Analysis of xx-mith-te3-00005869-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 1.3.....9.571...366..7..15.....48......32796.73.6.1...37...5.9..........9.5....1. initial

Autosolve

position: 1.3.....9.571...366..7..15.....48......32796.73.6.1...37...5.9..........9.5....1. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # G4: 2,7 => CTR => G4: 3,5
* DIS # I4: 2,7 => CTR => I4: 1,3,5
* CNT   2 HDP CHAINS /  12 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # G4: 2,7 => CTR => G4: 3,5
* DIS G4: 3,5 # I4: 2,7 => CTR => I4: 1,3,5
* DIS G4: 3,5 + I4: 1,3,5 # G8: 2,4,6,8 => CTR => G8: 3,5
* STA G4: 3,5 + I4: 1,3,5 + G8: 3,5
* CNT   3 HDP CHAINS /  30 HYP OPENED

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

Pair Reduction Position

position: 1.3...7.9.571...366..7..15.....48.7....32796.73.6.1...37...5.9..........9.5....1. pair_reduction
Pair Reduction

See section Pair Reduction for the HDP chains leading to this result.

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:29.217985

The following important HDP chains were detected:

* PRF # I8: 7 # I5: 4,8 => SOL
* STA # I8: 7 + I5: 4,8
* CNT   1 HDP CHAINS / 128 HYP OPENED

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

Details

Positions

1.3.....9.571...366..7..15.....48......32796.73.6.1...37...5.9..........9.5....1. initial
1.3.....9.571...366..7..15.....48......32796.73.6.1...37...5.9..........9.5....1. autosolve
1.3...7.9.571...366..7..15.....48.7....32796.73.6.1...37...5.9..........9.5....1. pair_reduction
123456789457189236689732154296548371541327968738691425374815692812963547965274813 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (6)
E2: 8,9
E3: 3,8
A4: 2,5
D4: 5,9
E6: 5,9
H4: 2,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
I4,I5: 1.. / I4 = 1  =>  7 pairs (_) / I5 = 1  => 17 pairs (_)
E7,E8: 1.. / E7 = 1  =>  6 pairs (_) / E8 = 1  =>  8 pairs (_)
C7,E7: 1.. / C7 = 1  =>  8 pairs (_) / E7 = 1  =>  6 pairs (_)
E3,F3: 3.. / E3 = 3  =>  6 pairs (_) / F3 = 3  => 13 pairs (_)
G4,I4: 3.. / G4 = 3  =>  6 pairs (_) / I4 = 3  => 13 pairs (_)
D1,E1: 5.. / D1 = 5  => 12 pairs (_) / E1 = 5  =>  0 pairs (*)
A4,A5: 5.. / A4 = 5  => 12 pairs (_) / A5 = 5  =>  7 pairs (_)
D4,E6: 5.. / D4 = 5  =>  0 pairs (*) / E6 = 5  =>  0 pairs (X)
G8,I8: 5.. / G8 = 5  =>  6 pairs (_) / I8 = 5  => 13 pairs (_)
A5,I5: 5.. / A5 = 5  =>  7 pairs (_) / I5 = 5  => 12 pairs (_)
D1,D4: 5.. / D1 = 5  => 12 pairs (_) / D4 = 5  =>  0 pairs (*)
E1,E6: 5.. / E1 = 5  =>  0 pairs (*) / E6 = 5  =>  0 pairs (X)
E1,F1: 6.. / E1 = 6  => 12 pairs (_) / F1 = 6  =>  9 pairs (_)
B4,C4: 6.. / B4 = 6  =>  6 pairs (_) / C4 = 6  =>  6 pairs (_)
G1,H1: 7.. / G1 = 7  =>  6 pairs (_) / H1 = 7  =>  0 pairs (X)
E8,E9: 7.. / E8 = 7  =>  6 pairs (_) / E9 = 7  =>  6 pairs (_)
B3,C3: 9.. / B3 = 9  =>  6 pairs (_) / C3 = 9  =>  0 pairs (*)
E2,F2: 9.. / E2 = 9  => 12 pairs (_) / F2 = 9  => 10 pairs (_)
D4,E6: 9.. / D4 = 9  => 12 pairs (_) / E6 = 9  =>  0 pairs (*)
C6,E6: 9.. / C6 = 9  => 12 pairs (_) / E6 = 9  =>  0 pairs (*)
B3,B4: 9.. / B3 = 9  =>  6 pairs (_) / B4 = 9  =>  0 pairs (*)
D4,D8: 9.. / D4 = 9  => 12 pairs (_) / D8 = 9  =>  0 pairs (*)
F2,F8: 9.. / F2 = 9  => 10 pairs (_) / F8 = 9  => 12 pairs (_)
* DURATION: 0:00:06.642724  START: 05:50:29.528287  END: 05:50:36.171011 2025-04-04
* CP COUNT: (23)
* SOLUTION FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:28.939139  START: 05:50:43.626132  END: 05:51:12.565271 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00005869-base-pr-002.dot
* REASONING
* PRF # I8: 7 # I5: 4,8 => SOL
* STA # I8: 7 + I5: 4,8
* CNT   1 HDP CHAINS / 128 HYP OPENED

