Analysis of xx-mith-te3-00082881-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 1.3..67.9.57..9.3669....15..........5.9.3..71..6.....5.6...5.....584.........7513 initial

Autosolve

position: 1.3..67.9.57..9.3669....15..........5.9.3..71..6.....5.6...5.....584.........7513 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D7: 1,2 => CTR => D7: 3,9
* CNT   1 HDP CHAINS /   9 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 # D7: 1,2 => CTR => D7: 3,9
* STA D7: 3,9
* CNT   1 HDP CHAINS /  24 HYP OPENED

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

Pair Reduction Position

position: 1.3..67.9.57..9.3669....15..........5.9.3..71..6.....5.6...5.....584.........7513 pair_reduction
Pair Reduction

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

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:23.471747

The following important HDP chains were detected:

* DIS # C4: 1,2 # F3: 4,8 => CTR => F3: 2,3
* PRF # C4: 1,2 + F3: 2,3 # F8: 2,3 => SOL
* STA # C4: 1,2 + F3: 2,3 + F8: 2,3
* CNT   2 HDP CHAINS /  91 HYP OPENED

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

Details

Positions

1.3..67.9.57..9.3669....15..........5.9.3..71..6.....5.6...5.....584.........7513 initial
1.3..67.9.57..9.3669....15..........5.9.3..71..6.....5.6...5.....584.........7513 autosolve
1.3..67.9.57..9.3669....15..........5.9.3..71..6.....5.6...5.....584.........7513 pair_reduction
123456789457189236698372154271564398549238671836791425362915847715843962984627513 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (2)
C7: 1,2
I8: 2,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D2,E2: 1.. / D2 = 1  =>  3 pairs (_) / E2 = 1  =>  6 pairs (_)
C7,B8: 1.. / C7 = 1  =>  6 pairs (_) / B8 = 1  =>  0 pairs (*)
B8,F8: 1.. / B8 = 1  =>  0 pairs (*) / F8 = 1  =>  0 pairs (X)
C4,C7: 1.. / C4 = 1  =>  0 pairs (*) / C7 = 1  =>  0 pairs (X)
D3,F3: 3.. / D3 = 3  =>  0 pairs (*) / F3 = 3  =>  0 pairs (X)
G4,G6: 3.. / G4 = 3  =>  5 pairs (_) / G6 = 3  =>  3 pairs (_)
D7,F8: 3.. / D7 = 3  =>  4 pairs (_) / F8 = 3  =>  0 pairs (*)
A7,D7: 3.. / A7 = 3  =>  0 pairs (*) / D7 = 3  =>  0 pairs (X)
D3,D7: 3.. / D3 = 3  =>  0 pairs (*) / D7 = 3  =>  0 pairs (X)
F3,F8: 3.. / F3 = 3  =>  4 pairs (_) / F8 = 3  =>  0 pairs (*)
D1,E1: 5.. / D1 = 5  =>  4 pairs (_) / E1 = 5  =>  3 pairs (_)
D4,E4: 5.. / D4 = 5  =>  3 pairs (_) / E4 = 5  =>  4 pairs (_)
D1,D4: 5.. / D1 = 5  =>  4 pairs (_) / D4 = 5  =>  3 pairs (_)
E1,E4: 5.. / E1 = 5  =>  3 pairs (_) / E4 = 5  =>  4 pairs (_)
D9,E9: 6.. / D9 = 6  =>  0 pairs (*) / E9 = 6  =>  0 pairs (X)
G8,H8: 6.. / G8 = 6  =>  4 pairs (_) / H8 = 6  =>  3 pairs (_)
D5,G5: 6.. / D5 = 6  =>  3 pairs (_) / G5 = 6  =>  0 pairs (*)
E4,E9: 6.. / E4 = 6  =>  0 pairs (*) / E9 = 6  =>  0 pairs (X)
H4,H8: 6.. / H4 = 6  =>  4 pairs (_) / H8 = 6  =>  3 pairs (_)
D3,E3: 7.. / D3 = 7  =>  5 pairs (_) / E3 = 7  =>  2 pairs (_)
I7,I8: 7.. / I7 = 7  =>  9 pairs (_) / I8 = 7  =>  4 pairs (_)
A7,I7: 7.. / A7 = 7  =>  4 pairs (_) / I7 = 7  =>  9 pairs (_)
* DURATION: 0:00:06.589834  START: 12:22:27.918341  END: 12:22:34.508175 2025-04-06
* CP COUNT: (22)
* SOLUTION FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:23.219551  START: 12:22:40.002902  END: 12:23:03.222453 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00082881-base-pr-002.dot
* REASONING
* DIS # C4: 1,2 # F3: 4,8 => CTR => F3: 2,3
* PRF # C4: 1,2 + F3: 2,3 # F8: 2,3 => SOL
* STA # C4: 1,2 + F3: 2,3 + F8: 2,3
* CNT   2 HDP CHAINS /  91 HYP OPENED

