Analysis of xx-mith-te3-00115227-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: ..34.67..4.718....6...37......6.1...7.6....92..8...65.3.1.64..8.........86.71..43 initial

Autosolve

position: ..34.67..4.718....6...37......6.1...7.6....92..8...65.3.1.64..8.........86.71..43 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # H8: 2,7 => CTR => H8: 1,6
* CNT   1 HDP CHAINS /  16 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 # H8: 2,7 => CTR => H8: 1,6
* STA H8: 1,6
* CNT   1 HDP CHAINS /  31 HYP OPENED

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

Pair Reduction Position

position: ..34.67..4.718....6...37......6.1...7.6....92..8...65.3.1.64..8.........86.71..43 pair_reduction
Pair Reduction

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

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:23.364775

The following important HDP chains were detected:

* DIS # B5: 1,3 # G5: 4 => CTR => G5: 1,3
* DIS # I6: 1 # B1: 5,9 => CTR => B1: 2,8
* PRF # I6: 1 + B1: 2,8 # A4: 2,9 => SOL
* STA # I6: 1 + B1: 2,8 + A4: 2,9
* CNT   3 HDP CHAINS / 111 HYP OPENED

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

Details

Positions

..34.67..4.718....6...37......6.1...7.6....92..8...65.3.1.64..8.........86.71..43 initial
..34.67..4.718....6...37......6.1...7.6....92..8...65.3.1.64..8.........86.71..43 autosolve
..34.67..4.718....6...37......6.1...7.6....92..8...65.3.1.64..8.........86.71..43 pair_reduction
123456789457189236689237415235691874716548392948372651371964528594823167862715943 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
E5: 4,5
I4: 4,7
D8: 3,8
F8: 3,8
H7: 2,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G5,I6: 1.. / G5 = 1  =>  8 pairs (_) / I6 = 1  => 13 pairs (_)
B5,G5: 1.. / B5 = 1  => 13 pairs (_) / G5 = 1  =>  8 pairs (_)
A1,A6: 1.. / A1 = 1  => 16 pairs (_) / A6 = 1  => 10 pairs (_)
G2,H2: 3.. / G2 = 3  =>  7 pairs (_) / H2 = 3  => 13 pairs (_)
D8,F8: 3.. / D8 = 3  =>  5 pairs (_) / F8 = 3  =>  5 pairs (_)
H2,H4: 3.. / H2 = 3  => 13 pairs (_) / H4 = 3  =>  7 pairs (_)
G3,I3: 4.. / G3 = 4  =>  7 pairs (_) / I3 = 4  => 10 pairs (_)
B8,C8: 4.. / B8 = 4  =>  0 pairs (X) / C8 = 4  =>  5 pairs (_)
C4,C8: 4.. / C4 = 4  =>  0 pairs (X) / C8 = 4  =>  5 pairs (_)
H2,I2: 6.. / H2 = 6  =>  7 pairs (_) / I2 = 6  =>  7 pairs (_)
H8,I8: 6.. / H8 = 6  =>  7 pairs (_) / I8 = 6  =>  7 pairs (_)
H2,H8: 6.. / H2 = 6  =>  7 pairs (_) / H8 = 6  =>  7 pairs (_)
I2,I8: 6.. / I2 = 6  =>  7 pairs (_) / I8 = 6  =>  7 pairs (_)
E4,E6: 7.. / E4 = 7  => 10 pairs (_) / E6 = 7  =>  6 pairs (_)
B7,B8: 7.. / B7 = 7  => 13 pairs (_) / B8 = 7  =>  5 pairs (_)
E6,I6: 7.. / E6 = 7  =>  6 pairs (_) / I6 = 7  => 10 pairs (_)
B7,H7: 7.. / B7 = 7  => 13 pairs (_) / H7 = 7  =>  5 pairs (_)
B1,B3: 8.. / B1 = 8  =>  6 pairs (_) / B3 = 8  =>  8 pairs (_)
D5,F5: 8.. / D5 = 8  =>  5 pairs (_) / F5 = 8  =>  5 pairs (_)
G4,H4: 8.. / G4 = 8  =>  6 pairs (_) / H4 = 8  => 10 pairs (_)
D8,F8: 8.. / D8 = 8  =>  5 pairs (_) / F8 = 8  =>  5 pairs (_)
B1,H1: 8.. / B1 = 8  =>  6 pairs (_) / H1 = 8  =>  8 pairs (_)
D5,D8: 8.. / D5 = 8  =>  5 pairs (_) / D8 = 8  =>  5 pairs (_)
F5,F8: 8.. / F5 = 8  =>  5 pairs (_) / F8 = 8  =>  5 pairs (_)
G3,G4: 8.. / G3 = 8  => 10 pairs (_) / G4 = 8  =>  6 pairs (_)
* DURATION: 0:00:06.336671  START: 05:42:28.018354  END: 05:42:34.355025 2025-04-05
* CP COUNT: (25)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:22.972384  START: 05:42:41.720770  END: 05:43:04.693154 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00115227-base-pr-002.dot
* REASONING
* DIS # B5: 1,3 # G5: 4 => CTR => G5: 1,3
* DIS # I6: 1 # B1: 5,9 => CTR => B1: 2,8
* PRF # I6: 1 + B1: 2,8 # A4: 2,9 => SOL
* STA # I6: 1 + B1: 2,8 + A4: 2,9
* CNT   3 HDP CHAINS / 111 HYP OPENED

