Analysis of xx-top500-072-base.sdk
Contents
Original Sudoku
level: medium
position: ....56.......7..9.........1......37..6....5..1..4.....4..1...8..5....7.....2..... initial
Autosolve
position: .1..56.37....71.9.....24..1...51.376.6.7..514175463.2.4..1...8..516..74....24.1.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 7 => CTR => A3: 5,6 * DIS # B2: 3,8 => CTR => B2: 2,4 * DIS # C3: 6,8 => CTR => C3: 3,7,9 * DIS # A3: 7 => CTR => A3: 5,6 * DIS # C9: 6,7 => CTR => C9: 3,8,9 * DIS # A3: 5 => CTR => A3: 6,7 * DIS # C7: 3,9 => CTR => C7: 2,6,7 * DIS # I7: 3,9 => CTR => I7: 2,5 * CNT 8 HDP CHAINS / 39 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 7 => CTR => A3: 5,6 * PRF A3: 5,6 # E8: 8,9 => SOL * STA A3: 5,6 + E8: 8,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....56.......7..9.........1......37..6....5..1..4.....4..1...8..5....7.....2..... | initial |
| .1..56.37....71.9.....24..1...51.376.6.7..514175463.2.4..1...8..516..74....24.1.. | autosolve |
| 912856437548371692637924851824519376369782514175463928496137285251698743783245169 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) A2: 5,6 D1: 8,9 D2: 3,8 G3: 6,8 H3: 5,6 E5: 8,9 G6: 8,9 I6: 8,9 A9: 6,7 E7: 3,9 F7: 5,7 F8: 8,9 F9: 5,7 H9: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F4,F5: 2.. / F4 = 2 => 18 pairs (_) / F5 = 2 => 15 pairs (_) A8,I8: 2.. / A8 = 2 => 25 pairs (_) / I8 = 2 => 20 pairs (_) D2,D3: 3.. / D2 = 3 => 14 pairs (_) / D3 = 3 => 14 pairs (_) A5,C5: 3.. / A5 = 3 => 15 pairs (_) / C5 = 3 => 23 pairs (_) E7,E8: 3.. / E7 = 3 => 17 pairs (_) / E8 = 3 => 17 pairs (_) A5,A8: 3.. / A5 = 3 => 15 pairs (_) / A8 = 3 => 23 pairs (_) G1,G2: 4.. / G1 = 4 => 14 pairs (_) / G2 = 4 => 16 pairs (_) B4,C4: 4.. / B4 = 4 => 14 pairs (_) / C4 = 4 => 14 pairs (_) C1,G1: 4.. / C1 = 4 => 16 pairs (_) / G1 = 4 => 14 pairs (_) B2,B4: 4.. / B2 = 4 => 14 pairs (_) / B4 = 4 => 14 pairs (_) A2,A3: 5.. / A2 = 5 => 16 pairs (_) / A3 = 5 => 0 pairs (X) I2,H3: 5.. / I2 = 5 => 0 pairs (X) / H3 = 5 => 16 pairs (_) F7,F9: 5.. / F7 = 5 => 0 pairs (X) / F9 = 5 => 16 pairs (_) A2,I2: 5.. / A2 = 5 => 16 pairs (_) / I2 = 5 => 0 pairs (X) A3,H3: 5.. / A3 = 5 => 0 pairs (X) / H3 = 5 => 16 pairs (_) F7,I7: 5.. / F7 = 5 => 0 pairs (X) / I7 = 5 => 16 pairs (_) H3,H9: 5.. / H3 = 5 => 16 pairs (_) / H9 = 5 => 0 pairs (X) G7,H9: 6.. / G7 = 6 => 0 pairs (X) / H9 = 6 => 16 pairs (_) C7,G7: 6.. / C7 = 6 => 16 pairs (_) / G7 = 6 => 0 pairs (X) H3,H9: 6.. / H3 = 6 => 0 pairs (X) / H9 = 6 => 16 pairs (_) A3,C3: 7.. / A3 = 7 => 0 pairs (X) / C3 = 7 => 16 pairs (_) F7,F9: 7.. / F7 = 7 => 16 pairs (_) / F9 = 7 => 0 pairs (X) C7,F7: 7.. / C7 = 7 => 0 pairs (X) / F7 = 7 => 16 pairs (_) A3,A9: 7.. / A3 = 7 => 0 pairs (X) / A9 = 7 => 16 pairs (_) G6,I6: 8.. / G6 = 8 => 0 pairs (X) / I6 = 8 => 14 pairs (_) B9,C9: 8.. / B9 = 8 => 18 pairs (_) / C9 = 8 => 17 pairs (_) E8,F8: 8.. / E8 = 8 => 16 pairs (_) / F8 = 8 => 15 pairs (_) E5,E8: 8.. / E5 = 8 => 15 pairs (_) / E8 = 8 => 16 pairs (_) I2,I6: 8.. / I2 = 8 => 0 pairs (X) / I6 = 8 => 14 pairs (_) D1,D3: 9.. / D1 = 9 => 15 pairs (_) / D3 = 9 => 15 pairs (_) G6,I6: 9.. / G6 = 9 => 14 pairs (_) / I6 = 9 => 0 pairs (X) G6,G7: 9.. / G6 = 9 => 14 pairs (_) / G7 = 9 => 0 pairs (X) * DURATION: 0:01:02.372948 START: 05:09:40.000733 END: 05:10:42.373681 2017-05-04 * CP COUNT: (32) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,D1,D2,E5,E7,F7,F8,F9,G3,G6,H3,H9,I6) * .1..56.37....71.9.....24..1...51.376.6.7..514175463.2.4..1...8..516..74....24.1.. * PAIR A2: 5,6 BLK 1 A3: 5,6,7 # reduction candidate for 5,6 A3: 7 => CTR * .1..56.375...71.9.7...24.51...51.376.6.7..514175463.2.4..1...8..516..74.6..24.1.. A3: 5,6 # 16 pairs * PAIR D1: 8,9 BLK 2 D3: 8,9,3 # reduction candidate for 8,9 D3: 8,9 # 14 pairs D3: 3 # 14 pairs * PAIR D1: 8,9 ROW 1 A1: 8,9,2 # reduction candidate for 8,9 A1: 8,9 # 17 pairs C1: 8,9,2,4 # reduction candidate for 8,9 C1: 8,9 # 20 pairs * PAIR D2: 3,8 BLK 2 D3: 3,8,9 # reduction candidate for 3,8 D3: 9 # 15 pairs D3: 3,8 # 15 pairs * PAIR D2: 3,8 ROW 2 B2: 3,8,2,4 # reduction candidate for 3,8 B2: 3,8 => CTR * .1..56.376...71.955.7.24861.4.51.376.6.7..51417546392842.1...8..516..742...24.1.. B2: 2,4 # 15 pairs C2: 3,8,2,4,6 # reduction candidate for 3,8 C2: 3,8 # 19 pairs * PAIR G3: 6,8 BLK 3 G2: 6,8,2,4 # reduction candidate for 6,8 G2: 6,8 # 16 pairs G2: 2,4 # 16 pairs * PAIR G3: 6,8 ROW 3 C3: 6,8,3,7,9 # reduction candidate for 6,8 C3: 6,8 => CTR * .1..56.37....71.9.7...24.51...51.376.6.7..514175463.2.4..1...8..516..74.6..24.1.. C3: 3,7,9 # 14 pairs * PAIR H3: 5,6 ROW 3 A3: 5,6,7 # reduction candidate for 5,6 A3: 7 => CTR * .1..56.375...71.9.7...24.51...51.376.6.7..514175463.2.4..1...8..516..74.6..24.1.. A3: 5,6 # 16 pairs * PAIR E5: 8,9 BLK 5 F4: 8,9,2 # reduction candidate for 8,9 F4: 8,9 # 15 pairs F5: 8,9,2 # reduction candidate for 8,9 F5: 8,9 # 18 pairs * PAIR E5: 8,9 ROW 5 A5: 8,9,2,3 # reduction candidate for 8,9 A5: 8,9 # 25 pairs C5: 8,9,2,3 # reduction candidate for 8,9 C5: 8,9 # 17 pairs * PAIR E5: 8,9 COL E E8: 8,9,3 # reduction candidate for 8,9 E8: 8,9 # 17 pairs E8: 3 # 17 pairs * PAIR A9: 6,7 BLK 7 C7: 6,7,2,3,9 # reduction candidate for 6,7 C7: 6,7 # 15 pairs C9: 6,7,3,8,9 # reduction candidate for 6,7 C9: 6,7 => CTR * .1..56.37....71.9.....24..1...51.376.6.7..514175463.2.4..1...8..516..74..8.24.1.. C9: 3,8,9 # 15 pairs * PAIR A9: 6,7 COL A A3: 6,7,5 # reduction candidate for 6,7 A3: 5 => CTR * .1..56.37....71.9.5.7.24.61...51.376.6.7..514175463.2.4..1.7685.516..74....24.1.. A3: 6,7 # 16 pairs * PAIR E7: 3,9 BLK 8 E8: 3,9,8 # reduction candidate for 3,9 E8: 8 # 16 pairs E8: 3,9 # 15 pairs * PAIR E7: 3,9 ROW 7 B7: 3,9,2 # reduction candidate for 3,9 B7: 3,9 # 25 pairs C7: 3,9,2,6,7 # reduction candidate for 3,9 C7: 3,9 => CTR * .1..56.37....71.9.....24..1...51.376.6.7..514175463.2.4..1.7685.516..74....24.1.. C7: 2,6,7 # 14 pairs I7: 3,9,2,5 # reduction candidate for 3,9 I7: 3,9 => CTR * .1..56.37....71.9.7...24.51...51.376.6.7..514175463.2.4.71.568..516..74....2471.. I7: 2,5 # 15 pairs * PAIR F8: 8,9 BLK 8 E8: 8,9,3 # reduction candidate for 8,9 E8: 8,9 # 17 pairs E8: 3 # 17 pairs * PAIR F8: 8,9 COL F F4: 8,9,2 # reduction candidate for 8,9 F4: 8,9 # 15 pairs F5: 8,9,2 # reduction candidate for 8,9 F5: 8,9 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-072-base-pr-000.dot * REASONING * DIS # A3: 7 => CTR => A3: 5,6 * DIS # B2: 3,8 => CTR => B2: 2,4 * DIS # C3: 6,8 => CTR => C3: 3,7,9 * DIS # A3: 7 => CTR => A3: 5,6 * DIS # C9: 6,7 => CTR => C9: 3,8,9 * DIS # A3: 5 => CTR => A3: 6,7 * DIS # C7: 3,9 => CTR => C7: 2,6,7 * DIS # I7: 3,9 => CTR => I7: 2,5 * CNT 8 HDP CHAINS / 39 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,D1,D2,E5,E7,F7,F8,F9,G3,G6,H3,H9,I6) * .1..56.37....71.9.....24..1...51.376.6.7..514175463.2.4..1...8..516..74....24.1.. * PAIR A2: 5,6 BLK 1 A3: 5,6,7 # reduction candidate for 5,6 A3: 7 => CTR * .1..56.375...71.9.7...24.51...51.376.6.7..514175463.2.4..1...8..516..74.6..24.1.. * PAIR E5: 8,9 COL E E8: 8,9,3 # reduction candidate for 8,9 E8: 8,9 => SOLVED * 912856437548371692637924851824519376369782514175463928496137285251698743783245169 * DURATION: 0:00:04.998887 START: 05:11:21.688774 END: 05:11:26.687661 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-072-base-pr-001.dot * REASONING * DIS # A3: 7 => CTR => A3: 5,6 * PRF A3: 5,6 # E8: 8,9 => SOL * STA A3: 5,6 + E8: 8,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 072 solution: 912856437548371692637924851824519376369782514175463928496137285251698743783245169 info: 1467 FNBTHXY S8.f 5042 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 912856437548371692637924851824519376369782514175463928496137285251698743783245169 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 # A3: 5,6 => UNS * DIS # A3: 7 => CTR => A3: 5,6 * INC # D3: 8,9 => UNS * INC # D3: 3 => UNS * INC # A1: 8,9 => UNS * INC # C1: 8,9 => UNS * INC # D3: 3,8 => UNS * INC # D3: 9 => UNS * DIS # B2: 3,8 => CTR => B2: 2,4 * INC # B2: 2,4 => UNS * INC # C2: 3,8 => UNS * INC # G2: 6,8 => UNS * INC # G2: 2,4 => UNS * DIS # C3: 6,8 => CTR => C3: 3,7,9 * INC # C3: 3,7,9 => UNS * INC # A3: 5,6 => UNS * DIS # A3: 7 => CTR => A3: 5,6 * INC # F4: 8,9 => UNS * INC # F5: 8,9 => UNS * INC # A5: 8,9 => UNS * INC # C5: 8,9 => UNS * INC # E8: 8,9 => UNS * INC # E8: 3 => UNS * INC # C7: 6,7 => UNS * DIS # C9: 6,7 => CTR => C9: 3,8,9 * INC # C9: 3,8,9 => UNS * INC # A3: 6,7 => UNS * DIS # A3: 5 => CTR => A3: 6,7 * INC # E8: 3,9 => UNS * INC # E8: 8 => UNS * INC # B7: 3,9 => UNS * DIS # C7: 3,9 => CTR => C7: 2,6,7 * INC # C7: 2,6,7 => UNS * DIS # I7: 3,9 => CTR => I7: 2,5 * INC # I7: 2,5 => UNS * INC # E8: 8,9 => UNS * INC # E8: 3 => UNS * INC # F4: 8,9 => UNS * INC # F5: 8,9 => UNS * CNT 39 HDP CHAINS / 39 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 5,6 => UNS * DIS # A3: 7 => CTR => A3: 5,6 * PRF A3: 5,6 # E8: 8,9 => SOL * STA A3: 5,6 + E8: 8,9 * CNT 3 HDP CHAINS / 3 HYP OPENED