Analysis of xx-top500-283-base.sdk
Contents
Original Sudoku
level: medium
position: .462........4..5....1......5..3.2...7......6.........13.....2...8..6...........4. initial
Autosolve
position: .46251..32374.651..51.3.62456.3124..71.54..6242.6...513.41.52.6182.64.356.5.2314. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # F3: 8,9 => SOL * PRF # F3: 8,9 => SOL * PRF # E6: 8,9 => SOL * DIS # I4: 8,9 => CTR => I4: 7 * DIS # I4: 8,9 => CTR => I4: 7 * PRF # E6: 8,9 => SOL * PRF # F3: 8,9 => SOL * DIS # H7: 7,9 => CTR => H7: 8 * DIS # D9: 7,9 => CTR => D9: 8 * DIS # D9: 7,9 => CTR => D9: 8 * DIS # D3: 8 => CTR => D3: 7,9 * DIS # H7: 7,9 => CTR => H7: 8 * DIS # G1: 8 => CTR => G1: 7,9 * CNT 13 HDP CHAINS / 44 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # F3: 8,9 => SOL * STA F3: 8,9 * CNT 1 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .462........4..5....1......5..3.2...7......6.........13.....2...8..6...........4. | initial |
| .46251..32374.651..51.3.62456.3124..71.54..6242.6...513.41.52.6182.64.356.5.2314. | autosolve |
| 846251973237496518951738624568312497713549862429687351394175286182964735675823149 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) A1: 8,9 A3: 8,9 E2: 8,9 I2: 8,9 C4: 8,9 F5: 8,9 B7: 7,9 B9: 7,9 D8: 7,9 G8: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C5,C6: 3.. / C5 = 3 => 12 pairs (_) / C6 = 3 => 12 pairs (_) G5,G6: 3.. / G5 = 3 => 12 pairs (_) / G6 = 3 => 12 pairs (_) C5,G5: 3.. / C5 = 3 => 12 pairs (_) / G5 = 3 => 12 pairs (_) C6,G6: 3.. / C6 = 3 => 12 pairs (_) / G6 = 3 => 12 pairs (_) D3,F3: 7.. / D3 = 7 => 0 pairs (*) / F3 = 7 => 0 pairs (X) G1,H1: 7.. / G1 = 7 => 20 pairs (_) / H1 = 7 => 15 pairs (_) E6,F6: 7.. / E6 = 7 => 13 pairs (_) / F6 = 7 => 0 pairs (*) H4,I4: 7.. / H4 = 7 => 0 pairs (X) / I4 = 7 => 12 pairs (_) B7,B9: 7.. / B7 = 7 => 14 pairs (_) / B9 = 7 => 14 pairs (_) D8,G8: 7.. / D8 = 7 => 20 pairs (_) / G8 = 7 => 15 pairs (_) E6,E7: 7.. / E6 = 7 => 13 pairs (_) / E7 = 7 => 0 pairs (*) F3,F6: 7.. / F3 = 7 => 13 pairs (_) / F6 = 7 => 0 pairs (*) G1,G8: 7.. / G1 = 7 => 20 pairs (_) / G8 = 7 => 15 pairs (_) I4,I9: 7.. / I4 = 7 => 12 pairs (_) / I9 = 7 => 0 pairs (X) A1,A3: 8.. / A1 = 8 => 0 pairs (*) / A3 = 8 => 0 pairs (X) E7,D9: 8.. / E7 = 8 => 0 pairs (X) / D9 = 8 => 15 pairs (_) H7,I9: 8.. / H7 = 8 => 15 pairs (_) / I9 = 8 => 0 pairs (X) E2,I2: 8.. / E2 = 8 => 0 pairs (X) / I2 = 8 => 0 pairs (_) E7,H7: 8.. / E7 = 8 => 0 pairs (X) / H7 = 8 => 15 pairs (_) D9,I9: 8.. / D9 = 8 => 15 pairs (_) / I9 = 8 => 0 pairs (X) D3,D9: 8.. / D3 = 8 => 0 pairs (X) / D9 = 8 => 15 pairs (_) A1,A3: 9.. / A1 = 9 => 0 pairs (X) / A3 = 9 => 0 pairs (_) B7,B9: 9.. / B7 = 9 => 14 pairs (_) / B9 = 9 => 14 pairs (_) E2,I2: 9.. / E2 = 9 => 0 pairs (*) / I2 = 9 => 0 pairs (X) D8,G8: 9.. / D8 = 9 => 15 pairs (_) / G8 = 9 => 20 pairs (_) * DURATION: 0:00:43.321103 START: 12:35:45.026101 END: 12:36:28.347204 2017-05-04 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B7,B9,C4,D8,E2,F5,G8,I2) * .46251..32374.651..51.3.62456.3124..71.54..6242.6...513.41.52.6182.64.356.5.2314. * PAIR A1: 8,9 ROW 1 G1: 8,9,7 # reduction candidate