Analysis of xx-mith-te3-00025672-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: .23.56......18.......3724.52.5...9...46...3..9..........269.54...........9453.6.2 initial

Autosolve

position: .23.56......18.......3724.52.5...9...46...3..9........3.269.54...........9453.6.2 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # H2: 2,7 => CTR => H2: 3,6,9
* CNT   1 HDP CHAINS /  20 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # H2: 2,7 => CTR => H2: 3,6,9
* STA H2: 3,6,9
* CNT   1 HDP CHAINS /  29 HYP OPENED

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

Pair Reduction Position

position: .23.56......18.2.....3724.52.5...9...46...3..9........3.269.54...........9453.6.2 pair_reduction
Pair Reduction

See section Pair Reduction for the HDP chains leading to this result.

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:29.424527

The following important HDP chains were detected:

* DIS # E6: 1,2 # I2: 7 => CTR => I2: 3,9
* DIS # E6: 4,6 # I6: 1,7,8 => CTR => I6: 4,6
* DIS # E8: 1,2 # D5: 7,8 => CTR => D5: 2,9
* DIS # E8: 1,2 + D5: 2,9 # F5: 7,8 => CTR => F5: 1,5,9
* PRF # E8: 1,2 + D5: 2,9 + F5: 1,5,9 # I4: 7,8 => SOL
* STA # E8: 1,2 + D5: 2,9 + F5: 1,5,9 + I4: 7,8
* CNT   5 HDP CHAINS / 118 HYP OPENED

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

Details

Positions

.23.56......18.......3724.52.5...9...46...3..9..........269.54...........9453.6.2 initial
.23.56......18.......3724.52.5...9...46...3..9........3.269.54...........9453.6.2 autosolve
.23.56......18.2.....3724.52.5...9...46...3..9........3.269.54...........9453.6.2 pair_reduction
123456789457189236689372415215843967746915328938267154372698541561724893894531672 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
C2: 7,9
D1: 4,9
F2: 4,9
G2: 2,7
E5: 1,2
A8: 5,6
B8: 5,6
H8: 3,9
I8: 3,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G2,H2: 2.. / G2 = 2  => 10 pairs (_) / H2 = 2  =>  0 pairs (X)
D8,E8: 2.. / D8 = 2  => 10 pairs (_) / E8 = 2  => 16 pairs (_)
G2,G6: 2.. / G2 = 2  => 10 pairs (_) / G6 = 2  =>  0 pairs (X)
H2,I2: 3.. / H2 = 3  => 12 pairs (_) / I2 = 3  =>  9 pairs (_)
B4,B6: 3.. / B4 = 3  => 19 pairs (_) / B6 = 3  =>  9 pairs (_)
F4,F6: 3.. / F4 = 3  =>  9 pairs (_) / F6 = 3  => 19 pairs (_)
H8,I8: 3.. / H8 = 3  =>  9 pairs (_) / I8 = 3  => 12 pairs (_)