Header Info

rating: 1168; r2: 23826; index: 5869

Solution

position: 123456789457189236689732154296548371541327968738691425374815692812963547965274813 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 # E8: 8,9 => UNS
* INC # E8: 1,3,6,7 => UNS
* INC # E8: 3,8 => UNS
* INC # E9: 3,8 => UNS
* INC # G4: 2,5 => UNS
* INC # I4: 2,5 => UNS
* DIS # G4: 2,7 => CTR => G4: 3,5
* INC # G4: 3,5 => UNS
* DIS # I4: 2,7 => CTR => I4: 1,3,5
* INC # I4: 1,3,5 => UNS
* INC # H1: 2,7 => UNS
* INC # H8: 2,7 => UNS
* CNT  12 HDP CHAINS /  12 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E8: 8,9 => UNS
* INC # E8: 1,3,6,7 => UNS
* INC # E8: 3,8 => UNS
* INC # E9: 3,8 => UNS
* INC # G4: 2,5 => UNS
* INC # I4: 2,5 => UNS
* DIS # G4: 2,7 => CTR => G4: 3,5
* DIS G4: 3,5 # I4: 2,7 => CTR => I4: 1,3,5
* INC G4: 3,5 + I4: 1,3,5 # E8: 8,9 => UNS
* INC G4: 3,5 + I4: 1,3,5 # E8: 1,3,6,7 => UNS
* INC G4: 3,5 + I4: 1,3,5 # E8: 3,8 => UNS
* INC G4: 3,5 + I4: 1,3,5 # E9: 3,8 => UNS
* INC G4: 3,5 + I4: 1,3,5 # I4: 3,5 => UNS
* INC G4: 3,5 + I4: 1,3,5 # I4: 1 => UNS
* INC G4: 3,5 + I4: 1,3,5 # G8: 3,5 => UNS
* DIS G4: 3,5 + I4: 1,3,5 # G8: 2,4,6,8 => CTR => G8: 3,5
* INC G4: 3,5 + I4: 1,3,5 + G8: 3,5 # I4: 3,5 => UNS
* INC G4: 3,5 + I4: 1,3,5 + G8: 3,5 # I4: 1 => UNS
* INC G4: 3,5 + I4: 1,3,5 + G8: 3,5 # E8: 8,9 => UNS
* INC G4: 3,5 + I4: 1,3,5 + G8: 3,5 # E8: 1,3,6,7 => UNS
* INC G4: 3,5 + I4: 1,3,5 + G8: 3,5 # E8: 3,8 => UNS
* INC G4: 3,5 + I4: 1,3,5 + G8: 3,5 # E9: 3,8 => UNS
* INC G4: 3,5 + I4: 1,3,5 + G8: 3,5 # I4: 3,5 => UNS
* INC G4: 3,5 + I4: 1,3,5 + G8: 3,5 # I4: 1 => UNS
* INC G4: 3,5 + I4: 1,3,5 + G8: 3,5 # I8: 3,5 => UNS
* INC G4: 3,5 + I4: 1,3,5 + G8: 3,5 # I8: 7 => UNS
* INC G4: 3,5 + I4: 1,3,5 + G8: 3,5 # I8: 3,7 => UNS
* INC G4: 3,5 + I4: 1,3,5 + G8: 3,5 # I8: 5 => UNS
* INC G4: 3,5 + I4: 1,3,5 + G8: 3,5 # E9: 3,7 => UNS
* INC G4: 3,5 + I4: 1,3,5 + G8: 3,5 # E9: 6,8 => UNS
* STA G4: 3,5 + I4: 1,3,5 + G8: 3,5
* CNT  30 HDP CHAINS /  30 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # E8: 8,9 => UNS
