Analysis of xx-mith-te3-00003048-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .234.6...4.67...2.78...........4.8....43.8....7826.3....7...65....6......62...471 initial

Autosolve

position: .234.6.8.4.678..2378........3..4.8....43.8....7826.3....7...65....6...3..62...471 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # E8: 2,9 => SOL
* CNT   1 HDP CHAINS /  13 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # E8: 2,9 => SOL
* STA E8: 2,9
* CNT   1 HDP CHAINS /  11 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Details

Positions

.234.6...4.67...2.78...........4.8....43.8....7826.3....7...65....6......62...471 initial
.234.6.8.4.678..2378........3..4.8....43.8....7826.3....7...65....6...3..62...471 autosolve
123456789456789123789132546235941867614378295978265314397814652541627938862593471 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
E3: 2,3
F3: 2,3
H3: 4,6
I3: 4,6
A4: 2,6
A5: 2,6
I6: 4,5
G8: 2,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E3,F3: 2.. / E3 = 2  => 10 pairs (_) / F3 = 2  =>  7 pairs (_)
A4,A5: 2.. / A4 = 2  =>  7 pairs (_) / A5 = 2  => 10 pairs (_)
A4,I4: 2.. / A4 = 2  =>  7 pairs (_) / I4 = 2  => 10 pairs (_)
G5,G8: 2.. / G5 = 2  => 14 pairs (_) / G8 = 2  => 11 pairs (_)
E3,F3: 3.. / E3 = 3  =>  7 pairs (_) / F3 = 3  => 10 pairs (_)
A7,A9: 3.. / A7 = 3  =>  8 pairs (_) / A9 = 3  => 16 pairs (_)
H3,I3: 4.. / H3 = 4  =>  6 pairs (_) / I3 = 4  => 12 pairs (_)
H6,I6: 4.. / H6 = 4  => 12 pairs (_) / I6 = 4  =>  6 pairs (_)
B7,B8: 4.. / B7 = 4  =>  9 pairs (_) / B8 = 4  =>  9 pairs (_)
F7,F8: 4.. / F7 = 4  =>  9 pairs (_) / F8 = 4  =>  9 pairs (_)
B7,F7: 4.. / B7 = 4  =>  9 pairs (_) / F7 = 4  =>  9 pairs (_)
B8,F8: 4.. / B8 = 4  =>  9 pairs (_) / F8 = 4  =>  9 pairs (_)
H3,H6: 4.. / H3 = 4  =>  6 pairs (_) / H6 = 4  => 12 pairs (_)
I3,I6: 4.. / I3 = 4  => 12 pairs (_) / I6 = 4  =>  6 pairs (_)
H3,I3: 6.. / H3 = 6  => 12 pairs (_) / I3 = 6  =>  6 pairs (_)
A4,A5: 6.. / A4 = 6  => 10 pairs (_) / A5 = 6  =>  7 pairs (_)
G1,I1: 7.. / G1 = 7  => 10 pairs (_) / I1 = 7  =>  9 pairs (_)
F4,E5: 7.. / F4 = 7  =>  8 pairs (_) / E5 = 7  => 14 pairs (_)
E8,F8: 7.. / E8 = 7  =>  8 pairs (_) / F8 = 7  => 14 pairs (_)
F4,I4: 7.. / F4 = 7  =>  8 pairs (_) / I4 = 7  => 14 pairs (_)
E5,E8: 7.. / E5 = 7  => 14 pairs (_) / E8 = 7  =>  8 pairs (_)
F4,F8: 7.. / F4 = 7  =>  8 pairs (_) / F8 = 7  => 14 pairs (_)
G1,G5: 7.. / G1 = 7  => 10 pairs (_) / G5 = 7  =>  9 pairs (_)
D7,D9: 8.. / D7 = 8  => 11 pairs (_) / D9 = 8  =>  9 pairs (_)
I7,I8: 8.. / I7 = 8  => 11 pairs (_) / I8 = 8  => 12 pairs (_)
A8,I8: 8.. / A8 = 8  => 11 pairs (_) / I8 = 8  => 12 pairs (_)
A9,D9: 8.. / A9 = 8  => 11 pairs (_) / D9 = 8  =>  9 pairs (_)
* DURATION: 0:00:09.677109  START: 05:12:41.469330  END: 05:12:51.146439 2025-04-04
* CP COUNT: (27)
* INCONCLUSIVE

