Analysis of xx-mith-te3-00016896-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: .2345...945.......6.9..2...2.....5133.5....78......4..5..36.....3..9.6..96.2.43.. initial

Autosolve

position: .2345...945.....3.6.9.32...2.6...5133.5....78...5.34..5..36.....3..956..96.2.43.. 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: 0:00:19.267464

The following important HDP chains were detected:

* DIS # F1: 6,8 # I2: 1,7 => CTR => I2: 2,6
* DIS # H6: 6 # C2: 8 => CTR => C2: 1,7
* DIS # H6: 6 + C2: 1,7 # D2: 8,9 => CTR => D2: 1,7
* PRF # H6: 6 + C2: 1,7 + D2: 1,7 => SOL
* STA H6: 6
* CNT   4 HDP CHAINS /  90 HYP OPENED

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

Details

Positions

.2345...945.......6.9..2...2.....5133.5....78......4..5..36.....3..9.6..96.2.43.. initial
.2345...945.....3.6.9.32...2.6...5133.5....78...5.34..5..36.....3..956..96.2.43.. autosolve
123456789457189236689732145276948513345621978891573462512367894734895621968214357 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
H1: 6,8
H3: 4,5
I3: 4,5
G5: 2,9
I6: 2,6
C7: 2,4
C8: 2,4
H9: 5,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G2,I2: 2.. / G2 = 2  => 13 pairs (_) / I2 = 2  => 10 pairs (_)
E5,E6: 2.. / E5 = 2  => 12 pairs (_) / E6 = 2  => 10 pairs (_)
C7,C8: 2.. / C7 = 2  =>  7 pairs (_) / C8 = 2  =>  9 pairs (_)
E5,G5: 2.. / E5 = 2  => 12 pairs (_) / G5 = 2  => 10 pairs (_)
H3,I3: 4.. / H3 = 4  =>  7 pairs (_) / I3 = 4  => 10 pairs (_)
B4,B5: 4.. / B4 = 4  => 10 pairs (_) / B5 = 4  =>  9 pairs (_)
E4,E5: 4.. / E4 = 4  =>  9 pairs (_) / E5 = 4  => 10 pairs (_)
C7,C8: 4.. / C7 = 4  =>  9 pairs (_) / C8 = 4  =>  7 pairs (_)
B4,E4: 4.. / B4 = 4  => 10 pairs (_) / E4 = 4  =>  9 pairs (_)
B5,E5: 4.. / B5 = 4  =>  9 pairs (_) / E5 = 4  => 10 pairs (_)
H3,I3: 5.. / H3 = 5  => 10 pairs (_) / I3 = 5  =>  7 pairs (_)
H9,I9: 5.. / H9 = 5  =>  7 pairs (_) / I9 = 5  => 10 pairs (_)
H3,H9: 5.. / H3 = 5  => 10 pairs (_) / H9 = 5  =>  7 pairs (_)
I3,I9: 5.. / I3 = 5  =>  7 pairs (_) / I9 = 5  => 10 pairs (_)
H1,I2: 6.. / H1 = 6  =>  9 pairs (_) / I2 = 6  => 14 pairs (_)
D5,F5: 6.. / D5 = 6  =>  9 pairs (_) / F5 = 6  =>  9 pairs (_)
H6,I6: 6.. / H6 = 6  => 14 pairs (_) / I6 = 6  =>  9 pairs (_)
F1,H1: 6.. / F1 = 6  => 14 pairs (_) / H1 = 6  =>  9 pairs (_)
D2,D5: 6.. / D2 = 6  =>  9 pairs (_) / D5 = 6  =>  9 pairs (_)
H1,H6: 6.. / H1 = 6  =>  9 pairs (_) / H6 = 6  => 14 pairs (_)
I2,I6: 6.. / I2 = 6  => 14 pairs (_) / I6 = 6  =>  9 pairs (_)
D2,F2: 9.. / D2 = 9  => 10 pairs (_) / F2 = 9  => 10 pairs (_)
G5,H6: 9.. / G5 = 9  => 12 pairs (_) / H6 = 9  => 10 pairs (_)
G7,H7: 9.. / G7 = 9  => 10 pairs (_) / H7 = 9  => 12 pairs (_)
B6,H6: 9.. / B6 = 9  => 12 pairs (_) / H6 = 9  => 10 pairs (_)
G5,G7: 9.. / G5 = 9  => 12 pairs (_) / G7 = 9  => 10 pairs (_)
H6,H7: 9.. / H6 = 9  => 10 pairs (_) / H7 = 9  => 12 pairs (_)
* DURATION: 0:00:09.205209  START: 07:55:22.685516  END: 07:55:31.890725 2025-04-04
* CP COUNT: (27)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:19.064535  START: 07:55:37.341638  END: 07:55:56.406173 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00016896-base-pr-002.dot
* REASONING
* DIS # F1: 6,8 # I2: 1,7 => CTR => I2: 2,6
* DIS # H6: 6 # C2: 8 => CTR => C2: 1,7
* DIS # H6: 6 + C2: 1,7 # D2: 8,9 => CTR => D2: 1,7
* PRF # H6: 6 + C2: 1,7 + D2: 1,7 => SOL
* STA H6: 6
* CNT   4 HDP CHAINS /  90 HYP OPENED

