Analysis of xx-mith-te3-00026920-base.sdk
Contents
Original Sudoku
level: hard
position: 1..4.678.4..1..........3....786.134........17.1.7..6.8.958.....7.1...86...23..... initial
Autosolve
position: 1..4.678.4..1....6.....3....786.134........17.1.7..6.8.958.....7.1...86...23..... autosolve
Pair Reduction Variants
Deep Pair Reduction
Time used: 0:00:19.138154
The following important HDP chains were detected:
* DIS # C2: 3,9 # B2: 2,5 => CTR => B2: 8 * DIS # I1: 3,9 # E2: 2,5 => CTR => E2: 7,8,9 * DIS # I1: 3,9 + E2: 7,8,9 # E3: 2,5 => CTR => E3: 7,8,9 * PRF # I1: 3,9 + E2: 7,8,9 + E3: 7,8,9 # E5: 2,5 => SOL * STA # I1: 3,9 + E2: 7,8,9 + E3: 7,8,9 + E5: 2,5 * CNT 4 HDP CHAINS / 89 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1..4.678.4..1..........3....786.134........17.1.7..6.8.958.....7.1...86...23..... | initial |
| 1..4.678.4..1....6.....3....786.134........17.1.7..6.8.958.....7.1...86...23..... | autosolve |
| 123456789457189236986273154278691345364528917519734628695812473731945862842367591 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (8) C1: 3,9 G3: 1,4 I3: 1,4 A7: 3,6 B8: 3,4 A9: 6,8 E7: 1,6 E9: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G3,I3: 1.. / G3 = 1 => 7 pairs (_) / I3 = 1 => 7 pairs (_) E7,E9: 1.. / E7 = 1 => 9 pairs (_) / E9 = 1 => 14 pairs (_) I1,H2: 3.. / I1 = 3 => 10 pairs (_) / H2 = 3 => 10 pairs (_) E5,E6: 3.. / E5 = 3 => 9 pairs (_) / E6 = 3 => 9 pairs (_) A7,B8: 3.. / A7 = 3 => 14 pairs (_) / B8 = 3 => 9 pairs (_) B8,I8: 3.. / B8 = 3 => 9 pairs (_) / I8 = 3 => 14 pairs (_) H2,H7: 3.. / H2 = 3 => 10 pairs (_) / H7 = 3 => 10 pairs (_) G3,I3: 4.. / G3 = 4 => 7 pairs (_) / I3 = 4 => 7 pairs (_) C5,C6: 4.. / C5 = 4 => 9 pairs (_) / C6 = 4 => 10 pairs (_) B8,B9: 4.. / B8 = 4 => 14 pairs (_) / B9 = 4 => 9 pairs (_) E7,E9: 6.. / E7 = 6 => 14 pairs (_) / E9 = 6 => 9 pairs (_) A7,E7: 6.. / A7 = 6 => 9 pairs (_) / E7 = 6 => 14 pairs (_) C3,C5: 6.. / C3 = 6 => 8 pairs (_) / C5 = 6 => 12 pairs (_) C2,C3: 7.. / C2 = 7 => 9 pairs (_) / C3 = 7 => 12 pairs (_) E2,E3: 7.. / E2 = 7 => 12 pairs (_) / E3 = 7 => 9 pairs (_) F7,F9: 7.. / F7 = 7 => 9 pairs (_) / F9 = 7 => 11 pairs (_) H7,H9: 7.. / H7 = 7 => 11 pairs (_) / H9 = 7 => 9 pairs (_) C2,E2: 7.. / C2 = 7 => 9 pairs (_) / E2 = 7 => 12 pairs (_) C3,E3: 7.. / C3 = 7 => 12 pairs (_) / E3 = 7 => 9 pairs (_) F7,H7: 7.. / F7 = 7 => 9 pairs (_) / H7 = 7 => 11 pairs (_) F9,H9: 7.. / F9 = 7 => 11 pairs (_) / H9 = 7 => 9 pairs (_) E5,F5: 8.. / E5 = 8 => 0 pairs (X) / F5 = 8 => 10 pairs (_) A9,B9: 8.. / A9 = 8 => 8 pairs (_) / B9 = 8 => 12 pairs (_) A3,A9: 8.. / A3 = 8 => 12 pairs (_) / A9 = 8 => 8 pairs (_) F2,F5: 8.. / F2 = 8 => 0 pairs (X) / F5 = 8 => 10 pairs (_) * DURATION: 0:00:07.484320 START: 10:21:08.796139 END: 10:21:16.280459 2025-04-04 * CP COUNT: (25) * CLUE FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:18.946488 START: 10:21:22.056865 END: 10:21:41.003353 2025-04-04 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00026920-base-pr-002.dot * REASONING * DIS # C2: 3,9 # B2: 2,5 => CTR => B2: 8 * DIS # I1: 3,9 # E2: 2,5 => CTR => E2: 7,8,9 * DIS # I1: 3,9 + E2: 7,8,9 # E3: 2,5 => CTR => E3: 7,8,9 * PRF # I1: 3,9 + E2: 7,8,9 + E3: 7,8,9 # E5: 2,5 => SOL * STA # I1: 3,9 + E2: 7,8,9 + E3: 7,8,9 + E5: 2,5 * CNT 4 HDP CHAINS / 89 HYP OPENED
Header Info
rating: 5570; r2: 194335; index: 26920
Solution
position: 123456789457189236986273154278691345364528917519734628695812473731945862842367591 solved
See section Deep 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 # C2: 3,9 => UNS * INC # C2: 7 => UNS * INC # I1: 3,9 => UNS * INC # I1: 2,5 => UNS * INC # C5: 3,9 => UNS * INC # C6: 3,9 => UNS * INC # G7: 1,4 => UNS * INC # G9: 1,4 => UNS * INC # I7: 1,4 => UNS * INC # I9: 1,4 => UNS * INC # A5: 3,6 => UNS * INC # A5: 2,5,9 => UNS * INC # I8: 3,4 => UNS * INC # I8: 2,5,9 => UNS * INC # B9: 6,8 => UNS * INC # B9: 4 => UNS * INC # A3: 6,8 => UNS * INC # A3: 2,5,9 => UNS * CNT 18 HDP CHAINS / 18 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 3,9 => UNS * INC # C2: 7 => UNS * INC # I1: 3,9 => UNS * INC # I1: 2,5 => UNS * INC # C5: 3,9 => UNS * INC # C6: 3,9 => UNS * INC # G7: 1,4 => UNS * INC # G9: 1,4 => UNS * INC # I7: 1,4 => UNS * INC # I9: 1,4 => UNS * INC # A5: 3,6 => UNS * INC # A5: 2,5,9 => UNS * INC # I8: 3,4 => UNS * INC # I8: 2,5,9 => UNS * INC # B9: 6,8 => UNS * INC # B9: 4 => UNS * INC # A3: 6,8 => UNS * INC # A3: 2,5,9 => UNS * CNT 18 HDP CHAINS / 18 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 3,9 => UNS * INC # C2: 7 => UNS * INC # I1: 3,9 => UNS * INC # I1: 2,5 => UNS * INC # C5: 3,9 => UNS * INC # C6: 3,9 => UNS * INC # G7: 1,4 => UNS * INC # G9: 1,4 => UNS * INC # I7: 1,4 => UNS * INC # I9: 1,4 => UNS * INC # A5: 3,6 => UNS * INC # A5: 2,5,9 => UNS * INC # I8: 3,4 => UNS * INC # I8: 2,5,9 => UNS * INC # B9: 6,8 => UNS * INC # B9: 4 => UNS * INC # A3: 6,8 => UNS * INC # A3: 2,5,9 => UNS * DIS # C2: 3,9 # B2: 2,5 => CTR => B2: 8 * INC # C2: 3,9 + B2: 8 # A3: 2,5 => UNS * INC # C2: 3,9 + B2: 8 # B3: 2,5 => UNS * INC # C2: 3,9 + B2: 8 # E1: 2,5 => UNS * INC # C2: 3,9 + B2: 8 # I1: 2,5 => UNS * INC # C2: 3,9 + B2: 8 # B5: 2,5 => UNS * INC # C2: 3,9 + B2: 8 # B5: 3 => UNS * INC # C2: 3,9 + B2: 8 # I1: 3,9 => UNS * INC # C2: 3,9 + B2: 8 # I1: 2,5 => UNS * INC # C2: 3,9 + B2: 8 # H2: 3,9 => UNS * INC # C2: 3,9 + B2: 8 # H2: 2,5 => UNS * INC # C2: 3,9 + B2: 8 # G7: 1,4 => UNS * INC # C2: 3,9 + B2: 8 # G9: 1,4 => UNS * INC # C2: 3,9 + B2: 8 # I7: 1,4 => UNS * INC # C2: 3,9 + B2: 8 # I9: 1,4 => UNS * INC # C2: 3,9 + B2: 8 # I8: 3,4 => UNS * INC # C2: 3,9 + B2: 8 # I8: 2,5,9 => UNS * INC # C2: 3,9 + B2: 8 # A3: 2,5 => UNS * INC # C2: 3,9 + B2: 8 # B3: 2,5 => UNS * INC # C2: 3,9 + B2: 8 # E1: 2,5 => UNS * INC # C2: 3,9 + B2: 8 # I1: 2,5 => UNS * INC # C2: 3,9 + B2: 8 # B5: 2,5 => UNS * INC # C2: 3,9 + B2: 8 # B5: 3 => UNS * INC # C2: 3,9 + B2: 8 # I1: 3,9 => UNS * INC # C2: 3,9 + B2: 8 # I1: 2,5 => UNS * INC # C2: 3,9 + B2: 8 # H2: 3,9 => UNS * INC # C2: 3,9 + B2: 8 # H2: 2,5 => UNS * INC # C2: 3,9 + B2: 8 # G7: 1,4 => UNS * INC # C2: 3,9 + B2: 8 # G9: 1,4 => UNS * INC # C2: 3,9 + B2: 8 # I7: 1,4 => UNS * INC # C2: 3,9 + B2: 8 # I9: 1,4 => UNS * INC # C2: 3,9 + B2: 8 # I8: 3,4 => UNS * INC # C2: 3,9 + B2: 8 # I8: 2,5,9 => UNS * INC # C2: 3,9 + B2: 8 => UNS * INC # C2: 7 # I1: 3,9 => UNS * INC # C2: 7 # I1: 2,5 => UNS * INC # C2: 7 # C5: 3,9 => UNS * INC # C2: 7 # C6: 3,9 => UNS * INC # C2: 7 # A3: 6,9 => UNS * INC # C2: 7 # A3: 2,5,8 => UNS * INC # C2: 7 # C5: 6,9 => UNS * INC # C2: 7 # C5: 3,4 => UNS * INC # C2: 7 # G7: 1,4 => UNS * INC # C2: 7 # G9: 1,4 => UNS * INC # C2: 7 # I7: 1,4 => UNS * INC # C2: 7 # I9: 1,4 => UNS * INC # C2: 7 # A5: 3,6 => UNS * INC # C2: 7 # A5: 2,5,9 => UNS * INC # C2: 7 # I8: 3,4 => UNS * INC # C2: 7 # I8: 2,5,9 => UNS * INC # C2: 7 # B9: 6,8 => UNS * INC # C2: 7 # B9: 4 => UNS * INC # C2: 7 # A3: 6,8 => UNS * INC # C2: 7 # A3: 2,5,9 => UNS * INC # C2: 7 => UNS * INC # I1: 3,9 # B2: 2,5 => UNS * INC # I1: 3,9 # A3: 2,5 => UNS * INC # I1: 3,9 # B3: 2,5 => UNS * INC # I1: 3,9 # B5: 2,5 => UNS * INC # I1: 3,9 # B5: 3,6 => UNS * INC # I1: 3,9 # C2: 3,9 => UNS * INC # I1: 3,9 # C2: 7 => UNS * INC # I1: 3,9 # C5: 3,9 => UNS * INC # I1: 3,9 # C6: 3,9 => UNS * DIS # I1: 3,9 # E2: 2,5 => CTR => E2: 7,8,9 * INC # I1: 3,9 + E2: 7,8,9 # F2: 2,5 => UNS * INC # I1: 3,9 + E2: 7,8,9 # D3: 2,5 => UNS * DIS # I1: 3,9 + E2: 7,8,9 # E3: 2,5 => CTR => E3: 7,8,9 * INC # I1: 3,9 + E2: 7,8,9 + E3: 7,8,9 # E4: 2,5 => UNS * PRF # I1: 3,9 + E2: 7,8,9 + E3: 7,8,9 # E5: 2,5 => SOL * STA # I1: 3,9 + E2: 7,8,9 + E3: 7,8,9 + E5: 2,5 * CNT 88 HDP CHAINS / 89 HYP OPENED