for 8,9 G1: 8,9 # 15 pairs H1: 8,9,7 # reduction candidate for 8,9 H1: 8,9 # 20 pairs * PAIR A3: 8,9 ROW 3 D3: 8,9,7 # reduction candidate for 8,9 D3: 8,9 # 13 pairs F3: 8,9,7 # reduction candidate for 8,9 F3: 8,9 => SOLVED * 846251973237496518951738624568312497713549862429687351394175286182964735675823149 F3: 7 # 13 pairs * PAIR E2: 8,9 BLK 2 D3: 8,9,7 # reduction candidate for 8,9 D3: 8,9 # 13 pairs F3: 8,9,7 # reduction candidate for 8,9 F3: 8,9 => SOLVED * 846251973237496518951738624568312497713549862429687351394175286182964735675823149 F3: 7 # 13 pairs * PAIR E2: 8,9 COL E E6: 8,9,7 # reduction candidate for 8,9 E6: 8,9 => SOLVED * 846251973237496518951738624568312497713549862429687351394175286182964735675823149 E6: 7 # 13 pairs E7: 8,9,7 # reduction candidate for 8,9 E7: 8,9 # 13 pairs * PAIR I2: 8,9 BLK 3 G1: 8,9,7 # reduction candidate for 8,9 G1: 8,9 # 15 pairs H1: 8,9,7 # reduction candidate for 8,9 H1: 8,9 # 20 pairs * PAIR I2: 8,9 COL I I4: 8,9,7 # reduction candidate for 8,9 I4: 8,9 => CTR * 84625179323749651..51.3.62456.31247.71.54..6242.6...513741.5286182764935695823147 I4: 7 # 12 pairs I9: 8,9,7 # reduction candidate for 8,9 I9: 8,9 # 12 pairs * PAIR C4: 8,9 BLK 4 C5: 8,9,3 # reduction candidate for 8,9 C5: 8,9 # 12 pairs C6: 8,9,3 # reduction candidate for 8,9 C6: 8,9 # 12 pairs * PAIR C4: 8,9 ROW 4 H4: 8,9,7 # reduction candidate for 8,9 H4: 8,9 # 12 pairs I4: 8,9,7 # reduction candidate for 8,9 I4: 8,9 => CTR * 84625179323749651..51.3.62456.31247.71.54..6242.6...513741.5286182764935695823147 I4: 7 # 12 pairs * PAIR F5: 8,9 BLK 5 E6: 8,9,7 # reduction candidate for 8,9 E6: 8,9 => SOLVED * 846251973237496518951738624568312497713549862429687351394175286182964735675823149 E6: 7 # 13 pairs F6: 8,9,7 # reduction candidate for 8,9 F6: 8,9 # 13 pairs * PAIR F5: 8,9 ROW 5 C5: 8,9,3 # reduction candidate for 8,9 C5: 8,9 # 12 pairs G5: 8,9,3 # reduction candidate for 8,9 G5: 8,9 # 12 pairs * PAIR F5: 8,9 COL F F3: 8,9,7 # reduction candidate for 8,9 F3: 8,9 => SOLVED * 846251973237496518951738624568312497713549862429687351394175286182964735675823149 F3: 7 # 13 pairs * PAIR B7: 7,9 ROW 7 E7: 7,9,8 # reduction candidate for 7,9 E7: 7,9 # 15 pairs H7: 7,9,8 # reduction candidate for 7,9 H7: 7,9 => CTR * .46251..32374.651..51.3.62456.3124..71.54..6242.6...513.41852.6182.64.356.5.23148 H7: 8 # 15 pairs * PAIR B9: 7,9 ROW 9 D9: 7,9,8 # reduction candidate for 7,9 D9: 7,9 => CTR * .46251..32374.651..5183762456.3124..71.54..6242.67..513.41852.6182.64.356.5.23148 D9: 8 # 15 pairs I9: 7,9,8 # reduction candidate for 7,9 I9: 7,9 # 15 pairs * PAIR D8: 7,9 BLK 8 E7: 7,9,8 # reduction candidate for 7,9 E7: 7,9 # 15 pairs D9: 7,9,8 # reduction candidate for 7,9 D9: 7,9 => CTR * .46251..32374.651..5183762456.3124..71.54..6242.67..513.41852.6182.64.356.5.23148 D9: 8 # 15 pairs * PAIR D8: 7,9 COL D D3: 7,9,8 # reduction candidate for 7,9 D3: 8 => CTR * .46251..32374.651..5183762456.3124..71.54..6242.67..513.41852.6182.64.356.5.23148 D3: 7,9 # 15 pairs * PAIR G8: 7,9 BLK 9 H7: 7,9,8 # reduction candidate for 7,9 H7: 7,9 => CTR * .46251..32374.651..51.3.62456.3124..71.54..6242.6...513.41852.6182.64.356.5.23148 