Analysis of xx-mith-te3-00135988-base.sdk
Contents
Original Sudoku
level: medium
position: .2....78..571..2.6..82...15..........8..6..72.1....56.56..43...87.59.........2.5. initial
Autosolve
position: .2....78..571..2.6..82...15..6.......85.6..72.1....56.56..43...87.59.........2.5. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E4: 3,8 => CTR => E4: 1,2,5,7 * PRF # E9: 7,8 => SOL * PRF # D4: 7,8 => SOL * DIS # D6: 7,8 => CTR => D6: 3,4,9 * CNT 4 HDP CHAINS / 24 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E4: 3,8 => CTR => E4: 1,2,5,7 * PRF E4: 1,2,5,7 # E9: 7,8 => SOL * STA E4: 1,2,5,7 + E9: 7,8 * CNT 2 HDP CHAINS / 16 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2....78..571..2.6..82...15..........8..6..72.1....56.56..43...87.59.........2.5. | initial |
| .2....78..571..2.6..82...15..6.......85.6..72.1....56.56..43...87.59.........2.5. | autosolve |
| 123456789457189236698237415246715398385964172719328564561843927872591643934672851 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) E1: 3,5 E2: 3,8 E3: 3,7 A4: 2,7 A6: 2,7 D7: 7,8 F8: 1,6 H7: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,C1: 1.. / A1 = 1 => 8 pairs (_) / C1 = 1 => 0 pairs (X) F8,E9: 1.. / F8 = 1 => 0 pairs (*) / E9 = 1 => 0 pairs (X) F5,G5: 1.. / F5 = 1 => 15 pairs (_) / G5 = 1 => 0 pairs (*) A1,A9: 1.. / A1 = 1 => 8 pairs (_) / A9 = 1 => 0 pairs (X) E4,E9: 1.. / E4 = 1 => 0 pairs (*) / E9 = 1 => 0 pairs (X) A4,A6: 2.. / A4 = 2 => 6 pairs (_) / A6 = 2 => 13 pairs (_) E4,E6: 2.. / E4 = 2 => 13 pairs (_) / E6 = 2 => 6 pairs (_) C7,C8: 2.. / C7 = 2 => 11 pairs (_) / C8 = 2 => 9 pairs (_) H7,H8: 2.. / H7 = 2 => 9 pairs (_) / H8 = 2 => 11 pairs (_) A4,E4: 2.. / A4 = 2 => 6 pairs (_) / E4 = 2 => 13 pairs (_) A6,E6: 2.. / A6 = 2 => 13 pairs (_) / E6 = 2 => 6 pairs (_) C7,H7: 2.. / C7 = 2 => 11 pairs (_) / H7 = 2 => 9 pairs (_) C8,H8: 2.. / C8 = 2 => 9 pairs (_) / H8 = 2 => 11 pairs (_) E1,F1: 5.. / E1 = 5 => 7 pairs (_) / F1 = 5 => 12 pairs (_) E4,F4: 5.. / E4 = 5 => 12 pairs (_) / F4 = 5 => 7 pairs (_) E1,E4: 5.. / E1 = 5 => 7 pairs (_) / E4 = 5 => 12 pairs (_) F1,F4: 5.. / F1 = 5 => 12 pairs (_) / F4 = 5 => 7 pairs (_) A1,A3: 6.. / A1 = 6 => 0 pairs (X) / A3 = 6 => 8 pairs (_) F8,D9: 6.. / F8 = 6 => 15 pairs (_) / D9 = 6 => 0 pairs (*) G8,G9: 6.. / G8 = 6 => 0 pairs (*) / G9 = 6 => 0 pairs (X) A3,F3: 6.. / A3 = 6 => 8 pairs (_) / F3 = 6 => 0 pairs (X) F8,G8: 6.. / F8 = 6 => 15 pairs (_) / G8 = 6 => 0 pairs (*) D9,G9: 6.. / D9 = 6 => 0 pairs (*) / G9 = 6 => 0 pairs (X) D1,D9: 6.. / D1 = 6 => 15 pairs (_) / D9 = 6 => 0 pairs (*) E3,F3: 7.. / E3 = 7 => 17 pairs (_) / F3 = 7 => 10 pairs (_) A4,A6: 7.. / A4 = 7 => 13 