B4,F4: 3.. / B4 = 3  => 19 pairs (_) / F4 = 3  =>  9 pairs (_)
B6,F6: 3.. / B6 = 3  =>  9 pairs (_) / F6 = 3  => 19 pairs (_)
H2,H8: 3.. / H2 = 3  => 12 pairs (_) / H8 = 3  =>  9 pairs (_)
I2,I8: 3.. / I2 = 3  =>  9 pairs (_) / I8 = 3  => 12 pairs (_)
A1,A2: 4.. / A1 = 4  => 12 pairs (_) / A2 = 4  => 13 pairs (_)
D1,F2: 4.. / D1 = 4  => 13 pairs (_) / F2 = 4  => 12 pairs (_)
I4,I6: 4.. / I4 = 4  => 11 pairs (_) / I6 = 4  =>  9 pairs (_)
A1,D1: 4.. / A1 = 4  => 12 pairs (_) / D1 = 4  => 13 pairs (_)
A2,F2: 4.. / A2 = 4  => 13 pairs (_) / F2 = 4  => 12 pairs (_)
A2,B2: 5.. / A2 = 5  => 12 pairs (_) / B2 = 5  =>  8 pairs (_)
F5,F6: 5.. / F5 = 5  => 14 pairs (_) / F6 = 5  =>  9 pairs (_)
H5,H6: 5.. / H5 = 5  =>  9 pairs (_) / H6 = 5  => 14 pairs (_)
A8,B8: 5.. / A8 = 5  =>  8 pairs (_) / B8 = 5  => 12 pairs (_)
F5,H5: 5.. / F5 = 5  => 14 pairs (_) / H5 = 5  =>  9 pairs (_)
F6,H6: 5.. / F6 = 5  =>  9 pairs (_) / H6 = 5  => 14 pairs (_)
A2,A8: 5.. / A2 = 5  => 12 pairs (_) / A8 = 5  =>  8 pairs (_)
B2,B8: 5.. / B2 = 5  =>  8 pairs (_) / B8 = 5  => 12 pairs (_)
E4,E6: 6.. / E4 = 6  =>  9 pairs (_) / E6 = 6  => 10 pairs (_)
A8,B8: 6.. / A8 = 6  => 12 pairs (_) / B8 = 6  =>  8 pairs (_)
C2,C3: 9.. / C2 = 9  => 10 pairs (_) / C3 = 9  => 13 pairs (_)
D1,F2: 9.. / D1 = 9  => 12 pairs (_) / F2 = 9  => 13 pairs (_)
D5,F5: 9.. / D5 = 9  => 13 pairs (_) / F5 = 9  => 12 pairs (_)
H8,I8: 9.. / H8 = 9  => 12 pairs (_) / I8 = 9  =>  9 pairs (_)
C3,H3: 9.. / C3 = 9  => 13 pairs (_) / H3 = 9  => 10 pairs (_)
D1,D5: 9.. / D1 = 9  => 12 pairs (_) / D5 = 9  => 13 pairs (_)
F2,F5: 9.. / F2 = 9  => 13 pairs (_) / F5 = 9  => 12 pairs (_)
* DURATION: 0:00:10.936861  START: 06:34:50.385819  END: 06:35:01.322680 2025-04-06
* CP COUNT: (33)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:29.199273  START: 06:35:11.543092  END: 06:35:40.742365 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00025672-base-pr-002.dot
* REASONING
* DIS # E6: 1,2 # I2: 7 => CTR => I2: 3,9
* DIS # E6: 4,6 # I6: 1,7,8 => CTR => I6: 4,6
* DIS # E8: 1,2 # D5: 7,8 => CTR => D5: 2,9
* DIS # E8: 1,2 + D5: 2,9 # F5: 7,8 => CTR => F5: 1,5,9
* PRF # E8: 1,2 + D5: 2,9 + F5: 1,5,9 # I4: 7,8 => SOL
* STA # E8: 1,2 + D5: 2,9 + F5: 1,5,9 + I4: 7,8
* CNT   5 HDP CHAINS / 118 HYP OPENED