* INC # E8: 1,3,6,7 => UNS
* INC # E8: 3,8 => UNS
* INC # E9: 3,8 => UNS
* INC # I4: 3,5 => UNS
* INC # I4: 1 => UNS
* INC # I8: 3,5 => UNS
* INC # I8: 7 => UNS
* INC # I8: 3,7 => UNS
* INC # I8: 5 => UNS
* INC # E9: 3,7 => UNS
* INC # E9: 6,8 => UNS
* INC # E8: 8,9 # B1: 2,4 => UNS
* INC # E8: 8,9 # C3: 2,4 => UNS
* INC # E8: 8,9 # A8: 2,4 => UNS
* INC # E8: 8,9 # A8: 8 => UNS
* INC # E8: 8,9 # B1: 2,4 => UNS
* INC # E8: 8,9 # H1: 2,4 => UNS
* INC # E8: 8,9 # C3: 2,4 => UNS
* INC # E8: 8,9 # I3: 2,4 => UNS
* INC # E8: 8,9 # H1: 2,4 => UNS
* INC # E8: 8,9 # I3: 2,4 => UNS
* INC # E8: 8,9 # G6: 2,4 => UNS
* INC # E8: 8,9 # G9: 2,4 => UNS
* INC # E8: 8,9 # B4: 1,6 => UNS
* INC # E8: 8,9 # B4: 2 => UNS
* INC # E8: 8,9 # C4: 1,6 => UNS
* INC # E8: 8,9 # C4: 2 => UNS
* INC # E8: 8,9 => UNS
* INC # E8: 1,3,6,7 # E9: 3,8 => UNS
* INC # E8: 1,3,6,7 # E9: 6,7 => UNS
* INC # E8: 1,3,6,7 # I4: 3,5 => UNS
* INC # E8: 1,3,6,7 # I4: 1 => UNS
* INC # E8: 1,3,6,7 # I8: 3,5 => UNS
* INC # E8: 1,3,6,7 # I8: 7 => UNS
* INC # E8: 1,3,6,7 # I8: 3,7 => UNS
* INC # E8: 1,3,6,7 # I8: 5 => UNS
* INC # E8: 1,3,6,7 # E9: 3,7 => UNS
* INC # E8: 1,3,6,7 # E9: 6,8 => UNS
* INC # E8: 1,3,6,7 => UNS
* INC # E8: 3,8 # B1: 2,4 => UNS
* INC # E8: 3,8 # A2: 2,4 => UNS
* INC # E8: 3,8 # C7: 2,4 => UNS
* INC # E8: 3,8 # C7: 8 => UNS
* INC # E8: 3,8 # B1: 2,4 => UNS
* INC # E8: 3,8 # H1: 2,4 => UNS
* INC # E8: 3,8 # A2: 2,4 => UNS
* INC # E8: 3,8 # G2: 2,4 => UNS
* INC # E8: 3,8 # H1: 2,4 => UNS
* INC # E8: 3,8 # G2: 2,4 => UNS
* INC # E8: 3,8 # I6: 2,4 => UNS
* INC # E8: 3,8 # I7: 2,4 => UNS
* INC # E8: 3,8 # B4: 1,6 => UNS
* INC # E8: 3,8 # B4: 2 => UNS
* INC # E8: 3,8 # C4: 1,6 => UNS
* INC # E8: 3,8 # C4: 2 => UNS
* INC # E8: 3,8 => UNS
* INC # E9: 3,8 # B1: 2,4 => UNS
* INC # E9: 3,8 # A2: 2,4 => UNS
* INC # E9: 3,8 # C7: 2,4 => UNS
* INC # E9: 3,8 # C7: 8 => UNS
* INC # E9: 3,8 # B1: 2,4 => UNS
* INC # E9: 3,8 # H1: 2,4 => UNS
* INC # E9: 3,8 # A2: 2,4 => UNS
* INC # E9: 3,8 # G2: 2,4 => UNS
