Analysis of xx-mith-te3-00058231-base.sdk
Contents
Original Sudoku
level: medium
position: 1...56..9.5.1.9..669.27....27..9165..........5..6...7.......8.1....12.6.91....34. initial
Autosolve
position: 1...56..9.5.1.9..669.27....27..9165..6.......5..6...7.......8.1....12.6.91....34. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D8: 5,7 => CTR => D8: 3,4,8,9 * PRF # D8: 3,4,7,8 => SOL * PRF # I9: 5,7 => SOL * PRF # C8: 5,7 => SOL * DIS # D8: 5,7 => CTR => D8: 3,4,8,9 * CNT 5 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D8: 5,7 => CTR => D8: 3,4,8,9 * PRF D8: 3,4,8,9 # I9: 5,7 => SOL * STA D8: 3,4,8,9 + I9: 5,7 * CNT 2 HDP CHAINS / 16 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1...56..9.5.1.9..669.27....27..9165..........5..6...7.......8.1....12.6.91....34. | initial |
| 1...56..9.5.1.9..669.27....27..9165..6.......5..6...7.......8.1....12.6.91....34. | autosolve |
| 123456789457189236698273514274891653361527498589634172736945821845312967912768345 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) C5: 1,9 C6: 1,9 D5: 5,7 F5: 5,7 G6: 1,9 E9: 6,8 H7: 2,9 G8: 5,9 I8: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G3,H3: 1.. / G3 = 1 => 10 pairs (_) / H3 = 1 => 10 pairs (_) C5,C6: 1.. / C5 = 1 => 7 pairs (_) / C6 = 1 => 10 pairs (_) C6,G6: 1.. / C6 = 1 => 10 pairs (_) / G6 = 1 => 7 pairs (_) H3,H5: 1.. / H3 = 1 => 10 pairs (_) / H5 = 1 => 10 pairs (_) E5,E6: 2.. / E5 = 2 => 0 pairs (*) / E6 = 2 => 0 pairs (X) H7,I9: 2.. / H7 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) E6,I6: 2.. / E6 = 2 => 9 pairs (_) / I6 = 2 => 0 pairs (*) C9,I9: 2.. / C9 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) B1,B7: 2.. / B1 = 2 => 0 pairs (*) / B7 = 2 => 0 pairs (X) G3,I3: 5.. / G3 = 5 => 0 pairs (*) / I3 = 5 => 0 pairs (X) D5,F5: 5.. / D5 = 5 => 9 pairs (_) / F5 = 5 => 9 pairs (_) G3,G8: 5.. / G3 = 5 => 0 pairs (*) / G8 = 5 => 0 pairs (X) C7,C9: 6.. / C7 = 6 => 12 pairs (_) / C9 = 6 => 15 pairs (_) E7,E9: 6.. / E7 = 6 => 15 pairs (_) / E9 = 6 => 12 pairs (_) C7,E7: 6.. / C7 = 6 => 12 pairs (_) / E7 = 6 => 15 pairs (_) C9,E9: 6.. / C9 = 6 => 15 pairs (_) / E9 = 6 => 12 pairs (_) G1,G2: 7.. / G1 = 7 => 10 pairs (_) / G2 = 7 => 10 pairs (_) D5,F5: 7.. / D5 = 7 => 9 pairs (_) / F5 = 7 => 9 pairs (_) I8,I9: 7.. / I8 = 7 => 9 pairs (_) / I9 = 7 => 0 pairs (X) C1,G1: 7.. / C1 = 7 => 10 pairs (_) / G1 = 7 => 10 pairs (_) C5,C6: 9.. / C5 = 9 => 10 pairs (_) / C6 = 9 => 7 pairs (_) D7,D8: 9.. / D7 = 9 => 0 pairs (*) / D8 = 9 => 0 pairs (X) H7,G8: 9.. / H7 = 9 => 12 pairs (_) / G8 = 9 => 0 pairs (*) C6,G6: 9.. / C6 = 9 => 7 pairs (_) / G6 = 9 => 10 pairs (_) D7,H7: 9.. / D7 = 9 => 0 pairs (*) / H7 = 9 => 0 pairs (X) D8,G8: 9.. / D8 = 9 => 12 pairs (_) / G8 = 9 => 0 pairs (*) H5,H7: 9.. / H5 = 9 => 0 pairs (*) / H7 = 9 => 0 pairs (X) * DURATION: 0:00:08.918276 START: 09:24:53.167760 END: 09:25:02.086036 2025-04-06 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C5,C6,D5,E9,F5,G6,G8,H7,I8) * 1...56..9.5.1.9..669.27....27..9165..6.......5..6...7.......8.1....12.6.91....34. * PAIR C5: 1,9 ROW 5 G5: 1,9,2,4 # reduction candidate for 1,9 G5: 1,9 # 17 pairs H5: 1,9,2,3,8 # reduction candidate for 1,9 H5: 1,9 # 13 pairs * PAIR D5: 5,7 COL D D7: 5,7,3,4,9 # reduction candidate for 5,7 D7: 5,7 # 11 pairs D8: 5,7,3,4,8,9 # reduction candidate for 5,7 D8: 5,7 => CTR * 12..56..9.5.1.92.669.27.51.27..9165..6.....9.5.96..17...69.5821..571296.912.6.34. D8: 3,4,8,9 # 9 pairs D9: 5,7,8 # reduction candidate for 5,7 D9: 5,7 # 10 pairs * PAIR F5: 5,7 COL F F7: 5,7,3,4 # reduction candidate for 5,7 F7: 5,7 # 10 pairs F9: 5,7,8 # reduction candidate for 5,7 F9: 5,7 # 11 pairs * PAIR G6: 1,9 BLK 6 G5: 1,9,2,4 # reduction candidate for 1,9 G5: 1,9 # 17 pairs H5: 1,9,2,3,8 # reduction candidate for 1,9 H5: 1,9 # 13 pairs * PAIR E9: 6,8 ROW 9 C9: 6,8,2,5,7 # reduction candidate for 6,8 C9: 6,8 # 15 pairs C9: 2,5,7 # 12 pairs * PAIR H7: 2,9 COL H H5: 2,9,1,3,8 # reduction candidate for 2,9 H5: 2,9 # 18 pairs H5: 1,3,8 # 10 pairs * PAIR G8: 5,9 ROW 8 D8: 5,9,3,4,7,8 # reduction candidate for 5,9 D8: 3,4,7,8 => SOLVED * 123456789457189236698273514274891653361527498589634172736945821845312967912768345 D8: 5,9 # 12 pairs * PAIR I8: 5,7 BLK 9 I9: 5,7,2 # reduction candidate for 5,7 I9: 5,7 => SOLVED * 123456789457189236698273514274891653361527498589634172736945821845312967912768345 I9: 2 # 12 pairs * PAIR I8: 5,7 ROW 8 C8: 5,7,3,4,8 # reduction candidate for 5,7 C8: 5,7 => SOLVED * 123456789457189236698273514274891653361527498589634172736945821845312967912768345 C8: 3,4,8 # 12 pairs D8: 5,7,3,4,8,9 # reduction candidate for 5,7 D8: 5,7 => CTR * 12..56..9.5.1.92.669.27.51.27..9165..6.....9.5.96..17...69.5821..571296.912.6.34. D8: 3,4,8,9 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-mith-te3-00058231-base-pr-000.dot * REASONING * DIS # D8: 5,7 => CTR => D8: 3,4,8,9 * PRF # D8: 3,4,7,8 => SOL * PRF # I9: 5,7 => SOL * PRF # C8: 5,7 => SOL * DIS # D8: 5,7 => CTR => D8: 3,4,8,9 * CNT 5 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C5,C6,D5,E9,F5,G6,G8,H7,I8) * 1...56..9.5.1.9..669.27....27..9165..6.......5..6...7.......8.1....12.6.91....34. * PAIR C5: 1,9 ROW 5 G5: 1,9,2,4 # reduction candidate for 1,9 G5: 1,9 # 17 pairs H5: 1,9,2,3,8 # reduction candidate for 1,9 H5: 1,9 # 13 pairs * PAIR D5: 5,7 COL D D7: 5,7,3,4,9 # reduction candidate for 5,7 D7: 5,7 # 11 pairs D8: 5,7,3,4,8,9 # reduction