Header Info

rating: 5226; r2: 87747; index: 25672

Solution

position: 123456789457189236689372415215843967746915328938267154372698541561724893894531672 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 # H2: 7,9 => UNS
* INC # I2: 7,9 => UNS
* DIS # H2: 2,7 => CTR => H2: 3,6,9
* INC # H2: 3,6,9 => UNS
* INC # G6: 2,7 => UNS
* INC # G6: 1,8 => UNS
* INC # E6: 1,2 => UNS
* INC # E6: 4,6 => UNS
* INC # H5: 1,2 => UNS
* INC # H5: 5,7,8 => UNS
* INC # E8: 1,2 => UNS
* INC # E8: 4 => UNS
* INC # A2: 5,6 => UNS
* INC # A2: 4,7 => UNS
* INC # B2: 5,6 => UNS
* INC # B2: 7 => UNS
* INC # H2: 3,9 => UNS
* INC # H2: 2,6,7 => UNS
* INC # I2: 3,9 => UNS
* INC # I2: 6,7 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # H2: 7,9 => UNS
* INC # I2: 7,9 => UNS
* DIS # H2: 2,7 => CTR => H2: 3,6,9
* INC H2: 3,6,9 # E6: 1,2 => UNS
* INC H2: 3,6,9 # E6: 4,6 => UNS
* INC H2: 3,6,9 # E8: 1,2 => UNS
* INC H2: 3,6,9 # E8: 4 => UNS
* INC H2: 3,6,9 # A2: 5,6 => UNS
* INC H2: 3,6,9 # A2: 4,7 => UNS
* INC H2: 3,6,9 # B2: 5,6 => UNS
* INC H2: 3,6,9 # B2: 7 => UNS
* INC H2: 3,6,9 # H2: 3,9 => UNS
* INC H2: 3,6,9 # H2: 6 => UNS
* INC H2: 3,6,9 # I2: 3,9 => UNS
* INC H2: 3,6,9 # I2: 6,7 => UNS
* INC H2: 3,6,9 # I2: 7,9 => UNS
* INC H2: 3,6,9 # I2: 3,6 => UNS
* INC H2: 3,6,9 # E6: 1,2 => UNS
* INC H2: 3,6,9 # E6: 4,6 => UNS
* INC H2: 3,6,9 # E8: 1,2 => UNS
* INC H2: 3,6,9 # E8: 4 => UNS
* INC H2: 3,6,9 # A2: 5,6 => UNS
* INC H2: 3,6,9 # A2: 4,7 => UNS
* INC H2: 3,6,9 # B2: 5,6 => UNS
* INC H2: 3,6,9 # B2: 7 => UNS
* INC H2: 3,6,9 # H2: 3,9 => UNS
* INC H2: 3,6,9 # H2: 6 => UNS
* INC H2: 3,6,9 # I2: 3,9 => UNS
* INC H2: 3,6,9 # I2: 6,7 => UNS
* STA H2: 3,6,9
* CNT  29 HDP CHAINS /  29 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # I2: 7,9 => UNS
* INC # I2: 3,6 => UNS
* INC # E6: 1,2 => UNS
* INC # E6: 4,6 => UNS
* INC # E8: 1,2 => UNS
* INC # E8: 4 => UNS
* INC # A2: 5,6 => UNS
* INC # A2: 4,7 => UNS
* INC # B2: 5,6 => UNS
* INC # B2: 7 => UNS
* INC # H2: 3,9 => UNS
* INC # H2: 6 => UNS
* INC # I2: 3,9 => UNS
* INC # I2: 6,7 => UNS
* INC # I2: 7,9 # A5: 1,8 => UNS
* INC # I2: 7,9 # A9: 1,8 => UNS
* INC # I2: 7,9 # B4: 1,8 => UNS
* INC # I2: 7,9 # B7: 1,8 => UNS
* INC # I2: 7,9 # B4: 1,8 => UNS
* INC # I2: 7,9 # A5: 1,8 => UNS
* INC # I2: 7,9 # G6: 1,8 => UNS
* INC # I2: 7,9 # G6: 7 => UNS
* INC # I2: 7,9 # E4: 4,6 => UNS
* INC # I2: 7,9 # E4: 1 => UNS
* INC # I2: 7,9 # E6: 4,6 => UNS
* INC # I2: 7,9 # E6: 1 => UNS
* INC # I2: 7,9 # B7: 1,8 => UNS
* INC # I2: 7,9 # A9: 1,8 => UNS
* INC # I2: 7,9 # F8: 1,8 => UNS
* INC # I2: 7,9 # G8: 1,8 => UNS
* INC # I2: 7,9 => UNS
* INC # I2: 3,6 # H2: 3,6 => UNS
* INC # I2: 3,6 # H2: 9 => UNS
* INC # I2: 3,6 # E6: 1,2 => UNS
* INC # I2: 3,6 # E6: 4,6 => UNS
* INC # I2: 3,6 # E8: 1,2 => UNS
* INC # I2: 3,6 # E8: 4 => UNS
* INC # I2: 3,6 # A2: 5,6 => UNS
* INC # I2: 3,6 # A2: 4,7 => UNS
* INC # I2: 3,6 # B2: 5,6 => UNS
* INC # I2: 3,6 # B2: 7 => UNS
* INC # I2: 3,6 # H2: 3,9 => UNS
* INC # I2: 3,6 # H2: 6 => UNS
* INC # I2: 3,6 => UNS
