Analysis of xx-mith-te3-00036119-base.sdk

Contents

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

Original Sudoku

level: hard

position: .......8.4...8...66...72.45.36.......91......845....27.64..58.2..2.68.74...24.56. initial

Autosolve

position: .......8.4...8...66...72.45.36.......91......845....27.647.58.2..2.68.74...24.56. 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: 0:00:24.005215

The following important HDP chains were detected:

* DIS # B2: 1,5 # D2: 3,9 => CTR => D2: 1,5
* PRF # B2: 1,5 + D2: 1,5 # D4: 1,5 => SOL
* STA # B2: 1,5 + D2: 1,5 + D4: 1,5
* CNT   2 HDP CHAINS /  81 HYP OPENED

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

Details

Positions

`.......8.4...8...66...72.45.36.......91......845....27.64..58.2..2.68.74...24.56.`	initial
`.......8.4...8...66...72.45.36.......91......845....27.647.58.2..2.68.74...24.56.`	autosolve
`123456789457189236689372145236597418791824653845631927364715892512968374978243561`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
A1: 1,5
B3: 1,8
D1: 4,6
F1: 4,6
G1: 2,7
G2: 2,7
A4: 2,7
A5: 2,7
H5: 3,5
I5: 3,8
B8: 1,5
B9: 7,8
C9: 7,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B1,B2: 2.. / B1 = 2  => 12 pairs (_) / B2 = 2  => 14 pairs (_)
G1,G2: 2.. / G1 = 2  => 14 pairs (_) / G2 = 2  => 12 pairs (_)
A4,A5: 2.. / A4 = 2  => 11 pairs (_) / A5 = 2  => 14 pairs (_)
E4,E5: 2.. / E4 = 2  => 14 pairs (_) / E5 = 2  => 11 pairs (_)
B1,G1: 2.. / B1 = 2  => 12 pairs (_) / G1 = 2  => 14 pairs (_)
B2,G2: 2.. / B2 = 2  => 14 pairs (_) / G2 = 2  => 12 pairs (_)
A4,E4: 2.. / A4 = 2  => 11 pairs (_) / E4 = 2  => 14 pairs (_)
A5,E5: 2.. / A5 = 2  => 14 pairs (_) / E5 = 2  => 11 pairs (_)
D1,F1: 4.. / D1 = 4  => 13 pairs (_) / F1 = 4  => 15 pairs (_)
G4,G5: 4.. / G4 = 4  => 14 pairs (_) / G5 = 4  => 20 pairs (_)
E1,D2: 5.. / E1 = 5  => 14 pairs (_) / D2 = 5  => 15 pairs (_)
H4,H5: 5.. / H4 = 5  => 16 pairs (_) / H5 = 5  => 14 pairs (_)
A8,B8: 5.. / A8 = 5  => 16 pairs (_) / B8 = 5  => 13 pairs (_)
B2,D2: 5.. / B2 = 5  => 14 pairs (_) / D2 = 5  => 15 pairs (_)
A1,A8: 5.. / A1 = 5  => 13 pairs (_) / A8 = 5  => 16 pairs (_)
D1,F1: 6.. / D1 = 6  => 15 pairs (_) / F1 = 6  => 13 pairs (_)
G5,G6: 6.. / G5 = 6  => 13 pairs (_) / G6 = 6  => 18 pairs (_)
G1,G2: 7.. / G1 = 7  => 12 pairs (_) / G2 = 7  => 14 pairs (_)
A4,A5: 7.. / A4 = 7  => 14 pairs (_) / A5 = 7  => 11 pairs (_)
F4,F5: 7.. / F4 = 7  => 11 pairs (_) / F5 = 7  => 14 pairs (_)
B9,C9: 7.. / B9 = 7  => 11 pairs (_) / C9 = 7  => 16 pairs (_)
A4,F4: 7.. / A4 = 7  => 14 pairs (_) / F4 = 7  => 11 pairs (_)
A5,F5: 7.. / A5 = 7  => 11 pairs (_) / F5 = 7  => 14 pairs (_)
B3,C3: 8.. / B3 = 8  => 11 pairs (_) / C3 = 8  => 16 pairs (_)
D4,D5: 8.. / D4 = 8  => 13 pairs (_) / D5 = 8  => 14 pairs (_)
I4,I5: 8.. / I4 = 8  => 14 pairs (_) / I5 = 8  => 13 pairs (_)
B9,C9: 8.. / B9 = 8  => 16 pairs (_) / C9 = 8  => 11 pairs (_)
D4,I4: 8.. / D4 = 8  => 13 pairs (_) / I4 = 8  => 14 pairs (_)
D5,I5: 8.. / D5 = 8  => 14 pairs (_) / I5 = 8  => 13 pairs (_)
B3,B9: 8.. / B3 = 8  => 11 pairs (_) / B9 = 8  => 16 pairs (_)
C3,C9: 8.. / C3 = 8  => 16 pairs (_) / C9 = 8  => 11 pairs (_)
* DURATION: 0:00:10.308983  START: 07:19:54.826027  END: 07:20:05.135010 2025-04-06
* CP COUNT: (31)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:23.824017  START: 07:20:13.191878  END: 07:20:37.015895 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00036119-base-pr-002.dot
* REASONING
* DIS # B2: 1,5 # D2: 3,9 => CTR => D2: 1,5
* PRF # B2: 1,5 + D2: 1,5 # D4: 1,5 => SOL
* STA # B2: 1,5 + D2: 1,5 + D4: 1,5
* CNT   2 HDP CHAINS /  81 HYP OPENED