Header Info

rating: 29351; r2: 573318; index: 115227

Solution

position: 123456789457189236689237415235691874716548392948372651371964528594823167862715943 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 # E4: 4,5 => UNS
* INC # E4: 2,7,9 => UNS
* INC # B5: 4,5 => UNS
* INC # B5: 1,3 => UNS
* INC # I6: 4,7 => UNS
* INC # I6: 1 => UNS
* INC # E4: 4,7 => UNS
* INC # E4: 2,5,9 => UNS
* INC # D5: 3,8 => UNS
* INC # D5: 5 => UNS
* INC # F5: 3,8 => UNS
* INC # F5: 5 => UNS
* DIS # H8: 2,7 => CTR => H8: 1,6
* INC # H8: 1,6 => UNS
* INC # B7: 2,7 => UNS
* INC # B7: 5,9 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E4: 4,5 => UNS
* INC # E4: 2,7,9 => UNS
* INC # B5: 4,5 => UNS
* INC # B5: 1,3 => UNS
* INC # I6: 4,7 => UNS
* INC # I6: 1 => UNS
* INC # E4: 4,7 => UNS
* INC # E4: 2,5,9 => UNS
* INC # D5: 3,8 => UNS
* INC # D5: 5 => UNS
* INC # F5: 3,8 => UNS
* INC # F5: 5 => UNS
* DIS # H8: 2,7 => CTR => H8: 1,6
* INC H8: 1,6 # B7: 2,7 => UNS
* INC H8: 1,6 # B7: 5,9 => UNS
* INC H8: 1,6 # E4: 4,5 => UNS
* INC H8: 1,6 # E4: 2,7,9 => UNS
* INC H8: 1,6 # B5: 4,5 => UNS
* INC H8: 1,6 # B5: 1,3 => UNS
* INC H8: 1,6 # I6: 4,7 => UNS
* INC H8: 1,6 # I6: 1 => UNS
* INC H8: 1,6 # E4: 4,7 => UNS
* INC H8: 1,6 # E4: 2,5,9 => UNS
* INC H8: 1,6 # D5: 3,8 => UNS
* INC H8: 1,6 # D5: 5 => UNS
* INC H8: 1,6 # F5: 3,8 => UNS
* INC H8: 1,6 # F5: 5 => UNS
* INC H8: 1,6 # B7: 2,7 => UNS
* INC H8: 1,6 # B7: 5,9 => UNS
* INC H8: 1,6 # I8: 1,6 => UNS
* INC H8: 1,6 # I8: 5,7,9 => UNS
* STA H8: 1,6
* CNT  31 HDP CHAINS /  31 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # E4: 4,5 => UNS
* INC # E4: 2,7,9 => UNS
* INC # B5: 4,5 => UNS
* INC # B5: 1,3 => UNS
* INC # I6: 4,7 => UNS
* INC # I6: 1 => UNS
* INC # E4: 4,7 => UNS
* INC # E4: 2,5,9 => UNS
* INC # D5: 3,8 => UNS
* INC # D5: 5 => UNS
* INC # F5: 3,8 => UNS
* INC # F5: 5 => UNS
* INC # B7: 2,7 => UNS
* INC # B7: 5,9 => UNS
* INC # I8: 1,6 => UNS
* INC # I8: 5,7,9 => UNS
* INC # E4: 4,5 # H1: 1,8 => UNS
* INC # E4: 4,5 # H1: 2 => UNS
* INC # E4: 4,5 # H3: 1,8 => UNS
* INC # E4: 4,5 # H3: 2 => UNS
* INC # E4: 4,5 # F2: 2,9 => UNS
* INC # E4: 4,5 # D3: 2,9 => UNS
* INC # E4: 4,5 # A1: 2,9 => UNS
* INC # E4: 4,5 # A1: 5 => UNS
* INC # E4: 4,5 # B4: 4,5 => UNS
* INC # E4: 4,5 # B4: 2,9 => UNS
* INC # E4: 4,5 # B4: 4,5 => UNS
* INC # E4: 4,5 # B4: 2,9 => UNS
* INC # E4: 4,5 # D3: 2,9 => UNS
* INC # E4: 4,5 # D7: 2,9 => UNS
* INC # E4: 4,5 # F2: 2,9 => UNS
* INC # E4: 4,5 # F9: 2,9 => UNS
* INC # E4: 4,5 # D7: 2,9 => UNS
* INC # E4: 4,5 # F9: 2,9 => UNS
* INC # E4: 4,5 # A8: 2,9 => UNS
* INC # E4: 4,5 # G8: 2,9 => UNS
* INC # E4: 4,5 => UNS