* INC # E9: 3,8 # H1: 2,4 => UNS
* INC # E9: 3,8 # G2: 2,4 => UNS
* INC # E9: 3,8 # I6: 2,4 => UNS
* INC # E9: 3,8 # I7: 2,4 => UNS
* INC # E9: 3,8 # I4: 3,5 => UNS
* INC # E9: 3,8 # I4: 1 => UNS
* INC # E9: 3,8 # I4: 1,5 => UNS
* INC # E9: 3,8 # I4: 3 => UNS
* INC # E9: 3,8 # B4: 1,6 => UNS
* INC # E9: 3,8 # B4: 2 => UNS
* INC # E9: 3,8 # C4: 1,6 => UNS
* INC # E9: 3,8 # C4: 2 => UNS
* INC # E9: 3,8 # I4: 3,5 => UNS
* INC # E9: 3,8 # I4: 1 => UNS
* INC # E9: 3,8 => UNS
* INC # I4: 3,5 # B1: 4,8 => UNS
* INC # I4: 3,5 # C3: 4,8 => UNS
* INC # I4: 3,5 # G2: 4,8 => UNS
* INC # I4: 3,5 # G2: 2 => UNS
* INC # I4: 3,5 # B1: 4,8 => UNS
* INC # I4: 3,5 # B9: 4,8 => UNS
* INC # I4: 3,5 # C3: 4,8 => UNS
* INC # I4: 3,5 # C7: 4,8 => UNS
* INC # I4: 3,5 # I8: 3,5 => UNS
* INC # I4: 3,5 # I8: 7 => UNS
* INC # I4: 3,5 # C7: 4,8 => UNS
* INC # I4: 3,5 # B9: 4,8 => UNS
* INC # I4: 3,5 # D8: 4,8 => UNS
* INC # I4: 3,5 # H8: 4,8 => UNS
* INC # I4: 3,5 # E8: 3,9 => UNS
* INC # I4: 3,5 # E8: 7 => UNS
* INC # I4: 3,5 # E9: 3,6 => UNS
* INC # I4: 3,5 # E9: 7 => UNS
* INC # I4: 3,5 # I8: 3,5 => UNS
* INC # I4: 3,5 # I8: 7 => UNS
* INC # I4: 3,5 # I8: 3,7 => UNS
* INC # I4: 3,5 # I8: 5 => UNS
* INC # I4: 3,5 # E9: 3,7 => UNS
* INC # I4: 3,5 # E9: 6 => UNS
* INC # I4: 3,5 => UNS
* INC # I4: 1 # E8: 8,9 => UNS
* INC # I4: 1 # E8: 1,3,6,7 => UNS
* INC # I4: 1 # E8: 3,8 => UNS
* INC # I4: 1 # E9: 3,8 => UNS
* INC # I4: 1 # E8: 3,7 => UNS
* INC # I4: 1 # E8: 1,6,8,9 => UNS
* INC # I4: 1 # E9: 3,7 => UNS
* INC # I4: 1 # E9: 6,8 => UNS
* INC # I4: 1 => UNS
* INC # I8: 3,5 # E9: 3,8 => UNS
* INC # I8: 3,5 # E9: 6 => UNS
* INC # I8: 3,5 # I4: 3,5 => UNS
* INC # I8: 3,5 # I4: 1 => UNS
* INC # I8: 3,5 # I4: 3,5 => UNS
* INC # I8: 3,5 # I4: 1 => UNS
* INC # I8: 3,5 => UNS
* INC # I8: 7 # E8: 8,9 => UNS
* INC # I8: 7 # E8: 1,3,6 => UNS
* INC # I8: 7 # E8: 3,8 => UNS
* INC # I8: 7 # E8: 1,6,9 => UNS
* INC # I8: 7 # I5: 1,5 => UNS
* PRF # I8: 7 # I5: 4,8 => SOL
* STA # I8: 7 + I5: 4,8
* CNT 127 HDP CHAINS / 128 HYP OPENED