candidate for 5,7 D8: 5,7 => CTR * 12..56..9.5.1.92.669.27.51.27..9165..6.....9.5.96..17...69.5821..571296.912.6.34. D9: 5,7,8 # reduction candidate for 5,7 D9: 5,7 # 10 pairs * PAIR RESTART * PAIR D5: 5,7 COL D D7: 5,7,3,4,9 # reduction candidate for 5,7 D7: 5,7 # 11 pairs D9: 5,7,8 # reduction candidate for 5,7 D9: 5,7 # 10 pairs * PAIR F5: 5,7 COL F F7: 5,7,3,4 # reduction candidate for 5,7 F7: 5,7 # 10 pairs F9: 5,7,8 # reduction candidate for 5,7 F9: 5,7 # 11 pairs * PAIR G6: 1,9 BLK 6 G5: 1,9,2,4 # reduction candidate for 1,9 G5: 1,9 # 17 pairs H5: 1,9,2,3,8 # reduction candidate for 1,9 H5: 1,9 # 13 pairs * PAIR E9: 6,8 ROW 9 C9: 6,8,2,5,7 # reduction candidate for 6,8 C9: 6,8 # 15 pairs C9: 2,5,7 # 12 pairs * PAIR H7: 2,9 COL H H5: 2,9,1,3,8 # reduction candidate for 2,9 H5: 2,9 # 18 pairs H5: 1,3,8 # 10 pairs * PAIR I8: 5,7 BLK 9 I9: 5,7,2 # reduction candidate for 5,7 I9: 5,7 => SOLVED * 123456789457189236698273514274891653361527498589634172736945821845312967912768345 * DURATION: 0:00:03.261310 START: 09:25:06.585523 END: 09:25:09.846833 2025-04-06 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00058231-base-pr-001.dot * REASONING * DIS # D8: 5,7 => CTR => D8: 3,4,8,9 * PRF D8: 3,4,8,9 # I9: 5,7 => SOL * STA D8: 3,4,8,9 + I9: 5,7 * CNT 2 HDP CHAINS / 16 HYP OPENED
Header Info
rating: 12162; r2: 282612; index: 58231
Solution
position: 123456789457189236698273514274891653361527498589634172736945821845312967912768345 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 # G5: 1,9 => UNS * INC # H5: 1,9 => UNS * INC # D7: 5,7 => UNS * DIS # D8: 5,7 => CTR => D8: 3,4,8,9 * INC # D8: 3,4,8,9 => UNS * INC # D9: 5,7 => UNS * INC # F7: 5,7 => UNS * INC # F9: 5,7 => UNS * INC # G5: 1,9 => UNS * INC # H5: 1,9 => UNS * INC # C9: 6,8 => UNS * INC # C9: 2,5,7 => UNS * INC # H5: 2,9 => UNS * INC # H5: 1,3,8 => UNS * INC # D8: 5,9 => UNS * PRF # D8: 3,4,7,8 => SOL * PRF # I9: 5,7 => SOL * INC # I9: 2 => UNS * PRF # C8: 5,7 => SOL * INC # C8: 3,4,8 => UNS * DIS # D8: 5,7 => CTR => D8: 3,4,8,9 * INC # D8: 3,4,8,9 => UNS * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G5: 1,9 => UNS * INC # H5: 1,9 => UNS * INC # D7: 5,7 => UNS * DIS # D8: 5,7 => CTR => D8: 3,4,8,9 * INC D8: 3,4,8,9 # D9: 5,7 => UNS * INC D8: 3,4,8,9 # D7: 5,7 => UNS * INC D8: 3,4,8,9 # D9: 5,7 => UNS * INC D8: 3,4,8,9 # F7: 5,7 => UNS * INC D8: 3,4,8,9 # F9: 5,7 => UNS * INC D8: 3,4,8,9 # G5: 1,9 => UNS * INC D8: 3,4,8,9 # H5: 1,9 => UNS * INC D8: 3,4,8,9 # C9: 6,8 => UNS * INC D8: 3,4,8,9 # C9: 2,5,7 => UNS * INC D8: 3,4,8,9 # H5: 2,9 => UNS * INC D8: 3,4,8,9 # H5: 1,3,8 => UNS * PRF D8: 3,4,8,9 # I9: 5,7 => SOL * STA D8: 3,4,8,9 + I9: 5,7 * CNT 16 HDP CHAINS / 16 HYP OPENED