* INC # E4: 2,7,9 # I6: 4,7 => UNS
* INC # E4: 2,7,9 # I6: 1 => UNS
* INC # E4: 2,7,9 # D5: 3,8 => UNS
* INC # E4: 2,7,9 # D5: 5 => UNS
* INC # E4: 2,7,9 # F5: 3,8 => UNS
* INC # E4: 2,7,9 # F5: 5 => UNS
* INC # E4: 2,7,9 # B7: 2,7 => UNS
* INC # E4: 2,7,9 # B7: 5,9 => UNS
* INC # E4: 2,7,9 # I8: 1,6 => UNS
* INC # E4: 2,7,9 # I8: 5,7,9 => UNS
* INC # E4: 2,7,9 => UNS
* INC # B5: 4,5 # H1: 1,8 => UNS
* INC # B5: 4,5 # H1: 2 => UNS
* INC # B5: 4,5 # H3: 1,8 => UNS
* INC # B5: 4,5 # H3: 2 => UNS
* INC # B5: 4,5 # F2: 2,9 => UNS
* INC # B5: 4,5 # D3: 2,9 => UNS
* INC # B5: 4,5 # A1: 2,9 => UNS
* INC # B5: 4,5 # A1: 5 => UNS
* INC # B5: 4,5 # B4: 4,5 => UNS
* INC # B5: 4,5 # B4: 2,9 => UNS
* INC # B5: 4,5 # E4: 4,5 => UNS
* INC # B5: 4,5 # E4: 7 => UNS
* INC # B5: 4,5 # D3: 2,9 => UNS
* INC # B5: 4,5 # D7: 2,9 => UNS
* INC # B5: 4,5 # E4: 4,7 => UNS
* INC # B5: 4,5 # E4: 5 => UNS
* INC # B5: 4,5 # F2: 2,9 => UNS
* INC # B5: 4,5 # F9: 2,9 => UNS
* INC # B5: 4,5 # E4: 4,7 => UNS
* INC # B5: 4,5 # E4: 5 => UNS
* INC # B5: 4,5 # D7: 2,9 => UNS
* INC # B5: 4,5 # F9: 2,9 => UNS
* INC # B5: 4,5 # A8: 2,9 => UNS
* INC # B5: 4,5 # G8: 2,9 => UNS
* INC # B5: 4,5 => UNS
* INC # B5: 1,3 # B6: 1,3 => UNS
* INC # B5: 1,3 # B6: 2,4,9 => UNS
* INC # B5: 1,3 # G5: 1,3 => UNS
* DIS # B5: 1,3 # G5: 4 => CTR => G5: 1,3
* INC # B5: 1,3 + G5: 1,3 # I6: 4,7 => UNS
* INC # B5: 1,3 + G5: 1,3 # I6: 1 => UNS
* INC # B5: 1,3 + G5: 1,3 # B7: 2,7 => UNS
* INC # B5: 1,3 + G5: 1,3 # B7: 5,9 => UNS
* INC # B5: 1,3 + G5: 1,3 # I8: 1,6 => UNS
* INC # B5: 1,3 + G5: 1,3 # I8: 5,7,9 => UNS
* INC # B5: 1,3 + G5: 1,3 # I6: 4,7 => UNS
* INC # B5: 1,3 + G5: 1,3 # I6: 1 => UNS
* INC # B5: 1,3 + G5: 1,3 # B7: 2,7 => UNS
* INC # B5: 1,3 + G5: 1,3 # B7: 5,9 => UNS
* INC # B5: 1,3 + G5: 1,3 # I8: 1,6 => UNS
* INC # B5: 1,3 + G5: 1,3 # I8: 5,7,9 => UNS
* INC # B5: 1,3 + G5: 1,3 => UNS
* INC # I6: 4,7 # E4: 4,5 => UNS
* INC # I6: 4,7 # E4: 2,7,9 => UNS
* INC # I6: 4,7 # B5: 4,5 => UNS
* INC # I6: 4,7 # B5: 3 => UNS
* INC # I6: 4,7 # E4: 4,7 => UNS
* INC # I6: 4,7 # E4: 2,5,9 => UNS
* INC # I6: 4,7 # E6: 4,7 => UNS
* INC # I6: 4,7 # E6: 2,9 => UNS
* INC # I6: 4,7 # D5: 3,8 => UNS
* INC # I6: 4,7 # D5: 5 => UNS
* INC # I6: 4,7 # F5: 3,8 => UNS
* INC # I6: 4,7 # F5: 5 => UNS
* INC # I6: 4,7 => UNS
* INC # I6: 1 # B1: 2,8 => UNS
* DIS # I6: 1 # B1: 5,9 => CTR => B1: 2,8
* INC # I6: 1 + B1: 2,8 # G2: 5,9 => UNS
* INC # I6: 1 + B1: 2,8 # I3: 5,9 => UNS
* INC # I6: 1 + B1: 2,8 # I8: 5,9 => UNS
* INC # I6: 1 + B1: 2,8 # I8: 7 => UNS
* PRF # I6: 1 + B1: 2,8 # A4: 2,9 => SOL
* STA # I6: 1 + B1: 2,8 + A4: 2,9
* CNT 110 HDP CHAINS / 111 HYP OPENED