * ...1346824.18..3.........4..1.496578786251934549783216.9.5487636.831.42..346278.. A6: 1,9 # 24 pairs * PAIR H6: 1,9 COL H H9: 1,9,5 # reduction candidate for 1,9 H9: 5 => CTR * ...1346824.18..39.......14..1.496578786251934.4.783216.9.5487636.831.42.134627859 H9: 1,9 # 25 pairs * PAIR A7: 2,8 BLK 7 C7: 2,8,9 # reduction candidate for 2,8 C7: 9 => SOLVED * 957134682421869357863275941392416578786952134145783296219548763678391425534627819 C7: 2,8 # 25 pairs * PAIR B7: 1,9 BLK 7 A9: 1,9,5 # reduction candidate for 1,9 A9: 5 => SOLVED * 957134682421869357863275941392416578786952134145783296219548763678391425534627819 A9: 1,9 # 28 pairs * PAIR B7: 1,9 ROW 7 F7: 1,9,8 # reduction candidate for 1,9 F7: 8 => SOLVED * 957134682421869357863275941392416578786952134145783296219548763678391425534627819 F7: 1,9 # 25 pairs * PAIR B8: 5,7 BLK 7 C8: 5,7,8,9 # reduction candidate for 5,7 C8: 8,9 => SOLVED * 957134682421869357863275941392416578786952134145783296219548763678391425534627819 C8: 5,7 # 28 pairs * PAIR E8: 1,9 BLK 8 F7: 1,9,8 # reduction candidate for 1,9 F7: 1,9 # 25 pairs F8: 1,9,8 # reduction candidate for 1,9 F8: 1,9 => SOLVED * 957134682421869357863275941392416578786952134145783296219548763678391425534627819 F8: 8 # 25 pairs * PAIR E8: 1,9 ROW 8 I8: 1,9,5 # reduction candidate for 1,9 I8: 5 => SOLVED * 957134682421869357863275941392416578786952134145783296219548763678391425534627819 I8: 1,9 # 28 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-222-base-pr-000.dot * REASONING * DIS # A6: 5,9 => CTR => A6: 1 * PRF # A6: 1 => SOL * PRF # A9: 5,9 => SOL * DIS # A9: 1 => CTR => A9: 5,9 * DIS # F3: 2,9 => CTR => F3: 5 * DIS # I2: 5,9 => CTR => I2: 7 * DIS # I3: 5,9 => CTR => I3: 1,7 * DIS # F2: 2 => CTR => F2: 5,9 * DIS # H9: 5,9 => CTR => H9: 1 * PRF # H9: 1 => SOL * PRF # I3: 1,9 => SOL * DIS # I3: 5,7 => CTR => I3: 1,9 * DIS # A6: 5 => CTR => A6: 1,9 * DIS # A6: 5,9 => CTR => A6: 1 * PRF # A6: 1 => SOL * DIS # F5: 1,9 => CTR => F5: 2 * PRF # F5: 2 => SOL * PRF # F5: 2,9 => SOL * DIS # F5: 1 => CTR => F5: 2,9 * DIS # F5: 1,9 => CTR => F5: 2 * PRF # F5: 2 => SOL * DIS # A6: 5 => CTR => A6: 1,9 * DIS # H9: 5 => CTR => H9: 1,9 * PRF # C7: 9 => SOL * PRF # A9: 5 => SOL * PRF # F7: 8 => SOL * PRF # C8: 8,9 => SOL * PRF # F8: 1,9 => SOL * PRF # I8: 5 => SOL * CNT 29 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A4,A7,B1,B2,B3,B4,B7,B8,C3,C4,C6,D3,D5,E2,E3,E4,E8,G3,G5,H2,H6) * ...1346824.18..3.........4....4.6578786.5..34.4.7832.6...54.7636..3..42..346278.. * PAIR A1: 5,9 BLK 1 C1: 5,9,7 # reduction candidate for 5,9 C1: 5,9 # 26 pairs C1: 7 # 23 pairs * PAIR A1: 5,9 COL A A6: 5,9,1 # reduction candidate for 5,9 A6: 5,9 => CTR * ...1346824.18..3.........4..1.496578786251934.4.783216.9.5487636.8319425.346278.. A6: 1 => SOLVED * 957134682421869357863275941392416578786952134145783296219548763678391425534627819 * DURATION: 0:00:04.433823 START: 10:25:23.353743 END: 10:25:27.787566 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-222-base-pr-001.dot * REASONING * DIS # A6: 5,9 => CTR => A6: 1 * PRF A6: 1 => SOL * STA A6: 1 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 222 solution: 957134682421869357863275941392416578786952134145783296219548763678391425534627819 info: 1991 FNBTHWX S8.f 3786 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 957134682421869357863275941392416578786952134145783296219548763678391425534627819 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 # C1: 5,9 => UNS * INC # C1: 7 => UNS * DIS # A6: 5,9 => CTR => A6: 1 * PRF # A6: 1 => SOL * PRF # A9: 5,9 => SOL * DIS # A9: 1 => CTR => A9: 5,9 * INC # C1: 5,7 => UNS * INC # C1: 9 => UNS * INC # F2: 2,9 => UNS * DIS # F3: 2,9 => CTR => F3: 5 * INC # F3: 5 => UNS * DIS # I2: 5,9 => CTR => I2: 7 * INC # I2: 7 => UNS * DIS # I3: 5,9 => CTR => I3: 1,7 * INC # I3: 1,7 => UNS * INC # F2: 5,9 => UNS * DIS # F2: 2 => CTR => F2: 5,9 * DIS # H9: 5,9 => CTR => H9: 1 * PRF # H9: 1 => SOL * PRF # I3: 1,9 => SOL * DIS # I3: 5,7 => CTR => I3: 1,9 * INC # A6: 1,9 => UNS * DIS # A6: 5 => CTR => A6: 1,9 * DIS # A6: 5,9 => CTR => A6: 1 * PRF # A6: 1 => SOL * INC # C1: 5,9 => UNS * INC # C8: 5,9 => UNS * DIS # F5: 1,9 => CTR => F5: 2 * PRF # F5: 2 => SOL * PRF # F5: 2,9 => SOL * DIS # F5: 1 => CTR => F5: 2,9 * DIS # F5: 1,9 => CTR => F5: 2 * PRF # F5: 2 => SOL * INC # A6: 1,9 => UNS * DIS # A6: 5 => CTR => A6: 1,9 * INC # H9: 1,9 => UNS * DIS # H9: 5 => CTR => H9: 1,9 * INC # C7: 2,8 => UNS * PRF # C7: 9 => SOL * INC # A9: 1,9 => UNS * PRF # A9: 5 => SOL * INC # F7: 1,9 => UNS * PRF # F7: 8 => SOL * INC # C8: 5,7 => UNS * PRF # C8: 8,9 => SOL * INC # F7: 1,9 => UNS * PRF # F8: 1,9 => SOL * INC # F8: 8 => UNS * INC # I8: 1,9 => UNS * PRF # I8: 5 => SOL * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 5,9 => UNS * INC # C1: 7 => UNS * DIS # A6: 5,9 => CTR => A6: 1 * PRF A6: 1 => SOL * STA A6: 1 * CNT 4 HDP CHAINS / 3 HYP OPENED