Analysis of xx-top500-052-base.sdk
Contents
Original Sudoku
level: medium
position: 53.9...........6.1.........2.1...7..6...35..........9..8.4...7.....6.....5....... initial
Autosolve
position: 534916287829...6.1167.....92416..7..698735412375...8969864...7..13.6..2..52....6. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D3: 3,5 => CTR => D3: 2,8 * DIS # D3: 3,5 => CTR => D3: 2,8 * PRF # G7: 3,5 => SOL * DIS # E9: 7 => CTR => E9: 8,9 * DIS # F9: 8,9 => CTR => F9: 1,3,7 * DIS # F6: 4 => CTR => F6: 1,2 * DIS # E3: 2,4 => CTR => E3: 5,8 * PRF # G7: 3,5 => SOL * CNT 8 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D3: 3,5 => CTR => D3: 2,8 * PRF D3: 2,8 # G7: 3,5 => SOL * STA D3: 2,8 + G7: 3,5 * CNT 2 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 53.9...........6.1.........2.1...7..6...35..........9..8.4...7.....6.....5....... | initial |
| 534916287829...6.1167.....92416..7..698735412375...8969864...7..13.6..2..52....6. | autosolve |
| 534916287829374651167258349241689735698735412375142896986421573413567928752893164 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) D2: 3,5 G3: 3,5 E4: 8,9 F4: 8,9 D6: 1,2 E6: 2,4 H4: 3,5 I4: 3,5 A8: 4,7 A9: 4,7 E7: 2,5 D8: 5,8 I7: 3,5 G8: 5,9 I8: 4,8 I9: 4,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D6,F6: 1.. / D6 = 1 => 20 pairs (_) / F6 = 1 => 18 pairs (_) G7,G9: 1.. / G7 = 1 => 18 pairs (_) / G9 = 1 => 0 pairs (*) F7,G7: 1.. / F7 = 1 => 0 pairs (*) / G7 = 1 => 0 pairs (X) D6,D9: 1.. / D6 = 1 => 20 pairs (_) / D9 = 1 => 18 pairs (_) E7,F7: 2.. / E7 = 2 => 21 pairs (_) / F7 = 2 => 0 pairs (X) D3,D6: 2.. / D3 = 2 => 20 pairs (_) / D6 = 2 => 18 pairs (_) H4,I4: 3.. / H4 = 3 => 17 pairs (_) / I4 = 3 => 0 pairs (X) I4,I7: 3.. / I4 = 3 => 0 pairs (X) / I7 = 3 => 17 pairs (_) H2,H3: 4.. / H2 = 4 => 20 pairs (_) / H3 = 4 => 19 pairs (_) E6,F6: 4.. / E6 = 4 => 17 pairs (_) / F6 = 4 => 0 pairs (X) A8,A9: 4.. / A8 = 4 => 0 pairs (*) / A9 = 4 => 0 pairs (X) I8,I9: 4.. / I8 = 4 => 15 pairs (_) / I9 = 4 => 0 pairs (*) A8,I8: 4.. / A8 = 4 => 0 pairs (*) / I8 = 4 => 0 pairs (X) A9,I9: 4.. / A9 = 4 => 15 pairs (_) / I9 = 4 => 0 pairs (*) H4,I4: 5.. / H4 = 5 => 0 pairs (X) / I4 = 5 => 17 pairs (_) E7,D8: 5.. / E7 = 5 => 0 pairs (X) / D8 = 5 => 21 pairs (_) D8,G8: 5.. / D8 = 5 => 21 pairs (_) / G8 = 5 => 0 pairs (X) I4,I7: 5.. / I4 = 5 => 17 pairs (_) / I7 = 5 => 0 pairs (X) E2,F2: 7.. / E2 = 7 => 18 pairs (_) / F2 = 7 => 0 pairs (X) A8,A9: 7.. / A8 = 7 => 15 pairs (_) / A9 = 7 => 0 pairs (*) A8,F8: 7.. / A8 = 7 => 15 pairs (_) / F8 = 7 => 0 pairs (*) E2,E9: 7.. / E2 = 7 => 18 pairs (_) / E9 = 7 => 0 pairs (X) E4,F4: 8.. / E4 = 8 => 0 pairs (*) / F4 = 8 => 0 pairs (X) I8,I9: 8.. / I8 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) E4,F4: 