Analysis of xx-mith-te3-00104431-base.sdk

Contents

Original Sudoku
Autosolve
Pair Reduction Variants
Details
Solution
Appendix: Full HDP Chains

Original Sudoku

level: hard

position: ..34..7.94..7.913......3.452....7....9....5.76781.........3.9.......4....1.57.... initial

Autosolve

position: 1.34..7.94..7.913.....13.452..3.7...39....5.76781.........319...3.9.4..1.1.57.... autosolve

Pair Reduction Variants

Pair Reduction Analysis

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

Pair Reduction

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

Deep Pair Reduction

Time used: 0:00:10.663107

The following important HDP chains were detected:

* DIS # C4: 4,5 # I2: 6,8 => CTR => I2: 2
* DIS # C4: 4,5 + I2: 2 # E1: 6,8 => CTR => E1: 2,5
* PRF # C4: 4,5 + I2: 2 + E1: 2,5 # I9: 6,8 => SOL
* STA # C4: 4,5 + I2: 2 + E1: 2,5 + I9: 6,8
* CNT   3 HDP CHAINS /  29 HYP OPENED

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

Details

Positions

`..34..7.94..7.913......3.452....7....9....5.76781.........3.9.......4....1.57....`	initial
`1.34..7.94..7.913.....13.452..3.7...39....5.76781.........319...3.9.4..1.1.57....`	autosolve
`123456789456789132789213645245397816391648527678125493562831974837964251914572368`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
A3: 7,9
C3: 7,9
B4: 4,5
C5: 1,4
F6: 2,5
H6: 2,9
A9: 8,9
H7: 5,7
H8: 5,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C4,C5: 1.. / C4 = 1  => 10 pairs (_) / C5 = 1  => 18 pairs (_)
H4,H5: 1.. / H4 = 1  => 18 pairs (_) / H5 = 1  => 10 pairs (_)
C4,H4: 1.. / C4 = 1  => 10 pairs (_) / H4 = 1  => 18 pairs (_)
C5,H5: 1.. / C5 = 1  => 18 pairs (_) / H5 = 1  => 10 pairs (_)
G6,I6: 3.. / G6 = 3  => 10 pairs (_) / I6 = 3  => 11 pairs (_)
G9,I9: 3.. / G9 = 3  => 11 pairs (_) / I9 = 3  => 10 pairs (_)
G6,G9: 3.. / G6 = 3  => 10 pairs (_) / G9 = 3  => 11 pairs (_)
I6,I9: 3.. / I6 = 3  => 11 pairs (_) / I9 = 3  => 10 pairs (_)
C5,E5: 4.. / C5 = 4  => 10 pairs (_) / E5 = 4  => 18 pairs (_)
B4,B7: 4.. / B4 = 4  => 18 pairs (_) / B7 = 4  => 11 pairs (_)
B4,C4: 5.. / B4 = 5  => 11 pairs (_) / C4 = 5  => 18 pairs (_)
E6,F6: 5.. / E6 = 5  => 17 pairs (_) / F6 = 5  =>  8 pairs (_)
A7,A8: 5.. / A7 = 5  =>  8 pairs (_) / A8 = 5  =>  9 pairs (_)
H7,H8: 5.. / H7 = 5  =>  9 pairs (_) / H8 = 5  =>  8 pairs (_)
A7,H7: 5.. / A7 = 5  =>  8 pairs (_) / H7 = 5  =>  9 pairs (_)
A8,H8: 5.. / A8 = 5  =>  9 pairs (_) / H8 = 5  =>  8 pairs (_)
C2,C4: 5.. / C2 = 5  => 11 pairs (_) / C4 = 5  => 18 pairs (_)
F1,F6: 5.. / F1 = 5  => 17 pairs (_) / F6 = 5  =>  8 pairs (_)
A3,C3: 7.. / A3 = 7  =>  8 pairs (_) / C3 = 7  => 13 pairs (_)
H7,H8: 7.. / H7 = 7  =>  8 pairs (_) / H8 = 7  =>  9 pairs (_)
A3,C3: 9.. / A3 = 9  => 13 pairs (_) / C3 = 9  =>  8 pairs (_)
E4,E6: 9.. / E4 = 9  =>  9 pairs (_) / E6 = 9  => 13 pairs (_)
H4,H6: 9.. / H4 = 9  => 13 pairs (_) / H6 = 9  =>  9 pairs (_)
A9,C9: 9.. / A9 = 9  =>  8 pairs (_) / C9 = 9  => 13 pairs (_)
E4,H4: 9.. / E4 = 9  =>  9 pairs (_) / H4 = 9  => 13 pairs (_)
E6,H6: 9.. / E6 = 9  => 13 pairs (_) / H6 = 9  =>  9 pairs (_)
A3,A9: 9.. / A3 = 9  => 13 pairs (_) / A9 = 9  =>  8 pairs (_)
C3,C9: 9.. / C3 = 9  =>  8 pairs (_) / C9 = 9  => 13 pairs (_)
* DURATION: 0:00:09.774614  START: 01:42:28.798279  END: 01:42:38.572893 2025-04-05
* CP COUNT: (28)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:10.516201  START: 01:42:44.006971  END: 01:42:54.523172 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00104431-base-pr-002.dot
* REASONING
* DIS # C4: 4,5 # I2: 6,8 => CTR => I2: 2
* DIS # C4: 4,5 + I2: 2 # E1: 6,8 => CTR => E1: 2,5
* PRF # C4: 4,5 + I2: 2 + E1: 2,5 # I9: 6,8 => SOL
* STA # C4: 4,5 + I2: 2 + E1: 2,5 + I9: 6,8
* CNT   3 HDP CHAINS /  29 HYP OPENED