Header Info

rating: 20343; r2: 428298; index: 82881

Solution

position: 123456789457189236698372154271564398549238671836791425362915847715843962984627513 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:

* DIS # D7: 1,2 => CTR => D7: 3,9
* INC # D7: 3,9 => UNS
* INC # E7: 1,2 => UNS
* INC # C4: 1,2 => UNS
* INC # C4: 4,8 => UNS
* INC # I7: 2,7 => UNS
* INC # I7: 4,8 => UNS
* INC # A8: 2,7 => UNS
* INC # A8: 3,9 => UNS
* CNT   9 HDP CHAINS /   9 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # D7: 1,2 => CTR => D7: 3,9
* INC D7: 3,9 # E7: 1,2 => UNS
* INC D7: 3,9 # E7: 1,2 => UNS
* INC D7: 3,9 # E7: 9 => UNS
* INC D7: 3,9 # C4: 1,2 => UNS
* INC D7: 3,9 # C4: 4,8 => UNS
* INC D7: 3,9 # E7: 1,2 => UNS
* INC D7: 3,9 # E7: 9 => UNS
* INC D7: 3,9 # C4: 1,2 => UNS
* INC D7: 3,9 # C4: 4,8 => UNS
* INC D7: 3,9 # I7: 2,7 => UNS
* INC D7: 3,9 # I7: 4,8 => UNS
* INC D7: 3,9 # A8: 2,7 => UNS
* INC D7: 3,9 # A8: 3,9 => UNS
* INC D7: 3,9 # E7: 1,2 => UNS
* INC D7: 3,9 # E7: 9 => UNS
* INC D7: 3,9 # C4: 1,2 => UNS
* INC D7: 3,9 # C4: 4,8 => UNS
* INC D7: 3,9 # A7: 3,9 => UNS
* INC D7: 3,9 # A7: 2,7 => UNS
* INC D7: 3,9 # I7: 2,7 => UNS
* INC D7: 3,9 # I7: 4,8 => UNS
* INC D7: 3,9 # A8: 2,7 => UNS
* INC D7: 3,9 # A8: 3,9 => UNS
* STA D7: 3,9
* CNT  24 HDP CHAINS /  24 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # E7: 1,2 => UNS
* INC # E7: 9 => UNS
* INC # C4: 1,2 => UNS
* INC # C4: 4,8 => UNS
* INC # A7: 3,9 => UNS
* INC # A7: 2,7 => UNS
* INC # I7: 2,7 => UNS
* INC # I7: 4,8 => UNS
* INC # A8: 2,7 => UNS
* INC # A8: 3,9 => UNS
* INC # E7: 1,2 # C4: 1,2 => UNS
* INC # E7: 1,2 # C4: 4,8 => UNS
* INC # E7: 1,2 # A7: 3,9 => UNS
* INC # E7: 1,2 # A7: 7 => UNS
* INC # E7: 1,2 # E2: 1,2 => UNS
* INC # E7: 1,2 # E4: 1,2 => UNS
* INC # E7: 1,2 # E6: 1,2 => UNS
* INC # E7: 1,2 # B8: 1,3 => UNS
* INC # E7: 1,2 # B8: 7 => UNS
* INC # E7: 1,2 => UNS
* INC # E7: 9 # B1: 4,8 => UNS
* INC # E7: 9 # C3: 4,8 => UNS
* INC # E7: 9 # G2: 4,8 => UNS
* INC # E7: 9 # G2: 2 => UNS
* INC # E7: 9 # B4: 3,7 => UNS
* INC # E7: 9 # B6: 3,7 => UNS
* INC # E7: 9 # A8: 3,7 => UNS
* INC # E7: 9 # A8: 2 => UNS
* INC # E7: 9 # C4: 4,8 => UNS
* INC # E7: 9 # B5: 4,8 => UNS
* INC # E7: 9 # F6: 4,8 => UNS