Header Info

rating: 3640; r2: 86336; index: 16896

Solution

position: 123456789457189236689732145276948513345621978891573462512367894734895621968214357 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 # F1: 6,8 => UNS
* INC # F1: 1,7 => UNS
* INC # H6: 2,9 => UNS
* INC # H6: 6 => UNS
* INC # G7: 2,9 => UNS
* INC # G7: 1,7,8 => UNS
* INC # H6: 2,6 => UNS
* INC # H6: 9 => UNS
* INC # I2: 2,6 => UNS
* INC # I2: 1,7 => UNS
* INC # H7: 2,4 => UNS
* INC # I7: 2,4 => UNS
* INC # H8: 2,4 => UNS
* INC # I8: 2,4 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F1: 6,8 => UNS
* INC # F1: 1,7 => UNS
* INC # H6: 2,9 => UNS
* INC # H6: 6 => UNS
* INC # G7: 2,9 => UNS
* INC # G7: 1,7,8 => UNS
* INC # H6: 2,6 => UNS
* INC # H6: 9 => UNS
* INC # I2: 2,6 => UNS
* INC # I2: 1,7 => UNS
* INC # H7: 2,4 => UNS
* INC # I7: 2,4 => UNS
* INC # H8: 2,4 => UNS
* INC # I8: 2,4 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # F1: 6,8 => UNS
* INC # F1: 1,7 => UNS
* INC # H6: 2,9 => UNS
* INC # H6: 6 => UNS
* INC # G7: 2,9 => UNS
* INC # G7: 1,7,8 => UNS
* INC # H6: 2,6 => UNS
* INC # H6: 9 => UNS
* INC # I2: 2,6 => UNS
* INC # I2: 1,7 => UNS
* INC # H7: 2,4 => UNS
* INC # I7: 2,4 => UNS
* INC # H8: 2,4 => UNS
* INC # I8: 2,4 => UNS
* INC # F1: 6,8 # C2: 1,7 => UNS
* INC # F1: 6,8 # B3: 1,7 => UNS
* INC # F1: 6,8 # A6: 1,7 => UNS
* INC # F1: 6,8 # A8: 1,7 => UNS
* INC # F1: 6,8 # D2: 6,8 => UNS
* INC # F1: 6,8 # F2: 6,8 => UNS
* INC # F1: 6,8 # G2: 1,7 => UNS
* DIS # F1: 6,8 # I2: 1,7 => CTR => I2: 2,6
* INC # F1: 6,8 + I2: 2,6 # G3: 1,7 => UNS
* INC # F1: 6,8 + I2: 2,6 # G2: 1,7 => UNS
* INC # F1: 6,8 + I2: 2,6 # G3: 1,7 => UNS
* INC # F1: 6,8 + I2: 2,6 # H6: 2,9 => UNS
* INC # F1: 6,8 + I2: 2,6 # H6: 6 => UNS
* INC # F1: 6,8 + I2: 2,6 # G7: 2,9 => UNS
* INC # F1: 6,8 + I2: 2,6 # G7: 8 => UNS
* INC # F1: 6,8 + I2: 2,6 # H6: 2,6 => UNS
* INC # F1: 6,8 + I2: 2,6 # H6: 9 => UNS
* INC # F1: 6,8 + I2: 2,6 # H7: 2,4 => UNS
* INC # F1: 6,8 + I2: 2,6 # H7: 8,9 => UNS
* INC # F1: 6,8 + I2: 2,6 # H8: 2,4 => UNS
* INC # F1: 6,8 + I2: 2,6 # H8: 8 => UNS
