Analysis of xx-mith-te3-00121025-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 12.4.67.94.7...2.6.69.72......91..7...4....6.7...64.2.......817.......93971...6.2 initial

Autosolve

position: 12.4.67.94.71..2.6.69.72......91..7...42.7.6.7...64.2....6..817...7.1.93971...6.2 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

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

Pair Reduction

Pair Reduction

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

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:10.537611

The following important HDP chains were detected:

* PRF # A8: 2,6 # E7: 5,9 => SOL
* STA # A8: 2,6 + E7: 5,9
* CNT   1 HDP CHAINS /  34 HYP OPENED

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

Details

Positions

12.4.67.94.7...2.6.69.72......91..7...4....6.7...64.2.......817.......93971...6.2 initial
12.4.67.94.71..2.6.69.72......91..7...42.7.6.7...64.2....6..817...7.1.93971...6.2 autosolve
123456789457189236869372145236918574514237968798564321342695817685721493971843652 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
A4: 2,6
C4: 2,6
B5: 1,9
B6: 1,9
F7: 5,9
G8: 4,5
H9: 4,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G3,I3: 1.. / G3 = 1  =>  8 pairs (_) / I3 = 1  => 14 pairs (_)
B5,B6: 1.. / B5 = 1  =>  6 pairs (_) / B6 = 1  =>  6 pairs (_)
A4,C4: 2.. / A4 = 2  =>  6 pairs (_) / C4 = 2  =>  6 pairs (_)
E7,E8: 2.. / E7 = 2  => 13 pairs (_) / E8 = 2  =>  7 pairs (_)
G4,I4: 4.. / G4 = 4  => 10 pairs (_) / I4 = 4  =>  9 pairs (_)
B7,B8: 4.. / B7 = 4  =>  8 pairs (_) / B8 = 4  => 10 pairs (_)
G8,H9: 4.. / G8 = 4  => 21 pairs (_) / H9 = 4  => 10 pairs (_)
B7,E7: 4.. / B7 = 4  =>  8 pairs (_) / E7 = 4  => 10 pairs (_)
E9,H9: 4.. / E9 = 4  => 21 pairs (_) / H9 = 4  => 10 pairs (_)
H3,H9: 4.. / H3 = 4  => 21 pairs (_) / H9 = 4  => 10 pairs (_)
I3,I4: 4.. / I3 = 4  => 10 pairs (_) / I4 = 4  =>  9 pairs (_)
G8,H9: 5.. / G8 = 5  => 10 pairs (_) / H9 = 5  => 21 pairs (_)
A4,C4: 6.. / A4 = 6  =>  6 pairs (_) / C4 = 6  =>  6 pairs (_)
A8,C8: 6.. / A8 = 6  =>  6 pairs (_) / C8 = 6  =>  6 pairs (_)
A4,A8: 6.. / A4 = 6  =>  6 pairs (_) / A8 = 6  =>  6 pairs (_)
C4,C8: 6.. / C4 = 6  =>  6 pairs (_) / C8 = 6  =>  6 pairs (_)
E2,F2: 9.. / E2 = 9  =>  6 pairs (_) / F2 = 9  => 20 pairs (_)
B5,B6: 9.. / B5 = 9  =>  6 pairs (_) / B6 = 9  =>  6 pairs (_)
G5,G6: 9.. / G5 = 9  =>  6 pairs (_) / G6 = 9  =>  6 pairs (_)
E7,F7: 9.. / E7 = 9  => 20 pairs (_) / F7 = 9  =>  6 pairs (_)
B5,G5: 9.. / B5 = 9  =>  6 pairs (_) / G5 = 9  =>  6 pairs (_)
B6,G6: 9.. / B6 = 9  =>  6 pairs (_) / G6 = 9  =>  6 pairs (_)
E2,E7: 9.. / E2 = 9  =>  6 pairs (_) / E7 = 9  => 20 pairs (_)
F2,F7: 9.. / F2 = 9  => 20 pairs (_) / F7 = 9  =>  6 pairs (_)
* DURATION: 0:00:09.503824  START: 07:13:37.334738  END: 07:13:46.838562 2025-04-05
* CP COUNT: (24)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:10.387750  START: 07:13:55.366024  END: 07:14:05.753774 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00121025-base-pr-002.dot
* REASONING
* PRF # A8: 2,6 # E7: 5,9 => SOL
* STA # A8: 2,6 + E7: 5,9
* CNT   1 HDP CHAINS /  34 HYP OPENED

