Analysis of xx-mith-te3-00121190-base.sdk
Contents
Original Sudoku
level: hard
position: 1.....789.5...9...6........27.9...148..24.9.7......82...18.24.....79......2.14... initial
Autosolve
position: 12....789.5...9...6...2....27.9...148..24.9.7......82...18.24.....79......2.14..8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C8: 3,4 => CTR => C8: 5,6,8 * DIS # C3: 7 => CTR => C3: 8,9 * CNT 2 HDP CHAINS / 23 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C8: 3,4 => CTR => C8: 5,6,8 * DIS C8: 5,6,8 # C3: 7 => CTR => C3: 8,9 * STA C8: 5,6,8 + C3: 8,9 * CNT 2 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: 12....789.57.89...6...27...27.9.8.148..24.9.7....7.82...18.24.....79......2.14..8 pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:00:09.942897
The following important HDP chains were detected:
* PRF # D1: 3,4 # F6: 5,6 => SOL * STA # D1: 3,4 + F6: 5,6 * CNT 1 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.....789.5...9...6........27.9...148..24.9.7......82...18.24.....79......2.14... | initial |
| 12....789.5...9...6...2....27.9...148..24.9.7......82...18.24.....79......2.14..8 | autosolve |
| 12....789.57.89...6...27...27.9.8.148..24.9.7....7.82...18.24.....79......2.14..8 | pair_reduction |
| 123456789457189236689327541275938614836241957914675823391862475548793162762514398 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (10) C1: 3,4 A2: 3,4 C2: 7,8 B3: 8,9 E2: 7,8 F3: 7,8 H7: 7,9 G8: 1,2 I8: 1,2 H9: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,D3: 1.. / D2 = 1 => 11 pairs (_) / D3 = 1 => 17 pairs (_) B5,B6: 1.. / B5 = 1 => 8 pairs (_) / B6 = 1 => 17 pairs (_) F5,F6: 1.. / F5 = 1 => 17 pairs (_) / F6 = 1 => 8 pairs (_) G8,I8: 1.. / G8 = 1 => 9 pairs (_) / I8 = 1 => 9 pairs (_) B5,F5: 1.. / B5 = 1 => 8 pairs (_) / F5 = 1 => 17 pairs (_) B6,F6: 1.. / B6 = 1 => 17 pairs (_) / F6 = 1 => 8 pairs (_) G2,I2: 2.. / G2 = 2 => 9 pairs (_) / I2 = 2 => 9 pairs (_) G8,I8: 2.. / G8 = 2 => 9 pairs (_) / I8 = 2 => 9 pairs (_) G2,G8: 2.. / G2 = 2 => 9 pairs (_) / G8 = 2 => 9 pairs (_) I2,I8: 2.. / I2 = 2 => 9 pairs (_) / I8 = 2 => 9 pairs (_) C1,A2: 3.. / C1 = 3 => 23 pairs (_) / A2 = 3 => 12 pairs (_) C1,A2: 4.. / C1 = 4 => 12 pairs (_) / A2 = 4 => 23 pairs (_) H2,H3: 4.. / H2 = 4 => 12 pairs (_) / H3 = 4 => 12 pairs (_) C1,D1: 4.. / C1 = 4 => 12 pairs (_) / D1 = 4 => 23 pairs (_) D3,H3: 4.. / D3 = 4 => 12 pairs (_) / H3 = 4 => 12 pairs (_) B6,B8: 4.. / B6 = 4 => 9 pairs (_) / B8 = 4 => 8 pairs (_) C2,C3: 7.. / C2 = 7 => 