* INC # F1: 6,8 + I2: 2,6 # C2: 1,7 => UNS
* INC # F1: 6,8 + I2: 2,6 # B3: 1,7 => UNS
* INC # F1: 6,8 + I2: 2,6 # A6: 1,7 => UNS
* INC # F1: 6,8 + I2: 2,6 # A8: 1,7 => UNS
* INC # F1: 6,8 + I2: 2,6 # D2: 6,8 => UNS
* INC # F1: 6,8 + I2: 2,6 # F2: 6,8 => UNS
* INC # F1: 6,8 + I2: 2,6 # G2: 1,7 => UNS
* INC # F1: 6,8 + I2: 2,6 # G3: 1,7 => UNS
* INC # F1: 6,8 + I2: 2,6 # H6: 2,9 => UNS
* INC # F1: 6,8 + I2: 2,6 # H6: 6 => UNS
* INC # F1: 6,8 + I2: 2,6 # G7: 2,9 => UNS
* INC # F1: 6,8 + I2: 2,6 # G7: 8 => UNS
* INC # F1: 6,8 + I2: 2,6 # H6: 2,6 => UNS
* INC # F1: 6,8 + I2: 2,6 # H6: 9 => UNS
* INC # F1: 6,8 + I2: 2,6 # H7: 2,4 => UNS
* INC # F1: 6,8 + I2: 2,6 # H7: 8,9 => UNS
* INC # F1: 6,8 + I2: 2,6 # H8: 2,4 => UNS
* INC # F1: 6,8 + I2: 2,6 # H8: 8 => UNS
* INC # F1: 6,8 + I2: 2,6 => UNS
* INC # F1: 1,7 # E2: 1,7 => UNS
* INC # F1: 1,7 # D3: 1,7 => UNS
* INC # F1: 1,7 # A1: 1,7 => UNS
* INC # F1: 1,7 # G1: 1,7 => UNS
* INC # F1: 1,7 # F7: 1,7 => UNS
* INC # F1: 1,7 # F7: 8 => UNS
* INC # F1: 1,7 # D5: 6,9 => UNS
* INC # F1: 1,7 # D5: 1 => UNS
* INC # F1: 1,7 # F5: 6,9 => UNS
* INC # F1: 1,7 # F5: 1 => UNS
* INC # F1: 1,7 # G7: 2,9 => UNS
* INC # F1: 1,7 # G7: 1,7 => UNS
* INC # F1: 1,7 # H7: 2,9 => UNS
* INC # F1: 1,7 # H7: 4,8 => UNS
* INC # F1: 1,7 # H7: 2,4 => UNS
* INC # F1: 1,7 # I7: 2,4 => UNS
* INC # F1: 1,7 # H8: 2,4 => UNS
* INC # F1: 1,7 # I8: 2,4 => UNS
* INC # F1: 1,7 => UNS
* INC # H6: 2,9 # D5: 6,9 => UNS
* INC # H6: 2,9 # D5: 1 => UNS
* INC # H6: 2,9 # F5: 6,9 => UNS
* INC # H6: 2,9 # F5: 1 => UNS
* INC # H6: 2,9 # G7: 2,9 => UNS
* INC # H6: 2,9 # G7: 1,7 => UNS
* INC # H6: 2,9 # H7: 2,9 => UNS
* INC # H6: 2,9 # H7: 4,8 => UNS
* INC # H6: 2,9 # H7: 2,4 => UNS
* INC # H6: 2,9 # I7: 2,4 => UNS
* INC # H6: 2,9 # H8: 2,4 => UNS
* INC # H6: 2,9 # I8: 2,4 => UNS
* INC # H6: 2,9 => UNS
* INC # H6: 6 # C2: 1,7 => UNS
* DIS # H6: 6 # C2: 8 => CTR => C2: 1,7
* DIS # H6: 6 + C2: 1,7 # D2: 8,9 => CTR => D2: 1,7
* PRF # H6: 6 + C2: 1,7 + D2: 1,7 => SOL
* STA H6: 6
* CNT  90 HDP CHAINS /  90 HYP OPENED