Header Info

rating: 31508; r2: 785246; index: 121025

Solution

position: 123456789457189236869372145236918574514237968798564321342695817685721493971843652 solved
Solution

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 # A8: 2,6 => UNS
* INC # A8: 5,8 => UNS
* INC # C8: 2,6 => UNS
* INC # C8: 5,8 => UNS
* INC # G5: 1,9 => UNS
* INC # G5: 3,5 => UNS
* INC # G6: 1,9 => UNS
* INC # G6: 3,5 => UNS
* INC # E7: 5,9 => UNS
* INC # E7: 2,4 => UNS
* INC # F2: 5,9 => UNS
* INC # F2: 3,8 => UNS
* INC # B8: 4,5 => UNS
* INC # E8: 4,5 => UNS
* INC # G3: 4,5 => UNS
* INC # G4: 4,5 => UNS
* INC # E9: 4,5 => UNS
* INC # E9: 3,8 => UNS
* INC # H3: 4,5 => UNS
* INC # H3: 3,8 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A8: 2,6 => UNS
* INC # A8: 5,8 => UNS
* INC # C8: 2,6 => UNS
* INC # C8: 5,8 => UNS
* INC # G5: 1,9 => UNS
* INC # G5: 3,5 => UNS
* INC # G6: 1,9 => UNS
* INC # G6: 3,5 => UNS
* INC # E7: 5,9 => UNS
* INC # E7: 2,4 => UNS
* INC # F2: 5,9 => UNS
* INC # F2: 3,8 => UNS
* INC # B8: 4,5 => UNS
* INC # E8: 4,5 => UNS
* INC # G3: 4,5 => UNS
* INC # G4: 4,5 => UNS
* INC # E9: 4,5 => UNS
* INC # E9: 3,8 => UNS
* INC # H3: 4,5 => UNS
* INC # H3: 3,8 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A8: 2,6 => UNS
* INC # A8: 5,8 => UNS
* INC # C8: 2,6 => UNS
* INC # C8: 5,8 => UNS
* INC # G5: 1,9 => UNS
* INC # G5: 3,5 => UNS
* INC # G6: 1,9 => UNS
* INC # G6: 3,5 => UNS
* INC # E7: 5,9 => UNS
* INC # E7: 2,4 => UNS
* INC # F2: 5,9 => UNS
* INC # F2: 3,8 => UNS
* INC # B8: 4,5 => UNS
* INC # E8: 4,5 => UNS
* INC # G3: 4,5 => UNS
* INC # G4: 4,5 => UNS
* INC # E9: 4,5 => UNS
* INC # E9: 3,8 => UNS
* INC # H3: 4,5 => UNS
* INC # H3: 3,8 => UNS
* INC # A8: 2,6 # C8: 2,6 => UNS
* INC # A8: 2,6 # C8: 5,8 => UNS
* INC # A8: 2,6 # G5: 1,9 => UNS
* INC # A8: 2,6 # G5: 3,5 => UNS
* INC # A8: 2,6 # G6: 1,9 => UNS
* INC # A8: 2,6 # G6: 3,5 => UNS
* INC # A8: 2,6 # B7: 3,5 => UNS
* INC # A8: 2,6 # C7: 3,5 => UNS
* INC # A8: 2,6 # A3: 3,5 => UNS
* INC # A8: 2,6 # A5: 3,5 => UNS
* INC # A8: 2,6 # C8: 2,6 => UNS
* INC # A8: 2,6 # C8: 5,8 => UNS
* PRF # A8: 2,6 # E7: 5,9 => SOL
* STA # A8: 2,6 + E7: 5,9
* CNT  33 HDP CHAINS /  34 HYP OPENED