9.. / E4 = 9 => 16 pairs (_) / F4 = 9 => 0 pairs (*) G8,G9: 9.. / G8 = 9 => 21 pairs (_) / G9 = 9 => 0 pairs (X) F8,G8: 9.. / F8 = 9 => 0 pairs (X) / G8 = 9 => 21 pairs (_) E4,E9: 9.. / E4 = 9 => 16 pairs (_) / E9 = 9 => 0 pairs (*) * DURATION: 0:01:06.968284 START: 04:25:59.836349 END: 04:27:06.804633 2017-05-04 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,D2,D6,D8,E4,E6,E7,F4,G3,G8,H4,I4,I7,I8,I9) * 534916287829...6.1167.....92416..7..698735412375...8969864...7..13.6..2..52....6. * PAIR D2: 3,5 BLK 2 D3: 3,5,2,8 # reduction candidate for 3,5 D3: 3,5 => CTR * 534916287829...6.1167...3.924169873569873541237524189698645217371386952445217.968 D3: 2,8 # 17 pairs * PAIR D2: 3,5 ROW 2 H2: 3,5,4 # reduction candidate for 3,5 H2: 4 # 20 pairs H2: 3,5 # 19 pairs * PAIR G3: 3,5 BLK 3 H2: 3,5,4 # reduction candidate for 3,5 H2: 3,5 # 19 pairs H3: 3,5,4 # reduction candidate for 3,5 H3: 3,5 # 20 pairs * PAIR G3: 3,5 ROW 3 D3: 3,5,2,8 # reduction candidate for 3,5 D3: 3,5 => CTR * 534916287829...6.1167...3.924169873569873541237524189698645217371386952445217.968 D3: 2,8 # 17 pairs * PAIR G3: 3,5 COL G G7: 3,5,1 # reduction candidate for 3,5 G7: 3,5 => SOLVED * 534916287829374651167258349241689735698735412375142896986421573413567928752893164 G7: 1 # 18 pairs * PAIR E4: 8,9 COL E E9: 8,9,7 # reduction candidate for 8,9 E9: 7 => CTR * 534916287829..76.1167.8.3.9241698735698735412375...896986452173713869524452.73968 E9: 8,9 # 18 pairs * PAIR F4: 8,9 COL F F8: 8,9,7 # reduction candidate for 8,9 F8: 8,9 # 15 pairs F9: 8,9,1,3,7 # reduction candidate for 8,9 F9: 8,9 => CTR * 534916287829...6.11678....92416..7..698735412375241896986423175.135679287521..364 F9: 1,3,7 # 16 pairs * PAIR D6: 1,2 BLK 5 F6: 1,2,4 # reduction candidate for 1,2 F6: 4 => CTR * 5349162878295..6.11672..3592416987..698735412375124896986452173.1386.5244523.1968 F6: 1,2 # 17 pairs * PAIR E6: 2,4 BLK 5 F6: 2,4,1 # reduction candidate for 2,4 F6: 2,4 # 20 pairs F6: 1 # 18 pairs * PAIR E6: 2,4 COL E E3: 2,4,5,8 # reduction candidate for 2,4 E3: 2,4 => CTR * 534916287829.7.6.1167.....92416..7..698735412375...896986452173.1386.524452.9..6. E3: 5,8 # 17 pairs * PAIR H4: 3,5 COL H H2: 3,5,4 # reduction candidate for 3,5 H2: 3,5 # 19 pairs H3: 3,5,4 # reduction candidate for 3,5 H3: 3,5 # 20 pairs * PAIR E7: 2,5 COL E E3: 2,5,4,8 # reduction candidate for 2,5 E3: 2,5 # 19 pairs E3: 4,8 # 17 pairs * PAIR D8: 5,8 COL D D3: 5,8,2,3 # reduction candidate for 5,8 D3: 2,3 # 20 pairs D3: 5,8 # 19 pairs * PAIR I7: 3,5 BLK 9 G7: 3,5,1 # reduction candidate for 3,5 G7: 3,5 => SOLVED * 534916287829374651167258349241689735698735412375142896986421573413567928752893164 G7: 1 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-052-base-pr-000.dot * REASONING * DIS # D3: 3,5 => CTR => D3: 2,8 * DIS # D3: 3,5 => CTR => D3: 2,8 * PRF # G7: 3,5 => SOL * DIS # E9: 7 => CTR => E9: 8,9 * DIS # F9: 8,9 => CTR => F9: 1,3,7 * DIS # F6: 4 => CTR => F6: 1,2 * DIS # E3: 2,4 => CTR => E3: 5,8 * PRF # G7: 3,5 => SOL * CNT 8 HDP CHAINS / 29 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,D2,D6,D8,E4,E6,E7,F4,G3,G8,H4,I4,I7,I8,I9) * 534916287829...6.1167.....92416..7..698735412375...8969864...7..13.6..2..52....6. * PAIR D2: 3,5 BLK 2 D3: 3,5,2,8 # reduction candidate for 3,5 D3: 3,5 => CTR * 534916287829...6.1167...3.924169873569873541237524189698645217371386952445217.968 * PAIR D2: 3,5 ROW 2 H2: 3,5,4 # reduction candidate for 3,5 H2: 4 # 20 pairs H2: 3,5 # 20 pairs * PAIR G3: 3,5 BLK 3 H2: 3,5,4 # reduction candidate for 3,5 H2: 3,5 # 20 pairs H3: 3,5,4 # reduction candidate for 3,5 H3: 3,5 # 20 pairs * PAIR G3: 3,5 COL G G7: 3,5,1 # reduction candidate for 3,5 G7: 3,5 => SOLVED * 534916287829374651167258349241689735698735412375142896986421573413567928752893164 * DURATION: 0:00:09.997755 START: 04:27:44.634695 END: 04:27:54.632450 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-052-base-pr-001.dot * REASONING * DIS # D3: 3,5 => CTR => D3: 2,8 * PRF D3: 2,8 # G7: 3,5 => SOL * STA D3: 2,8 + G7: 3,5 * CNT 2 HDP CHAINS / 6 HYP OPENED
Header Info
Top 500 Minimum 17 052 solution: 534916287829374651167258349241689735698735412375142896986421573413567928752893164 info: 1396 FNBTHY S8.f 43019 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 534916287829374651167258349241689735698735412375142896986421573413567928752893164 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 # D3: 3,5 => CTR => D3: 2,8 * INC # D3: 2,8 => UNS * INC # H2: 3,5 => UNS * INC # H2: 4 => UNS * INC # H2: 3,5 => UNS * INC # H3: 3,5 => UNS * DIS # D3: 3,5 => CTR => D3: 2,8 * INC # D3: 2,8 => UNS * PRF # G7: 3,5 => SOL * INC # G7: 1 => UNS * INC # E9: 8,9 => UNS * DIS # E9: 7 => CTR => E9: 8,9 * INC # F8: 8,9 => UNS * DIS # F9: 8,9 => CTR => F9: 1,3,7 * INC # F9: 1,3,7 => UNS * INC # F6: 1,2 => UNS * DIS # F6: 4 => CTR => F6: 1,2 * INC # F6: 2,4 => UNS * INC # F6: 1 => UNS * DIS # E3: 2,4 => CTR => E3: 5,8 * INC # E3: 5,8 => UNS * INC # H2: 3,5 => UNS * INC # H3: 3,5 => UNS * INC # E3: 2,5 => UNS * INC # E3: 4,8 => UNS * INC # D3: 5,8 => UNS * INC # D3: 2,3 => UNS * PRF # G7: 3,5 => SOL * INC # G7: 1 => UNS * CNT 29 HDP CHAINS / 29 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D3: 3,5 => CTR => D3: 2,8 * INC D3: 2,8 # H2: 3,5 => UNS * INC D3: 2,8 # H2: 4 => UNS * INC D3: 2,8 # H2: 3,5 => UNS * INC D3: 2,8 # H3: 3,5 => UNS * PRF D3: 2,8 # G7: 3,5 => SOL * STA D3: 2,8 + G7: 3,5 * CNT 6 HDP CHAINS / 6 HYP OPENED