pairs (_) / A6 = 7 => 6 pairs (_) I7,I9: 7.. / I7 = 7 => 10 pairs (_) / I9 = 7 => 12 pairs (_) D7,I7: 7.. / D7 = 7 => 12 pairs (_) / I7 = 7 => 10 pairs (_) E2,F2: 8.. / E2 = 8 => 9 pairs (_) / F2 = 8 => 12 pairs (_) * DURATION: 0:00:09.016295 START: 11:37:51.041666 END: 11:38:00.057961 2025-04-05 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,D7,E1,E2,E3,F8,H7) * .2....78..571..2.6..82...15..6.......85.6..72.1....56.56..43...87.59.........2.5. * PAIR E1: 3,5 COL E E4: 3,5,1,2,7,8 # reduction candidate for 3,5 E4: 3,5 # 12 pairs E4: 1,2,7,8 # 7 pairs * PAIR E2: 3,8 COL E E4: 3,8,1,2,5,7 # reduction candidate for 3,8 E4: 3,8 => CTR * 12.65.78..571..2.66.827..152.67.5....85.61.7271..2.56.56.843...87.596.......1265. E4: 1,2,5,7 # 8 pairs E6: 3,8,2,7 # reduction candidate for 3,8 E6: 3,8 # 12 pairs * PAIR E3: 3,7 COL E E4: 3,7,1,2,5,8 # reduction candidate for 3,7 E4: 3,7 # 12 pairs E6: 3,7,2,8 # reduction candidate for 3,7 E6: 3,7 # 12 pairs * PAIR A4: 2,7 ROW 4 E4: 2,7,1,3,5,8 # reduction candidate for 2,7 E4: 2,7 # 15 pairs E4: 1,3,5,8 # 6 pairs * PAIR A6: 2,7 ROW 6 E6: 2,7,3,8 # reduction candidate for 2,7 E6: 3,8 # 12 pairs E6: 2,7 # 9 pairs * PAIR D7: 7,8 BLK 8 D9: 7,8,6 # reduction candidate for 7,8 D9: 7,8 # 15 pairs E9: 7,8,1 # reduction candidate for 7,8 E9: 7,8 => SOLVED * 123456789457189236698237415246715398385964172719328564561843927872591643934672851 E9: 1 # 15 pairs * PAIR D7: 7,8 ROW 7 I7: 7,8,1,9 # reduction candidate for 7,8 I7: 1,9 # 12 pairs I7: 7,8 # 10 pairs * PAIR D7: 7,8 COL D D4: 7,8,3,4,9 # reduction candidate for 7,8 D4: 7,8 => SOLVED * 123456789457189236698237415246715398385964172719328564561843927872591643934672851 D4: 3,4,9 # 15 pairs D6: 7,8,3,4,9 # reduction candidate for 7,8 D6: 7,8 => CTR * .2....78..571..2.6..82...15..6.15....85.6.172.1..2.56.56..43...87.5916.....6.2.5. D6: 3,4,9 # 8 pairs * PAIR F8: 1,6 ROW 8 G8: 1,6,3,4 # reduction candidate for 1,6 G8: 3,4 # 17 pairs G8: 1,6 # 10 pairs * PAIR H7: 2,9 ROW 7 C7: 2,9,1 # reduction candidate for 2,9 C7: 2,9 # 11 pairs C7: 1 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-mith-te3-00135988-base-pr-000.dot * REASONING * DIS # E4: 3,8 => CTR => E4: 1,2,5,7 * PRF # E9: 7,8 => SOL * PRF # D4: 7,8 => SOL * DIS # D6: 7,8 => CTR => D6: 3,4,9 * CNT 4 HDP CHAINS / 24 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,D7,E1,E2,E3,F8,H7) * .2....78..571..2.6..82...15..6.......85.6..72.1....56.56..43...87.59.........2.5. * PAIR E1: 3,5 COL E E4: 3,5,1,2,7,8 # reduction candidate for 3,5 E4: 3,5 # 12 pairs E4: 1,2,7,8 # 7 pairs * PAIR E2: 3,8 COL E E4: 3,8,1,2,5,7 # reduction candidate for 3,8 E4: 3,8 => CTR * 