Analysis of xx-mith-te3-00058988-base.sdk

Contents

Original Sudoku
Autosolve
Pair Reduction Variants
Details
Solution
Appendix: Full HDP Chains

Original Sudoku

level: hard

position: .....6......789.237..1.2...2..9......74....929.82.73.434..9.2.7....7...88.7.2.9.. initial

Autosolve

position: .....6......789.237..1.2...23.9......74....929.82.73.434..9.2.7....7...88.7.2.9.. autosolve

Pair Reduction Variants

Pair Reduction Analysis

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

Pair Reduction

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

Deep Pair Reduction

Time used: 0:00:14.323171

The following important HDP chains were detected:

* DIS # C1: 3 # B6: 5,6 => CTR => B6: 1
* PRF # C1: 3 + B6: 1 # E4: 4,5 => SOL
* STA # C1: 3 + B6: 1 + E4: 4,5
* CNT   2 HDP CHAINS /  70 HYP OPENED

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

Details

Positions

`.....6......789.237..1.2...2..9......74....929.82.73.434..9.2.7....7...88.7.2.9..`	initial
`.....6......789.237..1.2...23.9......74....929.82.73.434..9.2.7....7...88.7.2.9..`	autosolve
`123456789456789123789132546235948671674513892918267354341895267592671438867324915`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (4)
B3: 8,9
C3: 3,9
B8: 2,9
C8: 2,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B1,C1: 2.. / B1 = 2  =>  5 pairs (_) / C1 = 2  =>  3 pairs (_)
B8,C8: 2.. / B8 = 2  =>  3 pairs (_) / C8 = 2  =>  5 pairs (_)
B1,B8: 2.. / B1 = 2  =>  5 pairs (_) / B8 = 2  =>  3 pairs (_)
C1,C8: 2.. / C1 = 2  =>  3 pairs (_) / C8 = 2  =>  5 pairs (_)
C1,C3: 3.. / C1 = 3  => 11 pairs (_) / C3 = 3  =>  5 pairs (_)
H8,H9: 3.. / H8 = 3  =>  4 pairs (_) / H9 = 3  =>  4 pairs (_)
C3,E3: 3.. / C3 = 3  =>  5 pairs (_) / E3 = 3  => 11 pairs (_)
A1,A2: 4.. / A1 = 4  => 11 pairs (_) / A2 = 4  =>  6 pairs (_)
E4,F4: 4.. / E4 = 4  => 11 pairs (_) / F4 = 4  =>  7 pairs (_)
A2,G2: 4.. / A2 = 4  =>  6 pairs (_) / G2 = 4  => 11 pairs (_)
G1,H1: 7.. / G1 = 7  =>  4 pairs (_) / H1 = 7  =>  4 pairs (_)
G4,H4: 7.. / G4 = 7  =>  4 pairs (_) / H4 = 7  =>  4 pairs (_)
G1,G4: 7.. / G1 = 7  =>  4 pairs (_) / G4 = 7  =>  4 pairs (_)
H1,H4: 7.. / H1 = 7  =>  4 pairs (_) / H4 = 7  =>  4 pairs (_)
B1,B3: 8.. / B1 = 8  =>  2 pairs (_) / B3 = 8  =>  7 pairs (_)
D7,F7: 8.. / D7 = 8  =>  6 pairs (_) / F7 = 8  =>  9 pairs (_)
D5,D7: 8.. / D5 = 8  =>  9 pairs (_) / D7 = 8  =>  6 pairs (_)
I1,I3: 9.. / I1 = 9  =>  7 pairs (_) / I3 = 9  =>  9 pairs (_)
B8,C8: 9.. / B8 = 9  =>  5 pairs (_) / C8 = 9  =>  3 pairs (_)
* DURATION: 0:00:05.864967  START: 17:13:15.169132  END: 17:13:21.034099 2025-04-04
* CP COUNT: (19)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:14.062982  START: 17:13:24.163621  END: 17:13:38.226603 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00058988-base-pr-002.dot
* REASONING
* DIS # C1: 3 # B6: 5,6 => CTR => B6: 1
* PRF # C1: 3 + B6: 1 # E4: 4,5 => SOL
* STA # C1: 3 + B6: 1 + E4: 4,5
* CNT   2 HDP CHAINS /  70 HYP OPENED

Header Info

rating: 12387; r2: 246807; index: 58988

Solution

position: 123456789456789123789132546235948671674513892918267354341895267592671438867324915 solved

