Analysis of xx-mith-te3-00081990-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: .2345....45..89...9.82.35..2.58......943.5..8.....2.5......8.75.....4.61..9...3.2 initial

Autosolve

position: .2345....45..89...9.82.35..2.58......943.5..8.....2.5......8.75.....4.61..9...3.2 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

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

Pair Reduction

Pair Reduction

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

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:13.008292

The following important HDP chains were detected:

* PRF # H4: 4,9 # I4: 6,7 => SOL
* STA # H4: 4,9 + I4: 6,7
* CNT   1 HDP CHAINS /  57 HYP OPENED

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

Details

Positions

.2345....45..89...9.82.35..2.58......943.5..8.....2.5......8.75.....4.61..9...3.2 initial
.2345....45..89...9.82.35..2.58......943.5..8.....2.5......8.75.....4.61..9...3.2 autosolve
123456789457189236968273514235841697794365128816792453341628975572934861689517342 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
H3: 1,4
E4: 4,9
E6: 4,9
H5: 1,2
C8: 2,7
E7: 2,3
E8: 2,3
G7: 4,9
G8: 8,9
H9: 4,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G2,H2: 2.. / G2 = 2  => 10 pairs (_) / H2 = 2  => 19 pairs (_)
G5,H5: 2.. / G5 = 2  => 19 pairs (_) / H5 = 2  => 10 pairs (_)
C7,C8: 2.. / C7 = 2  => 14 pairs (_) / C8 = 2  =>  9 pairs (_)
E7,E8: 2.. / E7 = 2  =>  9 pairs (_) / E8 = 2  => 14 pairs (_)
C7,E7: 2.. / C7 = 2  => 14 pairs (_) / E7 = 2  =>  9 pairs (_)
C8,E8: 2.. / C8 = 2  =>  9 pairs (_) / E8 = 2  => 14 pairs (_)
G2,G5: 2.. / G2 = 2  => 10 pairs (_) / G5 = 2  => 19 pairs (_)
H2,H5: 2.. / H2 = 2  => 19 pairs (_) / H5 = 2  => 10 pairs (_)
H2,I2: 3.. / H2 = 3  => 10 pairs (_) / I2 = 3  => 18 pairs (_)
E7,E8: 3.. / E7 = 3  => 14 pairs (_) / E8 = 3  =>  9 pairs (_)
H2,H4: 3.. / H2 = 3  => 10 pairs (_) / H4 = 3  => 18 pairs (_)
H3,I3: 4.. / H3 = 4  => 15 pairs (_) / I3 = 4  => 13 pairs (_)
E4,E6: 4.. / E4 = 4  =>  8 pairs (_) / E6 = 4  => 13 pairs (_)
B7,B9: 4.. / B7 = 4  =>  9 pairs (_) / B9 = 4  => 14 pairs (_)
G7,H9: 4.. / G7 = 4  => 14 pairs (_) / H9 = 4  =>  9 pairs (_)
B7,G7: 4.. / B7 = 4  =>  9 pairs (_) / G7 = 4  => 14 pairs (_)
B9,H9: 4.. / B9 = 4  => 14 pairs (_) / H9 = 4  =>  9 pairs (_)
A8,A9: 5.. / A8 = 5  => 11 pairs (_) / A9 = 5  => 12 pairs (_)
D8,D9: 5.. / D8 = 5  => 12 pairs (_) / D9 = 5  => 11 pairs (_)
A8,D8: 5.. / A8 = 5  => 11 pairs (_) / D8 = 5  => 12 pairs (_)
A9,D9: 5.. / A9 = 5  => 12 pairs (_) / D9 = 5  => 11 pairs (_)
G1,H1: 8.. / G1 = 8  => 14 pairs (_) / H1 = 8  =>  9 pairs (_)
A6,B6: 8.. / A6 = 8  => 12 pairs (_) / B6 = 8  => 13 pairs (_)
G8,H9: 8.. / G8 = 8  =>  9 pairs (_) / H9 = 8  => 14 pairs (_)
G1,G8: 8.. / G1 = 8  => 14 pairs (_) / G8 = 8  =>  9 pairs (_)
H1,H9: 8.. / H1 = 8  =>  9 pairs (_) / H9 = 8  => 14 pairs (_)
H1,I1: 9.. / H1 = 9  => 15 pairs (_) / I1 = 9  =>  9 pairs (_)
E4,E6: 9.. / E4 = 9  => 13 pairs (_) / E6 = 9  =>  8 pairs (_)
D7,D8: 9.. / D7 = 9  => 14 pairs (_) / D8 = 9  =>  9 pairs (_)
G7,G8: 9.. / G7 = 9  =>  9 pairs (_) / G8 = 9  => 14 pairs (_)
E6,I6: 9.. / E6 = 9  =>  8 pairs (_) / I6 = 9  => 13 pairs (_)
D7,G7: 9.. / D7 = 9  => 14 pairs (_) / G7 = 9  =>  9 pairs (_)
D8,G8: 9.. / D8 = 9  =>  9 pairs (_) / G8 = 9  => 14 pairs (_)
H1,H4: 9.. / H1 = 9  => 15 pairs (_) / H4 = 9  =>  9 pairs (_)
* DURATION: 0:00:10.926734  START: 12:22:27.915867  END: 12:22:38.842601 2025-04-06
* CP COUNT: (34)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:12.833398  START: 12:22:43.273270  END: 12:22:56.106668 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00081990-base-pr-002.dot
* REASONING
* PRF # H4: 4,9 # I4: 6,7 => SOL
* STA # H4: 4,9 + I4: 6,7
* CNT   1 HDP CHAINS /  57 HYP OPENED