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,E3,F3,G8,H3,I3,I6)
* .234.6.8.4.678..2378........3..4.8....43.8....7826.3....7...65....6...3..62...471
* PAIR E3: 2,3 COL E
E7: 2,3,1,9                              # reduction candidate for 2,3
E7: 1,9                                  # 13 pairs
E7: 2,3                                  # 10 pairs
* PAIR F3: 2,3 COL F
F7: 2,3,1,4,9                            # reduction candidate for 2,3
F7: 2,3                                  # 11 pairs
F7: 1,4,9                                #  8 pairs
* PAIR A4: 2,6 ROW 4
I4: 2,6,5,7                              # reduction candidate for 2,6
I4: 2,6                                  # 10 pairs
I4: 5,7                                  #  6 pairs
* PAIR A5: 2,6 ROW 5
I5: 2,6,5,7                              # reduction candidate for 2,6
I5: 2,6                                  # 13 pairs
I5: 5,7                                  #  9 pairs
* PAIR G8: 2,9 BLK 9
I7: 2,9,8                                # reduction candidate for 2,9
I7: 2,9                                  # 12 pairs
I8: 2,9,8                                # reduction candidate for 2,9
I8: 2,9                                  # 11 pairs
* PAIR G8: 2,9 ROW 8
E8: 2,9,1,5,7                            # reduction candidate for 2,9
E8: 2,9 => SOLVED
* 123456789456789123789132546235941867614378295978265314397814652541627938862593471
E8: 1,5,7                                #  8 pairs
F8: 2,9,1,4,5,7                          # reduction candidate for 2,9
F8: 2,9                                  # 20 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-mith-te3-00003048-base-pr-000.dot
* REASONING
* PRF # E8: 2,9 => SOL
* CNT   1 HDP CHAINS /  13 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,E3,F3,G8,H3,I3,I6)
* .234.6.8.4.678..2378........3..4.8....43.8....7826.3....7...65....6...3..62...471
* PAIR E3: 2,3 COL E
E7: 2,3,1,9                              # reduction candidate for 2,3
E7: 1,9                                  # 13 pairs
E7: 2,3                                  # 10 pairs
* PAIR F3: 2,3 COL F
F7: 2,3,1,4,9                            # reduction candidate for 2,3
F7: 2,3                                  # 11 pairs
F7: 1,4,9                                #  8 pairs
* PAIR A4: 2,6 ROW 4
I4: 2,6,5,7                              # reduction candidate for 2,6
I4: 2,6                                  # 10 pairs
I4: 5,7                                  #  6 pairs
* PAIR A5: 2,6 ROW 5
I5: 2,6,5,7                              # reduction candidate for 2,6
I5: 2,6                                  # 13 pairs
I5: 5,7                                  #  9 pairs
* PAIR G8: 2,9 BLK 9
I7: 2,9,8                                # reduction candidate for 2,9
I7: 2,9                                  # 12 pairs
I8: 2,9,8                                # reduction candidate for 2,9
I8: 2,9                                  # 11 pairs
* PAIR G8: 2,9 ROW 8
E8: 2,9,1,5,7                            # reduction candidate for 2,9
E8: 2,9 => SOLVED
* 123456789456789123789132546235941867614378295978265314397814652541627938862593471
* DURATION: 0:00:02.386175  START: 05:12:54.013803  END: 05:12:56.399978 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00003048-base-pr-001.dot
* REASONING
* PRF # E8: 2,9 => SOL
* STA E8: 2,9
* CNT   1 HDP CHAINS /  11 HYP OPENED

Header Info

rating: 529; r2: 27759; index: 3048

Solution

position: 123456789456789123789132546235941867614378295978265314397814652541627938862593471 solved
Solution

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 # E7: 2,3 => UNS
* INC # E7: 1,9 => UNS
* INC # F7: 2,3 => UNS
* INC # F7: 1,4,9 => UNS
* INC # I4: 2,6 => UNS
* INC # I4: 5,7 => UNS
* INC # I5: 2,6 => UNS
* INC # I5: 5,7 => UNS
* INC # I7: 2,9 => UNS
* INC # I8: 2,9 => UNS
* PRF # E8: 2,9 => SOL
* INC # E8: 1,5,7 => UNS
* INC # F8: 2,9 => UNS
* CNT  13 HDP CHAINS /  13 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E7: 2,3 => UNS
* INC # E7: 1,9 => UNS
* INC # F7: 2,3 => UNS
* INC # F7: 1,4,9 => UNS
* INC # I4: 2,6 => UNS
* INC # I4: 5,7 => UNS
* INC # I5: 2,6 => UNS
* INC # I5: 5,7 => UNS
* INC # I7: 2,9 => UNS
* INC # I8: 2,9 => UNS
* PRF # E8: 2,9 => SOL
* STA E8: 2,9
* CNT  11 HDP CHAINS /  11 HYP OPENED