* INC # E6: 1,2 # I2: 7,9 => UNS
* INC # E6: 1,2 # I2: 3 => UNS
* INC # E6: 1,2 # D5: 7,8 => UNS
* INC # E6: 1,2 # D6: 7,8 => UNS
* INC # E6: 1,2 # B4: 7,8 => UNS
* INC # E6: 1,2 # H4: 7,8 => UNS
* INC # E6: 1,2 # A2: 5,6 => UNS
* INC # E6: 1,2 # A2: 4,7 => UNS
* INC # E6: 1,2 # B2: 5,6 => UNS
* INC # E6: 1,2 # B2: 7 => UNS
* INC # E6: 1,2 # H2: 3,9 => UNS
* INC # E6: 1,2 # H2: 6 => UNS
* INC # E6: 1,2 # I2: 3,9 => UNS
* DIS # E6: 1,2 # I2: 7 => CTR => I2: 3,9
* INC # E6: 1,2 + I2: 3,9 # H2: 3,9 => UNS
* INC # E6: 1,2 + I2: 3,9 # H2: 6 => UNS
* INC # E6: 1,2 + I2: 3,9 # D5: 7,8 => UNS
* INC # E6: 1,2 + I2: 3,9 # D6: 7,8 => UNS
* INC # E6: 1,2 + I2: 3,9 # B4: 7,8 => UNS
* INC # E6: 1,2 + I2: 3,9 # H4: 7,8 => UNS
* INC # E6: 1,2 + I2: 3,9 # A2: 5,6 => UNS
* INC # E6: 1,2 + I2: 3,9 # A2: 4,7 => UNS
* INC # E6: 1,2 + I2: 3,9 # B2: 5,6 => UNS
* INC # E6: 1,2 + I2: 3,9 # B2: 7 => UNS
* INC # E6: 1,2 + I2: 3,9 # H2: 3,9 => UNS
* INC # E6: 1,2 + I2: 3,9 # H2: 6 => UNS
* INC # E6: 1,2 + I2: 3,9 => UNS
* INC # E6: 4,6 # I2: 7,9 => UNS
* INC # E6: 4,6 # I2: 3,6 => UNS
* INC # E6: 4,6 # E8: 1,2 => UNS
* INC # E6: 4,6 # E8: 4 => UNS
* INC # E6: 4,6 # E4: 4,6 => UNS
* INC # E6: 4,6 # E4: 1 => UNS
* INC # E6: 4,6 # I6: 4,6 => UNS
* DIS # E6: 4,6 # I6: 1,7,8 => CTR => I6: 4,6
* INC # E6: 4,6 + I6: 4,6 # E4: 4,6 => UNS
* INC # E6: 4,6 + I6: 4,6 # E4: 1 => UNS
* INC # E6: 4,6 + I6: 4,6 # A2: 5,6 => UNS
* INC # E6: 4,6 + I6: 4,6 # A2: 4,7 => UNS
* INC # E6: 4,6 + I6: 4,6 # B2: 5,6 => UNS
* INC # E6: 4,6 + I6: 4,6 # B2: 7 => UNS
* INC # E6: 4,6 + I6: 4,6 # H2: 3,9 => UNS
* INC # E6: 4,6 + I6: 4,6 # H2: 6 => UNS
* INC # E6: 4,6 + I6: 4,6 # I2: 3,9 => UNS
* INC # E6: 4,6 + I6: 4,6 # I2: 6,7 => UNS
* INC # E6: 4,6 + I6: 4,6 # I2: 7,9 => UNS
* INC # E6: 4,6 + I6: 4,6 # I2: 3,6 => UNS
* INC # E6: 4,6 + I6: 4,6 # E8: 1,2 => UNS
* INC # E6: 4,6 + I6: 4,6 # E8: 4 => UNS
* INC # E6: 4,6 + I6: 4,6 # E4: 4,6 => UNS
* INC # E6: 4,6 + I6: 4,6 # E4: 1 => UNS
* INC # E6: 4,6 + I6: 4,6 # I4: 4,6 => UNS
* INC # E6: 4,6 + I6: 4,6 # I4: 1,7,8 => UNS
* INC # E6: 4,6 + I6: 4,6 # A2: 5,6 => UNS
* INC # E6: 4,6 + I6: 4,6 # A2: 4,7 => UNS
* INC # E6: 4,6 + I6: 4,6 # B2: 5,6 => UNS
* INC # E6: 4,6 + I6: 4,6 # B2: 7 => UNS
* INC # E6: 4,6 + I6: 4,6 # H2: 3,9 => UNS
* INC # E6: 4,6 + I6: 4,6 # H2: 6 => UNS
* INC # E6: 4,6 + I6: 4,6 # I2: 3,9 => UNS
* INC # E6: 4,6 + I6: 4,6 # I2: 6,7 => UNS
* INC # E6: 4,6 + I6: 4,6 => UNS
* INC # E8: 1,2 # I2: 7,9 => UNS
* INC # E8: 1,2 # I2: 3,6 => UNS
* INC # E8: 1,2 # F4: 7,8 => UNS
* DIS # E8: 1,2 # D5: 7,8 => CTR => D5: 2,9
* DIS # E8: 1,2 + D5: 2,9 # F5: 7,8 => CTR => F5: 1,5,9
* INC # E8: 1,2 + D5: 2,9 + F5: 1,5,9 # D6: 7,8 => UNS
* INC # E8: 1,2 + D5: 2,9 + F5: 1,5,9 # F6: 7,8 => UNS
* INC # E8: 1,2 + D5: 2,9 + F5: 1,5,9 # B4: 7,8 => UNS
* INC # E8: 1,2 + D5: 2,9 + F5: 1,5,9 # F4: 7,8 => UNS
* INC # E8: 1,2 + D5: 2,9 + F5: 1,5,9 # H4: 7,8 => UNS
* PRF # E8: 1,2 + D5: 2,9 + F5: 1,5,9 # I4: 7,8 => SOL
* STA # E8: 1,2 + D5: 2,9 + F5: 1,5,9 + I4: 7,8
* CNT 117 HDP CHAINS / 118 HYP OPENED