Header Info

rating: 19896; r2: 459923; index: 81990

Solution

position: 123456789457189236968273514235841697794365128816792453341628975572934861689517342 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 # H4: 1,4 => UNS
* INC # H4: 3,9 => UNS
* INC # H4: 4,9 => UNS
* INC # I4: 4,9 => UNS
* INC # I6: 4,9 => UNS
* INC # I6: 3,6,7 => UNS
* INC # G5: 1,2 => UNS
* INC # G5: 6,7 => UNS
* INC # H2: 1,2 => UNS
* INC # H2: 3 => UNS
* INC # B9: 4,8 => UNS
* INC # B9: 1,6,7 => UNS
* CNT  12 HDP CHAINS /  12 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # H4: 1,4 => UNS
* INC # H4: 3,9 => UNS
* INC # H4: 4,9 => UNS
* INC # I4: 4,9 => UNS
* INC # I6: 4,9 => UNS
* INC # I6: 3,6,7 => UNS
* INC # G5: 1,2 => UNS
* INC # G5: 6,7 => UNS
* INC # H2: 1,2 => UNS
* INC # H2: 3 => UNS
* INC # B9: 4,8 => UNS
* INC # B9: 1,6,7 => UNS
* CNT  12 HDP CHAINS /  12 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # H4: 1,4 => UNS
* INC # H4: 3,9 => UNS
* INC # H4: 4,9 => UNS
* INC # I4: 4,9 => UNS
* INC # I6: 4,9 => UNS
* INC # I6: 3,6,7 => UNS
* INC # G5: 1,2 => UNS
* INC # G5: 6,7 => UNS
* INC # H2: 1,2 => UNS
* INC # H2: 3 => UNS
* INC # B9: 4,8 => UNS
* INC # B9: 1,6,7 => UNS
* INC # H4: 1,4 # A1: 6,7 => UNS
* INC # H4: 1,4 # C2: 6,7 => UNS
* INC # H4: 1,4 # B4: 6,7 => UNS
* INC # H4: 1,4 # B4: 1 => UNS
* INC # H4: 1,4 # F1: 6,7 => UNS
* INC # H4: 1,4 # D2: 6,7 => UNS
* INC # H4: 1,4 # E5: 6,7 => UNS
* INC # H4: 1,4 # E9: 6,7 => UNS
* INC # H4: 1,4 # A1: 6,7 => UNS
* INC # H4: 1,4 # F1: 6,7 => UNS
* INC # H4: 1,4 # C2: 6,7 => UNS
* INC # H4: 1,4 # D2: 6,7 => UNS
* INC # H4: 1,4 # A8: 3,8 => UNS
* INC # H4: 1,4 # A8: 5,7 => UNS
* INC # H4: 1,4 # B8: 3,8 => UNS
* INC # H4: 1,4 # B8: 7 => UNS
* INC # H4: 1,4 # A8: 5,7 => UNS
* INC # H4: 1,4 # A8: 3,8 => UNS
* INC # H4: 1,4 # D9: 5,7 => UNS
* INC # H4: 1,4 # D9: 1,6 => UNS
* INC # H4: 1,4 # D9: 5,7 => UNS
* INC # H4: 1,4 # D9: 1,6 => UNS
* INC # H4: 1,4 # A8: 5,7 => UNS
* INC # H4: 1,4 # A8: 3,8 => UNS
* INC # H4: 1,4 => UNS
* INC # H4: 3,9 # I4: 4,9 => UNS
* INC # H4: 3,9 # I4: 3,6,7 => UNS
* INC # H4: 3,9 # I6: 4,9 => UNS
* INC # H4: 3,9 # I6: 3,6,7 => UNS
* INC # H4: 3,9 # I4: 3,9 => UNS
* INC # H4: 3,9 # I6: 3,9 => UNS
* INC # H4: 3,9 # G5: 1,2 => UNS
* INC # H4: 3,9 # G5: 6,7 => UNS
* INC # H4: 3,9 # H2: 1,2 => UNS
* INC # H4: 3,9 # H2: 3 => UNS
* INC # H4: 3,9 # B9: 4,8 => UNS
* INC # H4: 3,9 # B9: 1,6,7 => UNS
* INC # H4: 3,9 => UNS
* INC # H4: 4,9 # G1: 6,7 => UNS
* INC # H4: 4,9 # I1: 6,7 => UNS
* INC # H4: 4,9 # I3: 6,7 => UNS
* INC # H4: 4,9 # C2: 6,7 => UNS
* INC # H4: 4,9 # D2: 6,7 => UNS
* PRF # H4: 4,9 # I4: 6,7 => SOL
* STA # H4: 4,9 + I4: 6,7
* CNT  56 HDP CHAINS /  57 HYP OPENED