* INC # E7: 9 # H6: 4,8 => UNS
* INC # E7: 9 # D4: 1,7 => UNS
* INC # E7: 9 # E4: 1,7 => UNS
* INC # E7: 9 # D6: 1,7 => UNS
* INC # E7: 9 # B6: 1,7 => UNS
* INC # E7: 9 # B6: 3 => UNS
* INC # E7: 9 # G4: 6,9 => UNS
* INC # E7: 9 # G4: 3 => UNS
* INC # E7: 9 # G4: 3,9 => UNS
* INC # E7: 9 # G4: 6 => UNS
* INC # E7: 9 # A8: 2,7 => UNS
* INC # E7: 9 # A8: 3 => UNS
* INC # E7: 9 # I7: 2,7 => UNS
* INC # E7: 9 # I7: 4,8 => UNS
* INC # E7: 9 # A8: 3,7 => UNS
* INC # E7: 9 # A8: 2 => UNS
* INC # E7: 9 # B4: 3,7 => UNS
* INC # E7: 9 # B6: 3,7 => UNS
* INC # E7: 9 # B1: 4,8 => UNS
* INC # E7: 9 # B5: 4,8 => UNS
* INC # E7: 9 # C3: 4,8 => UNS
* INC # E7: 9 # C4: 4,8 => UNS
* INC # E7: 9 # G4: 6,9 => UNS
* INC # E7: 9 # G4: 3 => UNS
* INC # E7: 9 # I7: 2,7 => UNS
* INC # E7: 9 # I7: 4,8 => UNS
* INC # E7: 9 # A8: 2,7 => UNS
* INC # E7: 9 # A8: 3 => UNS
* INC # E7: 9 => UNS
* INC # C4: 1,2 # B1: 4,8 => UNS
* INC # C4: 1,2 # A2: 4,8 => UNS
* DIS # C4: 1,2 # F3: 4,8 => CTR => F3: 2,3
* INC # C4: 1,2 + F3: 2,3 # I3: 4,8 => UNS
* INC # C4: 1,2 + F3: 2,3 # I3: 4,8 => UNS
* INC # C4: 1,2 + F3: 2,3 # I3: 2 => UNS
* INC # C4: 1,2 + F3: 2,3 # B1: 4,8 => UNS
* INC # C4: 1,2 + F3: 2,3 # A2: 4,8 => UNS
* INC # C4: 1,2 + F3: 2,3 # I3: 4,8 => UNS
* INC # C4: 1,2 + F3: 2,3 # I3: 2 => UNS
* INC # C4: 1,2 + F3: 2,3 # D4: 1,2 => UNS
* INC # C4: 1,2 + F3: 2,3 # E4: 1,2 => UNS
* INC # C4: 1,2 + F3: 2,3 # F4: 1,2 => UNS
* INC # C4: 1,2 + F3: 2,3 # E7: 1,2 => UNS
* INC # C4: 1,2 + F3: 2,3 # E7: 9 => UNS
* INC # C4: 1,2 + F3: 2,3 # A9: 4,8 => UNS
* INC # C4: 1,2 + F3: 2,3 # B9: 4,8 => UNS
* INC # C4: 1,2 + F3: 2,3 # A7: 3,9 => UNS
* INC # C4: 1,2 + F3: 2,3 # A7: 2,7 => UNS
* INC # C4: 1,2 + F3: 2,3 # I7: 2,7 => UNS
* INC # C4: 1,2 + F3: 2,3 # I7: 4,8 => UNS
* INC # C4: 1,2 + F3: 2,3 # A8: 2,7 => UNS
* INC # C4: 1,2 + F3: 2,3 # A8: 3,9 => UNS
* INC # C4: 1,2 + F3: 2,3 # B1: 4,8 => UNS
* INC # C4: 1,2 + F3: 2,3 # A2: 4,8 => UNS
* INC # C4: 1,2 + F3: 2,3 # I3: 4,8 => UNS
* INC # C4: 1,2 + F3: 2,3 # I3: 2 => UNS
* INC # C4: 1,2 + F3: 2,3 # D3: 2,3 => UNS
* INC # C4: 1,2 + F3: 2,3 # D3: 4,7 => UNS
* PRF # C4: 1,2 + F3: 2,3 # F8: 2,3 => SOL
* STA # C4: 1,2 + F3: 2,3 + F8: 2,3
* CNT  90 HDP CHAINS /  91 HYP OPENED