Analysis of xx-mith-te3-00144541-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: .23..6...45.1.9...............74..987...681.48..9.167..8.6.49.1.6.....47......86. initial

Autosolve

position: .23..6...45.1.9...............74..987...681.48..9.167..8.6.49.1.6.8...47......86. 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: 0:00:09.249152

The following important HDP chains were detected:

* PRF # B3: 1,9 # G8: 2,3 => SOL
* STA # B3: 1,9 + G8: 2,3
* CNT   1 HDP CHAINS /  42 HYP OPENED

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

Details

Positions

.23..6...45.1.9...............74..987...681.48..9.167..8.6.49.1.6.....47......86. initial
.23..6...45.1.9...............74..987...681.48..9.167..8.6.49.1.6.8...47......86. autosolve
123456789457189236698237415216743598739568124845921673382674951561892347974315862 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
A1: 1,9
D1: 4,5
I1: 5,9
B4: 1,3
B5: 3,9
B6: 3,4
E8: 1,9
E9: 1,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H1,H3: 1.. / H1 = 1  => 11 pairs (_) / H3 = 1  =>  9 pairs (_)
E8,E9: 1.. / E8 = 1  =>  6 pairs (_) / E9 = 1  =>  6 pairs (_)
A1,H1: 1.. / A1 = 1  =>  9 pairs (_) / H1 = 1  => 11 pairs (_)
D1,D3: 4.. / D1 = 4  =>  8 pairs (_) / D3 = 4  => 11 pairs (_)
G1,G3: 4.. / G1 = 4  => 11 pairs (_) / G3 = 4  =>  8 pairs (_)
B6,C6: 4.. / B6 = 4  =>  8 pairs (_) / C6 = 4  =>  9 pairs (_)
B9,C9: 4.. / B9 = 4  =>  9 pairs (_) / C9 = 4  =>  8 pairs (_)
D1,G1: 4.. / D1 = 4  =>  8 pairs (_) / G1 = 4  => 11 pairs (_)
D3,G3: 4.. / D3 = 4  => 11 pairs (_) / G3 = 4  =>  8 pairs (_)
B6,B9: 4.. / B6 = 4  =>  8 pairs (_) / B9 = 4  =>  9 pairs (_)
C6,C9: 4.. / C6 = 4  =>  9 pairs (_) / C9 = 4  =>  8 pairs (_)
I2,I3: 6.. / I2 = 6  =>  9 pairs (_) / I3 = 6  => 12 pairs (_)
A4,C4: 6.. / A4 = 6  => 12 pairs (_) / C4 = 6  =>  9 pairs (_)
C2,I2: 6.. / C2 = 6  => 12 pairs (_) / I2 = 6  =>  9 pairs (_)
A3,A4: 6.. / A3 = 6  =>  9 pairs (_) / A4 = 6  => 12 pairs (_)
E7,F9: 7.. / E7 = 7  =>  8 pairs (_) / F9 = 7  =>  9 pairs (_)
E1,G1: 7.. / E1 = 7  => 10 pairs (_) / G1 = 7  =>  9 pairs (_)
C7,E7: 7.. / C7 = 7  =>  9 pairs (_) / E7 = 7  =>  8 pairs (_)
B3,B9: 7.. / B3 = 7  =>  9 pairs (_) / B9 = 7  =>  8 pairs (_)
F3,F9: 7.. / F3 = 7  =>  8 pairs (_) / F9 = 7  =>  9 pairs (_)
C2,C3: 8.. / C2 = 8  => 11 pairs (_) / C3 = 8  =>  9 pairs (_)
E1,H1: 8.. / E1 = 8  =>  9 pairs (_) / H1 = 8  => 10 pairs (_)
I1,I3: 9.. / I1 = 9  =>  9 pairs (_) / I3 = 9  => 11 pairs (_)
B5,C5: 9.. / B5 = 9  =>  9 pairs (_) / C5 = 9  => 10 pairs (_)
E8,E9: 9.. / E8 = 9  =>  6 pairs (_) / E9 = 9  =>  6 pairs (_)
A1,I1: 9.. / A1 = 9  => 11 pairs (_) / I1 = 9  =>  9 pairs (_)
* DURATION: 0:00:07.147036  START: 22:01:02.415754  END: 22:01:09.562790 2025-04-06
* CP COUNT: (26)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:09.086498  START: 22:01:17.229328  END: 22:01:26.315826 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00144541-base-pr-002.dot
* REASONING
* PRF # B3: 1,9 # G8: 2,3 => SOL
* STA # B3: 1,9 + G8: 2,3
* CNT   1 HDP CHAINS /  42 HYP OPENED