H7: 8 # 15 pairs I9: 7,9,8 # reduction candidate for 7,9 I9: 7,9 # 15 pairs * PAIR G8: 7,9 COL G G1: 7,9,8 # reduction candidate for 7,9 G1: 8 => CTR * .46251873237486519851.3.62456.3124.771.54..6242.6...513.41.5286182.64.356.5.2314. G1: 7,9 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-283-base-pr-000.dot * REASONING * PRF # F3: 8,9 => SOL * PRF # F3: 8,9 => SOL * PRF # E6: 8,9 => SOL * DIS # I4: 8,9 => CTR => I4: 7 * DIS # I4: 8,9 => CTR => I4: 7 * PRF # E6: 8,9 => SOL * PRF # F3: 8,9 => SOL * DIS # H7: 7,9 => CTR => H7: 8 * DIS # D9: 7,9 => CTR => D9: 8 * DIS # D9: 7,9 => CTR => D9: 8 * DIS # D3: 8 => CTR => D3: 7,9 * DIS # H7: 7,9 => CTR => H7: 8 * DIS # G1: 8 => CTR => G1: 7,9 * CNT 13 HDP CHAINS / 44 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B7,B9,C4,D8,E2,F5,G8,I2) * .46251..32374.651..51.3.62456.3124..71.54..6242.6...513.41.52.6182.64.356.5.2314. * PAIR A1: 8,9 ROW 1 G1: 8,9,7 # reduction candidate for 8,9 G1: 8,9 # 15 pairs H1: 8,9,7 # reduction candidate for 8,9 H1: 8,9 # 20 pairs * PAIR A3: 8,9 ROW 3 D3: 8,9,7 # reduction candidate for 8,9 D3: 8,9 # 13 pairs F3: 8,9,7 # reduction candidate for 8,9 F3: 8,9 => SOLVED * 846251973237496518951738624568312497713549862429687351394175286182964735675823149 * DURATION: 0:00:04.769462 START: 12:37:09.507713 END: 12:37:14.277175 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-283-base-pr-001.dot * REASONING * PRF # F3: 8,9 => SOL * STA F3: 8,9 * CNT 1 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 283 solution: 846251973237496518951738624568312497713549862429687351394175286182964735675823149 info: 2321 FNBWXY S8.f 19504 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 846251973237496518951738624568312497713549862429687351394175286182964735675823149 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 # G1: 8,9 => UNS * INC # H1: 8,9 => UNS * INC # D3: 8,9 => UNS * PRF # F3: 8,9 => SOL * INC # F3: 7 => UNS * INC # D3: 8,9 => UNS * PRF # F3: 8,9 => SOL * INC # F3: 7 => UNS * PRF # E6: 8,9 => SOL * INC # E6: 7 => UNS * INC # E7: 8,9 => UNS * INC # G1: 8,9 => UNS * INC # H1: 8,9 => UNS * DIS # I4: 8,9 => CTR => I4: 7 * INC # I4: 7 => UNS * INC # I9: 8,9 => UNS * INC # C5: 8,9 => UNS * INC # C6: 8,9 => UNS * INC # H4: 8,9 => UNS * DIS # I4: 8,9 => CTR => I4: 7 * INC # I4: 7 => UNS * PRF # E6: 8,9 => SOL * INC # E6: 7 => UNS * INC # F6: 8,9 => UNS * INC # C5: 8,9 => UNS * INC # G5: 8,9 => UNS * PRF # F3: 8,9 => SOL * INC # F3: 7 => UNS * INC # E7: 7,9 => UNS * DIS # H7: 7,9 => CTR => H7: 8 * INC # H7: 8 => UNS * DIS # D9: 7,9 => CTR => D9: 8 * INC # D9: 8 => UNS * INC # I9: 7,9 => UNS * INC # E7: 7,9 => UNS * DIS # D9: 7,9 => CTR => D9: 8 * INC # D9: 8 => UNS * INC # D3: 7,9 => UNS * DIS # D3: 8 => CTR => D3: 7,9 * DIS # H7: 7,9 => CTR => H7: 8 * INC # H7: 8 => UNS * INC # I9: 7,9 => UNS * INC # G1: 7,9 => UNS * DIS # G1: 8 => CTR => G1: 7,9 * CNT 44 HDP CHAINS / 44 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G1: 8,9 => UNS * INC # H1: 8,9 => UNS * INC # D3: 8,9 => UNS * PRF # F3: 8,9 => SOL * STA F3: 8,9 * CNT 4 HDP CHAINS / 4 HYP OPENED