Analysis of xx-mith-te3-00094094-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: .2.4.6.8.4........68.73....23..74...7.826.....468.3..2.72...45..6....91........23 initial

Autosolve

position: .2.4.6.8.4........68.73....23..74...7.826.....468.3..2.72...45..6....91........23 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: 0:00:12.452975

The following important HDP chains were detected:

* DIS # I3: 4,9 # C1: 1,5 => CTR => C1: 3,7,9
* DIS # I3: 4,9 + C1: 3,7,9 # C2: 1,5 => CTR => C2: 3,7,9
* PRF # I3: 1,5 # G3: 1,5 => SOL
* STA # I3: 1,5 + G3: 1,5
* CNT   3 HDP CHAINS /  79 HYP OPENED

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

Details

Positions

.2.4.6.8.4........68.73....23..74...7.826.....468.3..2.72...45..6....91........23 initial
.2.4.6.8.4........68.73....23..74...7.826.....468.3..2.72...45..6....91........23 autosolve
123456789457189236689732145235974861718265394946813572372691458564328917891547623 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (6)
H3: 4,9
H4: 6,9
H6: 7,9
D8: 3,5
I7: 6,8
I8: 7,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G2,G3: 2.. / G2 = 2  => 15 pairs (_) / G3 = 2  =>  8 pairs (_)
E8,F8: 2.. / E8 = 2  =>  8 pairs (_) / F8 = 2  =>  7 pairs (_)
F3,G3: 2.. / F3 = 2  => 15 pairs (_) / G3 = 2  =>  8 pairs (_)
E2,E8: 2.. / E2 = 2  =>  7 pairs (_) / E8 = 2  =>  8 pairs (_)
G5,H5: 3.. / G5 = 3  =>  6 pairs (_) / H5 = 3  =>  6 pairs (_)
D7,D8: 3.. / D7 = 3  =>  9 pairs (_) / D8 = 3  => 10 pairs (_)
A7,D7: 3.. / A7 = 3  => 10 pairs (_) / D7 = 3  =>  9 pairs (_)
H2,H5: 3.. / H2 = 3  =>  6 pairs (_) / H5 = 3  =>  6 pairs (_)
H3,I3: 4.. / H3 = 4  =>  6 pairs (_) / I3 = 4  =>  5 pairs (_)
H5,I5: 4.. / H5 = 4  =>  5 pairs (_) / I5 = 4  =>  6 pairs (_)
C8,C9: 4.. / C8 = 4  =>  8 pairs (_) / C9 = 4  =>  8 pairs (_)
E8,E9: 4.. / E8 = 4  =>  8 pairs (_) / E9 = 4  =>  8 pairs (_)
C8,E8: 4.. / C8 = 4  =>  8 pairs (_) / E8 = 4  =>  8 pairs (_)
C9,E9: 4.. / C9 = 4  =>  8 pairs (_) / E9 = 4  =>  8 pairs (_)
H3,H5: 4.. / H3 = 4  =>  6 pairs (_) / H5 = 4  =>  5 pairs (_)
I3,I5: 4.. / I3 = 4  =>  5 pairs (_) / I5 = 4  =>  6 pairs (_)
D7,D9: 6.. / D7 = 6  => 16 pairs (_) / D9 = 6  =>  6 pairs (_)
I7,G9: 6.. / I7 = 6  =>  6 pairs (_) / G9 = 6  => 16 pairs (_)
D7,I7: 6.. / D7 = 6  => 16 pairs (_) / I7 = 6  =>  6 pairs (_)
D9,G9: 6.. / D9 = 6  =>  6 pairs (_) / G9 = 6  => 16 pairs (_)
H2,H4: 6.. / H2 = 6  => 14 pairs (_) / H4 = 6  =>  5 pairs (_)
C1,C2: 7.. / C1 = 7  =>  6 pairs (_) / C2 = 7  =>  6 pairs (_)
G6,H6: 7.. / G6 = 7  =>  6 pairs (_) / H6 = 7  =>  6 pairs (_)
F8,F9: 7.. / F8 = 7  =>  8 pairs (_) / F9 = 7  =>  6 pairs (_)
I8,G9: 7.. / I8 = 7  =>  6 pairs (_) / G9 = 7  =>  8 pairs (_)
F8,I8: 7.. / F8 = 7  =>  8 pairs (_) / I8 = 7  =>  6 pairs (_)
F9,G9: 7.. / F9 = 7  =>  6 pairs (_) / G9 = 7  =>  8 pairs (_)
H2,H6: 7.. / H2 = 7  =>  6 pairs (_) / H6 = 7  =>  6 pairs (_)
E2,F2: 8.. / E2 = 8  =>  9 pairs (_) / F2 = 8  =>  7 pairs (_)
G4,I4: 8.. / G4 = 8  =>  7 pairs (_) / I4 = 8  =>  9 pairs (_)
G4,G9: 8.. / G4 = 8  =>  7 pairs (_) / G9 = 8  =>  9 pairs (_)
* DURATION: 0:00:06.986022  START: 14:45:09.907257  END: 14:45:16.893279 2025-04-06
* CP COUNT: (31)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:12.285077  START: 14:45:21.867900  END: 14:45:34.152977 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00094094-base-pr-002.dot
* REASONING
* DIS # I3: 4,9 # C1: 1,5 => CTR => C1: 3,7,9
* DIS # I3: 4,9 + C1: 3,7,9 # C2: 1,5 => CTR => C2: 3,7,9
* PRF # I3: 1,5 # G3: 1,5 => SOL
* STA # I3: 1,5 + G3: 1,5
* CNT   3 HDP CHAINS /  79 HYP OPENED