Header Info

rating: 7561; r2: 184967; index: 36119

Solution

position: 123456789457189236689372145236597418791824653845631927364715892512968374978243561 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: 1,5 => UNS
* INC # B2: 1,5 => UNS
* INC # E1: 1,5 => UNS
* INC # E1: 3,9 => UNS
* INC # A8: 1,5 => UNS
* INC # A8: 3,9 => UNS
* INC # D5: 4,6 => UNS
* INC # D5: 3,5,8 => UNS
* INC # F5: 4,6 => UNS
* INC # F5: 3,7 => UNS
* INC # B1: 2,7 => UNS
* INC # B1: 1,5 => UNS
* INC # B2: 2,7 => UNS
* INC # B2: 1,5 => UNS
* INC # D5: 3,5 => UNS
* INC # E5: 3,5 => UNS
* INC # D5: 3,8 => UNS
* INC # D5: 4,5,6 => UNS
* INC # A8: 1,5 => UNS
* INC # A8: 3,9 => UNS
* INC # B1: 1,5 => UNS
* INC # B2: 1,5 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 1,5 => UNS
* INC # B2: 1,5 => UNS
* INC # E1: 1,5 => UNS
* INC # E1: 3,9 => UNS
* INC # A8: 1,5 => UNS
* INC # A8: 3,9 => UNS
* INC # D5: 4,6 => UNS
* INC # D5: 3,5,8 => UNS
* INC # F5: 4,6 => UNS
* INC # F5: 3,7 => UNS
* INC # B1: 2,7 => UNS
* INC # B1: 1,5 => UNS
* INC # B2: 2,7 => UNS
* INC # B2: 1,5 => UNS
* INC # D5: 3,5 => UNS
* INC # E5: 3,5 => UNS
* INC # D5: 3,8 => UNS
* INC # D5: 4,5,6 => UNS
* INC # A8: 1,5 => UNS
* INC # A8: 3,9 => UNS
* INC # B1: 1,5 => UNS
* INC # B2: 1,5 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 1,5 => UNS
* INC # B2: 1,5 => UNS
* INC # E1: 1,5 => UNS
* INC # E1: 3,9 => UNS
* INC # A8: 1,5 => UNS
* INC # A8: 3,9 => UNS
* INC # D5: 4,6 => UNS
* INC # D5: 3,5,8 => UNS
* INC # F5: 4,6 => UNS
* INC # F5: 3,7 => UNS
* INC # B1: 2,7 => UNS
* INC # B1: 1,5 => UNS
* INC # B2: 2,7 => UNS
* INC # B2: 1,5 => UNS
* INC # D5: 3,5 => UNS
* INC # E5: 3,5 => UNS
* INC # D5: 3,8 => UNS
* INC # D5: 4,5,6 => UNS
* INC # A8: 1,5 => UNS
* INC # A8: 3,9 => UNS
* INC # B1: 1,5 => UNS
* INC # B2: 1,5 => UNS
* INC # B1: 1,5 # A8: 1,5 => UNS
* INC # B1: 1,5 # A8: 3,9 => UNS
* INC # B1: 1,5 # F2: 3,9 => UNS
* INC # B1: 1,5 # H2: 3,9 => UNS
* INC # B1: 1,5 # D3: 3,9 => UNS
* INC # B1: 1,5 # G3: 3,9 => UNS
* INC # B1: 1,5 # D5: 4,6 => UNS