Header Info

rating: 38576; r2: 739884; index: 144541

Solution

position: 123456789457189236698237415216743598739568124845921673382674951561892347974315862 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 # A3: 1,9 => UNS
* INC # B3: 1,9 => UNS
* INC # C3: 1,9 => UNS
* INC # A8: 1,9 => UNS
* INC # A9: 1,9 => UNS
* INC # D3: 4,5 => UNS
* INC # D3: 2,3 => UNS
* INC # G1: 4,5 => UNS
* INC # G1: 7 => UNS
* INC # I3: 5,9 => UNS
* INC # I3: 2,3,6 => UNS
* INC # A4: 1,3 => UNS
* INC # A4: 2,5,6 => UNS
* INC # B9: 1,3 => UNS
* INC # B9: 4,7,9 => UNS
* INC # B9: 3,9 => UNS
* INC # B9: 1,4,7 => UNS
* INC # B9: 3,4 => UNS
* INC # B9: 1,7,9 => UNS
* INC # A8: 1,9 => UNS
* INC # C8: 1,9 => UNS
* INC # A9: 1,9 => UNS
* INC # B9: 1,9 => UNS
* INC # C9: 1,9 => UNS
* CNT  24 HDP CHAINS /  24 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A3: 1,9 => UNS
* INC # B3: 1,9 => UNS
* INC # C3: 1,9 => UNS
* INC # A8: 1,9 => UNS
* INC # A9: 1,9 => UNS
* INC # D3: 4,5 => UNS
* INC # D3: 2,3 => UNS
* INC # G1: 4,5 => UNS
* INC # G1: 7 => UNS
* INC # I3: 5,9 => UNS
* INC # I3: 2,3,6 => UNS
* INC # A4: 1,3 => UNS
* INC # A4: 2,5,6 => UNS
* INC # B9: 1,3 => UNS
* INC # B9: 4,7,9 => UNS
* INC # B9: 3,9 => UNS
* INC # B9: 1,4,7 => UNS
* INC # B9: 3,4 => UNS
* INC # B9: 1,7,9 => UNS
* INC # A8: 1,9 => UNS
* INC # C8: 1,9 => UNS
* INC # A9: 1,9 => UNS
* INC # B9: 1,9 => UNS
* INC # C9: 1,9 => UNS
* CNT  24 HDP CHAINS /  24 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A3: 1,9 => UNS
* INC # B3: 1,9 => UNS
* INC # C3: 1,9 => UNS
* INC # A8: 1,9 => UNS
* INC # A9: 1,9 => UNS
* INC # D3: 4,5 => UNS
* INC # D3: 2,3 => UNS
* INC # G1: 4,5 => UNS
* INC # G1: 7 => UNS
* INC # I3: 5,9 => UNS
* INC # I3: 2,3,6 => UNS
* INC # A4: 1,3 => UNS
* INC # A4: 2,5,6 => UNS
* INC # B9: 1,3 => UNS
* INC # B9: 4,7,9 => UNS
* INC # B9: 3,9 => UNS
* INC # B9: 1,4,7 => UNS
* INC # B9: 3,4 => UNS
* INC # B9: 1,7,9 => UNS
* INC # A8: 1,9 => UNS
* INC # C8: 1,9 => UNS
* INC # A9: 1,9 => UNS
* INC # B9: 1,9 => UNS
* INC # C9: 1,9 => UNS
* INC # A3: 1,9 # D3: 4,5 => UNS
* INC # A3: 1,9 # D3: 2,3 => UNS
* INC # A3: 1,9 # G1: 4,5 => UNS
* INC # A3: 1,9 # G1: 7 => UNS
* INC # A3: 1,9 # I3: 5,9 => UNS
* INC # A3: 1,9 # I3: 2,3,6 => UNS
* INC # A3: 1,9 # B9: 1,9 => UNS
* INC # A3: 1,9 # C9: 1,9 => UNS
* INC # A3: 1,9 # B9: 1,9 => UNS
* INC # A3: 1,9 # C9: 1,9 => UNS
* INC # A3: 1,9 => UNS
* INC # B3: 1,9 # H2: 2,3 => UNS
* INC # B3: 1,9 # I3: 2,3 => UNS
* INC # B3: 1,9 # E2: 2,3 => UNS
* INC # B3: 1,9 # E2: 8 => UNS
* INC # B3: 1,9 # G4: 2,3 => UNS
* PRF # B3: 1,9 # G8: 2,3 => SOL
* STA # B3: 1,9 + G8: 2,3
* CNT  41 HDP CHAINS /  42 HYP OPENED