12.65.78..571..2.66.827..152.67.5....85.61.7271..2.56.56.843...87.596.......1265. E6: 3,8,2,7 # reduction candidate for 3,8 E6: 3,8 # 12 pairs * RESTART * PAIR E2: 3,8 COL E E6: 3,8,2,7 # reduction candidate for 3,8 E6: 3,8 # 12 pairs E6: 2,7 # 9 pairs * PAIR RESTART * PAIR E2: 3,8 COL E E6: 3,8,2,7 # reduction candidate for 3,8 E6: 3,8 # 12 pairs E6: 2,7 # 9 pairs * PAIR E3: 3,7 COL E E6: 3,7,2,8 # reduction candidate for 3,7 E6: 3,7 # 12 pairs E6: 2,8 # 9 pairs * PAIR A4: 2,7 ROW 4 E4: 2,7,1,5 # reduction candidate for 2,7 E4: 2,7 # 15 pairs E4: 1,5 # 7 pairs * PAIR A6: 2,7 ROW 6 E6: 2,7,3,8 # reduction candidate for 2,7 E6: 3,8 # 12 pairs E6: 2,7 # 9 pairs * PAIR D7: 7,8 BLK 8 D9: 7,8,6 # reduction candidate for 7,8 D9: 7,8 # 15 pairs E9: 7,8,1 # reduction candidate for 7,8 E9: 7,8 => SOLVED * 123456789457189236698237415246715398385964172719328564561843927872591643934672851 * DURATION: 0:00:02.953333 START: 11:38:04.349937 END: 11:38:07.303270 2025-04-05 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00135988-base-pr-001.dot * REASONING * DIS # E4: 3,8 => CTR => E4: 1,2,5,7 * PRF E4: 1,2,5,7 # E9: 7,8 => SOL * STA E4: 1,2,5,7 + E9: 7,8 * CNT 2 HDP CHAINS / 16 HYP OPENED
Header Info
rating: 36124; r2: 759524; index: 135988
Solution
position: 123456789457189236698237415246715398385964172719328564561843927872591643934672851 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 # E4: 3,5 => UNS * INC # E4: 1,2,7,8 => UNS * DIS # E4: 3,8 => CTR => E4: 1,2,5,7 * INC # E4: 1,2,5,7 => UNS * INC # E6: 3,8 => UNS * INC # E4: 3,7 => UNS * INC # E6: 3,7 => UNS * INC # E4: 2,7 => UNS * INC # E4: 1,3,5,8 => UNS * INC # E6: 2,7 => UNS * INC # E6: 3,8 => UNS * INC # D9: 7,8 => UNS * PRF # E9: 7,8 => SOL * INC # E9: 1 => UNS * INC # I7: 7,8 => UNS * INC # I7: 1,9 => UNS * PRF # D4: 7,8 => SOL * INC # D4: 3,4,9 => UNS * DIS # D6: 7,8 => CTR => D6: 3,4,9 * INC # D6: 3,4,9 => UNS * INC # G8: 1,6 => UNS * INC # G8: 3,4 => UNS * INC # C7: 2,9 => UNS * INC # C7: 1 => UNS * CNT 24 HDP CHAINS / 24 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E4: 3,5 => UNS * INC # E4: 1,2,7,8 => UNS * DIS # E4: 3,8 => CTR => E4: 1,2,5,7 * INC E4: 1,2,5,7 # E6: 3,8 => UNS * INC E4: 1,2,5,7 # E6: 3,8 => UNS * INC E4: 1,2,5,7 # E6: 2,7 => UNS * INC E4: 1,2,5,7 # E6: 3,8 => UNS * INC E4: 1,2,5,7 # E6: 2,7 => UNS * INC E4: 1,2,5,7 # E6: 3,7 => UNS * INC E4: 1,2,5,7 # E6: 2,8 => UNS * INC E4: 1,2,5,7 # E4: 2,7 => UNS * INC E4: 1,2,5,7 # E4: 1,5 => UNS * INC E4: 1,2,5,7 # E6: 2,7 => UNS * INC E4: 1,2,5,7 # E6: 3,8 => UNS * INC E4: 1,2,5,7 # D9: 7,8 => UNS * PRF E4: 1,2,5,7 # E9: 7,8 => SOL * STA E4: 1,2,5,7 + E9: 7,8 * CNT 16 HDP CHAINS / 16 HYP OPENED