Header Info

rating: 23840; r2: 721001; index: 94094

Solution

position: 123456789457189236689732145235974861718265394946813572372691458564328917891547623 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 # I3: 4,9 => UNS
* INC # I3: 1,5 => UNS
* INC # H5: 4,9 => UNS
* INC # H5: 3 => UNS
* INC # I4: 6,9 => UNS
* INC # I4: 1,5,8 => UNS
* INC # H2: 6,9 => UNS
* INC # H2: 3,7 => UNS
* INC # H2: 7,9 => UNS
* INC # H2: 3,6 => UNS
* INC # A8: 3,5 => UNS
* INC # C8: 3,5 => UNS
* INC # G9: 6,8 => UNS
* INC # G9: 7 => UNS
* INC # I4: 6,8 => UNS
* INC # I4: 1,5,9 => UNS
* INC # G9: 7,8 => UNS
* INC # G9: 6 => UNS
* INC # F8: 7,8 => UNS
* INC # F8: 2,5 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # I3: 4,9 => UNS
* INC # I3: 1,5 => UNS
* INC # H5: 4,9 => UNS
* INC # H5: 3 => UNS
* INC # I4: 6,9 => UNS
* INC # I4: 1,5,8 => UNS
* INC # H2: 6,9 => UNS
* INC # H2: 3,7 => UNS
* INC # H2: 7,9 => UNS
* INC # H2: 3,6 => UNS
* INC # A8: 3,5 => UNS
* INC # C8: 3,5 => UNS
* INC # G9: 6,8 => UNS
* INC # G9: 7 => UNS
* INC # I4: 6,8 => UNS
* INC # I4: 1,5,9 => UNS
* INC # G9: 7,8 => UNS
* INC # G9: 6 => UNS
* INC # F8: 7,8 => UNS
* INC # F8: 2,5 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # I3: 4,9 => UNS
* INC # I3: 1,5 => UNS
* INC # H5: 4,9 => UNS
* INC # H5: 3 => UNS
* INC # I4: 6,9 => UNS
* INC # I4: 1,5,8 => UNS
* INC # H2: 6,9 => UNS
* INC # H2: 3,7 => UNS
* INC # H2: 7,9 => UNS
* INC # H2: 3,6 => UNS
* INC # A8: 3,5 => UNS
* INC # C8: 3,5 => UNS
* INC # G9: 6,8 => UNS
* INC # G9: 7 => UNS
* INC # I4: 6,8 => UNS
* INC # I4: 1,5,9 => UNS
* INC # G9: 7,8 => UNS
* INC # G9: 6 => UNS
* INC # F8: 7,8 => UNS
* INC # F8: 2,5 => UNS
* INC # I3: 4,9 # A1: 1,5 => UNS
* DIS # I3: 4,9 # C1: 1,5 => CTR => C1: 3,7,9
* INC # I3: 4,9 + C1: 3,7,9 # B2: 1,5 => UNS
* DIS # I3: 4,9 + C1: 3,7,9 # C2: 1,5 => CTR => C2: 3,7,9
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # F3: 1,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # G3: 1,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # C4: 1,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # C9: 1,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # A1: 1,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # B2: 1,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # F3: 1,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # G3: 1,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # C4: 1,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # C9: 1,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # H5: 4,9 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # H5: 3 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # I5: 4,9 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # I5: 1,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # I4: 6,9 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # I4: 1,5,8 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # A8: 3,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # C8: 3,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # G9: 6,8 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # G9: 7 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # I4: 6,8 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # I4: 1,5,9 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # G9: 7,8 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # G9: 6 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # F8: 7,8 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # F8: 2,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # A1: 1,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # B2: 1,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # F3: 1,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # G3: 1,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # C4: 1,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # C9: 1,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # H5: 4,9 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # H5: 3 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # I5: 4,9 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # I5: 1,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # I4: 6,9 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # I4: 1,5,8 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # A8: 3,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # C8: 3,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # G9: 6,8 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # G9: 7 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # I4: 6,8 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # I4: 1,5,9 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # G9: 7,8 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # G9: 6 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # F8: 7,8 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 # F8: 2,5 => UNS
* INC # I3: 4,9 + C1: 3,7,9 + C2: 3,7,9 => UNS
* INC # I3: 1,5 # G1: 1,5 => UNS
* INC # I3: 1,5 # I1: 1,5 => UNS
* INC # I3: 1,5 # G2: 1,5 => UNS
* INC # I3: 1,5 # I2: 1,5 => UNS
* PRF # I3: 1,5 # G3: 1,5 => SOL
* STA # I3: 1,5 + G3: 1,5
* CNT  78 HDP CHAINS /  79 HYP OPENED