8 pairs (_) / C3 = 7 => 0 pairs (X) E2,F3: 7.. / E2 = 7 => 0 pairs (X) / F3 = 7 => 8 pairs (_) E6,F6: 7.. / E6 = 7 => 8 pairs (_) / F6 = 7 => 0 pairs (X) A7,A9: 7.. / A7 = 7 => 9 pairs (_) / A9 = 7 => 9 pairs (_) H7,H9: 7.. / H7 = 7 => 9 pairs (_) / H9 = 7 => 9 pairs (_) C2,E2: 7.. / C2 = 7 => 8 pairs (_) / E2 = 7 => 0 pairs (X) C3,F3: 7.. / C3 = 7 => 0 pairs (X) / F3 = 7 => 8 pairs (_) A7,H7: 7.. / A7 = 7 => 9 pairs (_) / H7 = 7 => 9 pairs (_) A9,H9: 7.. / A9 = 7 => 9 pairs (_) / H9 = 7 => 9 pairs (_) E2,E6: 7.. / E2 = 7 => 0 pairs (X) / E6 = 7 => 8 pairs (_) F3,F6: 7.. / F3 = 7 => 8 pairs (_) / F6 = 7 => 0 pairs (X) E2,F3: 8.. / E2 = 8 => 8 pairs (_) / F3 = 8 => 0 pairs (X) E4,F4: 8.. / E4 = 8 => 0 pairs (X) / F4 = 8 => 8 pairs (_) B8,C8: 8.. / B8 = 8 => 15 pairs (_) / C8 = 8 => 7 pairs (_) C2,E2: 8.. / C2 = 8 => 0 pairs (X) / E2 = 8 => 8 pairs (_) B3,B8: 8.. / B3 = 8 => 7 pairs (_) / B8 = 8 => 15 pairs (_) E2,E4: 8.. / E2 = 8 => 8 pairs (_) / E4 = 8 => 0 pairs (X) F3,F4: 8.. / F3 = 8 => 0 pairs (X) / F4 = 8 => 8 pairs (_) B3,C3: 9.. / B3 = 9 => 15 pairs (_) / C3 = 9 => 7 pairs (_) H7,H9: 9.. / H7 = 9 => 9 pairs (_) / H9 = 9 => 9 pairs (_) C3,C6: 9.. / C3 = 9 => 7 pairs (_) / C6 = 9 => 15 pairs (_) * DURATION: 0:00:13.647411 START: 19:10:32.873162 END: 19:10:46.520573 2025-04-06 * CP COUNT: (37) * CLUE FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:09.787734 START: 19:11:00.787205 END: 19:11:10.574939 2025-04-06 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00121190-base-pr-002.dot * REASONING * PRF # D1: 3,4 # F6: 5,6 => SOL * STA # D1: 3,4 + F6: 5,6 * CNT 1 HDP CHAINS / 29 HYP OPENED
Header Info
rating: 31527; r2: 817781; index: 121190
Solution
position: 123456789457189236689327541275938614836241957914675823391862475548793162762514398 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 # D1: 3,4 => UNS * INC # D1: 5,6 => UNS * INC # C6: 3,4 => UNS * DIS # C8: 3,4 => CTR => C8: 5,6,8 * INC # C8: 5,6,8 => UNS * INC # D2: 3,4 => UNS * INC # H2: 3,4 => UNS * INC # A6: 3,4 => UNS * INC # A8: 3,4 => UNS * INC # C3: 7,8 => UNS * INC # C3: 9 => UNS * INC # C3: 8,9 => UNS * DIS # C3: 7 => CTR => C3: 8,9 * INC # C3: 7,8 => UNS * INC # C3: 9 => UNS * INC # A7: 7,9 => UNS * INC # A7: 3,5 => UNS * INC # G2: 1,2 => UNS * INC # G2: 3,6 => UNS * INC # I2: 1,2 => UNS * INC # I2: 3,6 => UNS * INC # A9: 7,9 => UNS * INC # A9: 3,5 => UNS * CNT 23 HDP CHAINS / 23 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D1: 3,4 => UNS * INC # D1: 5,6 => UNS * INC # C6: 3,4 => UNS * DIS # C8: 3,4 => CTR => C8: 5,6,8 * INC C8: 5,6,8 # C6: 3,4 => UNS * INC C8: 5,6,8 # C6: 5,6,9 => UNS * INC C8: 5,6,8 # D1: 3,4 => UNS * INC C8: 5,6,8 # D1: 5,6 => UNS * INC C8: 5,6,8 # C6: 3,4 => UNS * INC C8: 5,6,8 # C6: 5,6,9 => UNS * INC C8: 5,6,8 # D2: 3,4 => UNS * INC C8: 5,6,8 # H2: 3,4 => UNS * INC C8: 5,6,8 # A6: 3,4 => UNS * INC C8: 5,6,8 # A8: 3,4 => UNS * INC C8: 5,6,8 # C3: 7,8 => UNS * INC C8: 5,6,8 # C3: 9 => UNS * INC C8: 5,6,8 # C3: 8,9 => UNS * DIS C8: 5,6,8 # C3: 7 => CTR => C3: 8,9 * INC C8: 5,6,8 + C3: 8,9 # A7: 7,9 => UNS * INC C8: 5,6,8 + C3: 8,9 # A7: 3,5 => UNS * INC C8: 5,6,8 + C3: 8,9 # G2: 1,2 => UNS * INC C8: 5,6,8 + C3: 8,9 # G2: 3,6 => UNS * INC C8: 5,6,8 + C3: 8,9 # I2: 1,2 => UNS * INC C8: 5,6,8 + C3: 8,9 # I2: 3,6 => UNS * INC C8: 5,6,8 + C3: 8,9 # A9: 7,9 => UNS * INC C8: 5,6,8 + C3: 8,9 # A9: 3,5 => UNS * INC C8: 5,6,8 + C3: 8,9 # D1: 3,4 => UNS * INC C8: 5,6,8 + C3: 8,9 # D1: 5,6 => UNS * INC C8: 5,6,8 + C3: 8,9 # C6: 3,4 => UNS * INC C8: 5,6,8 + C3: 8,9 # C6: 5,6,9 => UNS * INC C8: 5,6,8 + C3: 8,9 # D2: 3,4 => UNS * INC C8: 5,6,8 + C3: 8,9 # H2: 3,4 => UNS * INC C8: 5,6,8 + C3: 8,9 # A6: 3,4 => UNS * INC C8: 5,6,8 + C3: 8,9 # A8: 3,4 => UNS * INC C8: 5,6,8 + C3: 8,9 # A7: 7,9 => UNS * INC C8: 5,6,8 + C3: 8,9 # A7: 3,5 => UNS * INC C8: 5,6,8 + C3: 8,9 # G2: 1,2 => UNS * INC C8: 5,6,8 + C3: 8,9 # G2: 3,6 => UNS * INC C8: 5,6,8 + C3: 8,9 # I2: 1,2 => UNS * INC C8: 5,6,8 + C3: 8,9 # I2: 3,6 => UNS * INC C8: 5,6,8 + C3: 8,9 # A9: 7,9 => UNS * INC C8: 5,6,8 + C3: 8,9 # A9: 3,5 => UNS * STA C8: 5,6,8 + C3: 8,9 * CNT 42 HDP CHAINS / 42 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # D1: 3,4 => UNS * INC # D1: 5,6 => UNS * INC # C6: 3,4 => UNS * INC # C6: 5,6,9 => UNS * INC # D2: 3,4 => UNS * INC # H2: 3,4 => UNS * INC # A6: 3,4 => UNS * INC # A8: 3,4 => UNS * INC # A7: 7,9 => UNS * INC # A7: 3,5 => UNS * INC # G2: 1,2 => UNS * INC # G2: 3,6 => UNS * INC # I2: 1,2 => UNS * INC # I2: 3,6 => UNS * INC # A9: 7,9 => UNS * INC # A9: 3,5 => UNS * INC # D1: 3,4 # C6: 3,4 => UNS * INC # D1: 3,4 # C6: 5,6,9 => UNS * INC # D1: 3,4 # D2: 3,4 => UNS * INC # D1: 3,4 # H2: 3,4 => UNS * INC # D1: 3,4 # A6: 3,4 => UNS * INC # D1: 3,4 # A8: 3,4 => UNS * INC # D1: 3,4 # D2: 3,4 => UNS * INC # D1: 3,4 # D3: 3,4 => UNS * INC # D1: 3,4 # E4: 5,6 => UNS * INC # D1: 3,4 # E7: 5,6 => UNS * INC # D1: 3,4 # F5: 5,6 => UNS * PRF # D1: 3,4 # F6: 5,6 => SOL * STA # D1: 3,4 + F6: 5,6 * CNT 28 HDP CHAINS / 29 HYP OPENED