Header Info

rating: 26224; r2: 543415; index: 104431

Solution

position: 123456789456789132789213645245397816391648527678125493562831974837964251914572368 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 # C4: 4,5 => UNS
* INC # C4: 1 => UNS
* INC # C4: 1,4 => UNS
* INC # C4: 5 => UNS
* INC # E6: 2,5 => UNS
* INC # E6: 4,9 => UNS
* INC # F1: 2,5 => UNS
* INC # F1: 6,8 => UNS
* INC # E6: 2,9 => UNS
* INC # E6: 4,5 => UNS
* INC # A7: 5,7 => UNS
* INC # A7: 8 => UNS
* INC # A8: 5,7 => UNS
* INC # A8: 8 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C4: 4,5 => UNS
* INC # C4: 1 => UNS
* INC # C4: 1,4 => UNS
* INC # C4: 5 => UNS
* INC # E6: 2,5 => UNS
* INC # E6: 4,9 => UNS
* INC # F1: 2,5 => UNS
* INC # F1: 6,8 => UNS
* INC # E6: 2,9 => UNS
* INC # E6: 4,5 => UNS
* INC # A7: 5,7 => UNS
* INC # A7: 8 => UNS
* INC # A8: 5,7 => UNS
* INC # A8: 8 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # C4: 4,5 => UNS
* INC # C4: 1 => UNS
* INC # C4: 1,4 => UNS
* INC # C4: 5 => UNS
* INC # E6: 2,5 => UNS
* INC # E6: 4,9 => UNS
* INC # F1: 2,5 => UNS
* INC # F1: 6,8 => UNS
* INC # E6: 2,9 => UNS
* INC # E6: 4,5 => UNS
* INC # A7: 5,7 => UNS
* INC # A7: 8 => UNS
* INC # A8: 5,7 => UNS
* INC # A8: 8 => UNS
* DIS # C4: 4,5 # I2: 6,8 => CTR => I2: 2
* INC # C4: 4,5 + I2: 2 # B1: 6,8 => UNS
* DIS # C4: 4,5 + I2: 2 # E1: 6,8 => CTR => E1: 2,5
* INC # C4: 4,5 + I2: 2 + E1: 2,5 # F1: 6,8 => UNS
* INC # C4: 4,5 + I2: 2 + E1: 2,5 # B1: 6,8 => UNS
* INC # C4: 4,5 + I2: 2 + E1: 2,5 # F1: 6,8 => UNS
* INC # C4: 4,5 + I2: 2 + E1: 2,5 # D3: 6,8 => UNS
* INC # C4: 4,5 + I2: 2 + E1: 2,5 # D7: 6,8 => UNS
* INC # C4: 4,5 + I2: 2 + E1: 2,5 # F1: 6,8 => UNS
* INC # C4: 4,5 + I2: 2 + E1: 2,5 # F9: 6,8 => UNS
* INC # C4: 4,5 + I2: 2 + E1: 2,5 # F1: 2,5 => UNS
* INC # C4: 4,5 + I2: 2 + E1: 2,5 # F1: 6,8 => UNS
* INC # C4: 4,5 + I2: 2 + E1: 2,5 # I7: 6,8 => UNS
* PRF # C4: 4,5 + I2: 2 + E1: 2,5 # I9: 6,8 => SOL
* STA # C4: 4,5 + I2: 2 + E1: 2,5 + I9: 6,8
* CNT  28 HDP CHAINS /  29 HYP OPENED