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 # B1: 8,9 => UNS
* INC # B1: 2 => UNS
* INC # C1: 3,9 => UNS
* INC # C1: 2 => UNS
* INC # B1: 2,9 => UNS
* INC # B1: 8 => UNS
* INC # C1: 2,9 => UNS
* INC # C1: 3 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 8,9 => UNS
* INC # B1: 2 => UNS
* INC # C1: 3,9 => UNS
* INC # C1: 2 => UNS
* INC # B1: 2,9 => UNS
* INC # B1: 8 => UNS
* INC # C1: 2,9 => UNS
* INC # C1: 3 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 8,9 => UNS
* INC # B1: 2 => UNS
* INC # C1: 3,9 => UNS
* INC # C1: 2 => UNS
* INC # B1: 2,9 => UNS
* INC # B1: 8 => UNS
* INC # C1: 2,9 => UNS
* INC # C1: 3 => UNS
* INC # B1: 8,9 # D1: 4,5 => UNS
* INC # B1: 8,9 # E1: 4,5 => UNS
* INC # B1: 8,9 # G3: 4,5 => UNS
* INC # B1: 8,9 # H3: 4,5 => UNS
* INC # B1: 8,9 # E4: 4,5 => UNS
* INC # B1: 8,9 # E4: 1,6 => UNS
* INC # B1: 8,9 => UNS
* INC # B1: 2 # G4: 7,8 => UNS
* INC # B1: 2 # G4: 1,5,6 => UNS
* INC # B1: 2 # G4: 7,8 => UNS
* INC # B1: 2 # G4: 1,5,6 => UNS
* INC # B1: 2 => UNS
* INC # C1: 3,9 # G4: 7,8 => UNS
* INC # C1: 3,9 # G4: 1,5,6 => UNS
* INC # C1: 3,9 # G4: 7,8 => UNS
* INC # C1: 3,9 # G4: 1,5,6 => UNS
* INC # C1: 3,9 => UNS
* INC # C1: 2 # D1: 4,5 => UNS
* INC # C1: 2 # E1: 4,5 => UNS
* INC # C1: 2 # G3: 4,5 => UNS
* INC # C1: 2 # H3: 4,5 => UNS
* INC # C1: 2 # E4: 4,5 => UNS
* INC # C1: 2 # E4: 1,6 => UNS
* INC # C1: 2 => UNS
* INC # B1: 2,9 # C1: 2,9 => UNS
* INC # B1: 2,9 # C1: 3 => UNS
* INC # B1: 2,9 # C1: 3,9 => UNS
* INC # B1: 2,9 # C1: 2 => UNS
* INC # B1: 2,9 # G4: 7,8 => UNS
* INC # B1: 2,9 # G4: 1,5,6 => UNS
* INC # B1: 2,9 # G4: 7,8 => UNS
* INC # B1: 2,9 # G4: 1,5,6 => UNS
* INC # B1: 2,9 # C1: 2,9 => UNS
* INC # B1: 2,9 # C1: 3 => UNS
* INC # B1: 2,9 => UNS
* INC # B1: 8 # D1: 4,5 => UNS
* INC # B1: 8 # E1: 4,5 => UNS
* INC # B1: 8 # G3: 4,5 => UNS
* INC # B1: 8 # H3: 4,5 => UNS
* INC # B1: 8 # E4: 4,5 => UNS
* INC # B1: 8 # E4: 1,6 => UNS
* INC # B1: 8 # G3: 5,6 => UNS
* INC # B1: 8 # H3: 5,6 => UNS
* INC # B1: 8 # I4: 5,6 => UNS
* INC # B1: 8 # I9: 5,6 => UNS
* INC # B1: 8 => UNS
* INC # C1: 2,9 # B1: 2,9 => UNS
* INC # C1: 2,9 # B1: 8 => UNS
* INC # C1: 2,9 # B1: 8,9 => UNS
* INC # C1: 2,9 # B1: 2 => UNS
* INC # C1: 2,9 # D1: 4,5 => UNS
* INC # C1: 2,9 # E1: 4,5 => UNS
* INC # C1: 2,9 # G3: 4,5 => UNS
* INC # C1: 2,9 # H3: 4,5 => UNS
* INC # C1: 2,9 # E4: 4,5 => UNS
* INC # C1: 2,9 # E4: 1,6 => UNS
* INC # C1: 2,9 # B1: 2,9 => UNS
* INC # C1: 2,9 # B1: 8 => UNS
* INC # C1: 2,9 => UNS
* DIS # C1: 3 # B6: 5,6 => CTR => B6: 1
* PRF # C1: 3 + B6: 1 # E4: 4,5 => SOL
* STA # C1: 3 + B6: 1 + E4: 4,5
* CNT  69 HDP CHAINS /  70 HYP OPENED