* INC # B1: 1,5 # D5: 3,8 => UNS
* INC # B1: 1,5 # F2: 3,9 => UNS
* INC # B1: 1,5 # D3: 3,9 => UNS
* INC # B1: 1,5 # E6: 3,9 => UNS
* INC # B1: 1,5 # E7: 3,9 => UNS
* INC # B1: 1,5 # F5: 4,6 => UNS
* INC # B1: 1,5 # F5: 3,7 => UNS
* INC # B1: 1,5 # H2: 3,9 => UNS
* INC # B1: 1,5 # G3: 3,9 => UNS
* INC # B1: 1,5 # I9: 3,9 => UNS
* INC # B1: 1,5 # I9: 1 => UNS
* INC # B1: 1,5 # D5: 3,8 => UNS
* INC # B1: 1,5 # D5: 4,6 => UNS
* INC # B1: 1,5 # A8: 1,5 => UNS
* INC # B1: 1,5 # A8: 3,9 => UNS
* INC # B1: 1,5 => UNS
* INC # B2: 1,5 # E1: 1,5 => UNS
* INC # B2: 1,5 # E1: 3,9 => UNS
* INC # B2: 1,5 # A8: 1,5 => UNS
* INC # B2: 1,5 # A8: 3,9 => UNS
* INC # B2: 1,5 # E1: 3,9 => UNS
* INC # B2: 1,5 # I1: 3,9 => UNS
* INC # B2: 1,5 # D2: 1,5 => UNS
* DIS # B2: 1,5 # D2: 3,9 => CTR => D2: 1,5
* INC # B2: 1,5 + D2: 1,5 # D3: 3,9 => UNS
* INC # B2: 1,5 + D2: 1,5 # G3: 3,9 => UNS
* INC # B2: 1,5 + D2: 1,5 # D5: 4,6 => UNS
* INC # B2: 1,5 + D2: 1,5 # D5: 3,5,8 => UNS
* INC # B2: 1,5 + D2: 1,5 # F5: 4,6 => UNS
* INC # B2: 1,5 + D2: 1,5 # F5: 3,7 => UNS
* INC # B2: 1,5 + D2: 1,5 # D5: 3,5 => UNS
* INC # B2: 1,5 + D2: 1,5 # E5: 3,5 => UNS
* INC # B2: 1,5 + D2: 1,5 # D5: 3,8 => UNS
* INC # B2: 1,5 + D2: 1,5 # D5: 4,5,6 => UNS
* INC # B2: 1,5 + D2: 1,5 # A8: 1,5 => UNS
* INC # B2: 1,5 + D2: 1,5 # A8: 3,9 => UNS
* INC # B2: 1,5 + D2: 1,5 # E1: 1,5 => UNS
* INC # B2: 1,5 + D2: 1,5 # E1: 3,9 => UNS
* INC # B2: 1,5 + D2: 1,5 # A8: 1,5 => UNS
* INC # B2: 1,5 + D2: 1,5 # A8: 3,9 => UNS
* INC # B2: 1,5 + D2: 1,5 # E1: 3,9 => UNS
* INC # B2: 1,5 + D2: 1,5 # I1: 3,9 => UNS
* INC # B2: 1,5 + D2: 1,5 # D3: 3,9 => UNS
* INC # B2: 1,5 + D2: 1,5 # G3: 3,9 => UNS
* INC # B2: 1,5 + D2: 1,5 # D5: 4,6 => UNS
* INC # B2: 1,5 + D2: 1,5 # D5: 3,5,8 => UNS
* INC # B2: 1,5 + D2: 1,5 # F5: 4,6 => UNS
* INC # B2: 1,5 + D2: 1,5 # F5: 3,7 => UNS
* INC # B2: 1,5 + D2: 1,5 # E1: 1,5 => UNS
* INC # B2: 1,5 + D2: 1,5 # E1: 3,9 => UNS
* PRF # B2: 1,5 + D2: 1,5 # D4: 1,5 => SOL
* STA # B2: 1,5 + D2: 1,5 + D4: 1,5
* CNT  80 HDP CHAINS /  81 HYP OPENED