Analysis of xx-mith-te3-00002943-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: .23.56......18..3....372.4..3.59.46..65....939.463....3.2...9...9.....2..46....5. initial

Autosolve

position: .23.56......18..3....372.4.23.59.46..65....939.463....3.2...9...9.....2..46....5. 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: 0:00:18.812209

The following important HDP chains were detected:

* DIS # B7: 5,7 # G2: 5,7 => CTR => G2: 2,6
* DIS # B7: 5,7 + G2: 2,6 # I2: 5,7 => CTR => I2: 2,6,9
* PRF # B7: 5,7 + G2: 2,6 + I2: 2,6,9 # G3: 1,8 => SOL
* STA # B7: 5,7 + G2: 2,6 + I2: 2,6,9 + G3: 1,8
* CNT   3 HDP CHAINS /  89 HYP OPENED

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

Details

Positions

.23.56......18..3....372.4..3.59.46..65....939.463....3.2...9...9.....2..46....5. initial
.23.56......18..3....372.4.23.59.46..65....939.463....3.2...9...9.....2..46....5. autosolve
123456789457189236689372145238597461765214893914638572372865914591743628846921357 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
B2: 5,7
C2: 7,9
D1: 4,9
F2: 4,9
G6: 2,5
I6: 2,5
E9: 1,2

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G2,I2: 2.. / G2 = 2  =>  5 pairs (_) / I2 = 2  =>  5 pairs (_)
D5,E5: 2.. / D5 = 2  =>  7 pairs (_) / E5 = 2  => 15 pairs (_)
G6,I6: 2.. / G6 = 2  =>  5 pairs (_) / I6 = 2  =>  5 pairs (_)
D9,E9: 2.. / D9 = 2  => 15 pairs (_) / E9 = 2  =>  7 pairs (_)
D5,D9: 2.. / D5 = 2  =>  7 pairs (_) / D9 = 2  => 15 pairs (_)
E5,E9: 2.. / E5 = 2  => 15 pairs (_) / E9 = 2  =>  7 pairs (_)
G2,G6: 2.. / G2 = 2  =>  5 pairs (_) / G6 = 2  =>  5 pairs (_)
I2,I6: 2.. / I2 = 2  =>  5 pairs (_) / I6 = 2  =>  5 pairs (_)
F8,F9: 3.. / F8 = 3  =>  7 pairs (_) / F9 = 3  => 15 pairs (_)
G8,G9: 3.. / G8 = 3  => 15 pairs (_) / G9 = 3  =>  7 pairs (_)
F8,G8: 3.. / F8 = 3  =>  7 pairs (_) / G8 = 3  => 15 pairs (_)
F9,G9: 3.. / F9 = 3  => 15 pairs (_) / G9 = 3  =>  7 pairs (_)
A1,A2: 4.. / A1 = 4  => 12 pairs (_) / A2 = 4  => 14 pairs (_)
D1,F2: 4.. / D1 = 4  => 14 pairs (_) / F2 = 4  => 12 pairs (_)
I7,I8: 4.. / I7 = 4  =>  9 pairs (_) / I8 = 4  =>  9 pairs (_)
A1,D1: 4.. / A1 = 4  => 12 pairs (_) / D1 = 4  => 14 pairs (_)
A2,F2: 4.. / A2 = 4  => 14 pairs (_) / F2 = 4  => 12 pairs (_)
G6,I6: 5.. / G6 = 5  =>  5 pairs (_) / I6 = 5  =>  5 pairs (_)
B7,A8: 5.. / B7 = 5  =>  0 pairs (X) / A8 = 5  =>  7 pairs (_)
F7,F8: 5.. / F7 = 5  =>  7 pairs (_) / F8 = 5  =>  0 pairs (X)
B7,F7: 5.. / B7 = 5  =>  0 pairs (X) / F7 = 5  =>  7 pairs (_)
A8,F8: 5.. / A8 = 5  =>  7 pairs (_) / F8 = 5  =>  0 pairs (X)
A2,A3: 6.. / A2 = 6  => 12 pairs (_) / A3 = 6  => 10 pairs (_)
E7,E8: 6.. / E7 = 6  =>  8 pairs (_) / E8 = 6  => 10 pairs (_)
E7,I7: 6.. / E7 = 6  =>  8 pairs (_) / I7 = 6  => 10 pairs (_)
C2,C3: 9.. / C2 = 9  => 12 pairs (_) / C3 = 9  => 10 pairs (_)
D1,F2: 9.. / D1 = 9  => 12 pairs (_) / F2 = 9  => 14 pairs (_)
D9,F9: 9.. / D9 = 9  => 14 pairs (_) / F9 = 9  => 12 pairs (_)
D1,I1: 9.. / D1 = 9  => 12 pairs (_) / I1 = 9  => 14 pairs (_)
C3,I3: 9.. / C3 = 9  => 10 pairs (_) / I3 = 9  => 12 pairs (_)
D1,D9: 9.. / D1 = 9  => 12 pairs (_) / D9 = 9  => 14 pairs (_)
F2,F9: 9.. / F2 = 9  => 14 pairs (_) / F9 = 9  => 12 pairs (_)
* DURATION: 0:00:08.889514  START: 05:08:17.976667  END: 05:08:26.866181 2025-04-04
* CP COUNT: (32)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:18.594300  START: 05:08:31.189019  END: 05:08:49.783319 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00002943-base-pr-002.dot
* REASONING
* DIS # B7: 5,7 # G2: 5,7 => CTR => G2: 2,6
* DIS # B7: 5,7 + G2: 2,6 # I2: 5,7 => CTR => I2: 2,6,9
* PRF # B7: 5,7 + G2: 2,6 + I2: 2,6,9 # G3: 1,8 => SOL
* STA # B7: 5,7 + G2: 2,6 + I2: 2,6,9 + G3: 1,8
* CNT   3 HDP CHAINS /  89 HYP OPENED

Header Info

rating: 511; r2: 130627; index: 2943

Solution

position: 123456789457189236689372145238597461765214893914638572372865914591743628846921357 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 # A2: 5,7 => UNS
* INC # A2: 4,6 => UNS
* INC # G2: 5,7 => UNS
* INC # I2: 5,7 => UNS
* INC # B7: 5,7 => UNS
* INC # B7: 1,8 => UNS
* INC # I2: 7,9 => UNS
* INC # I2: 2,5,6 => UNS
* INC # G2: 2,5 => UNS
* INC # G2: 6,7 => UNS
* INC # I2: 2,5 => UNS
* INC # I2: 6,7,9 => UNS
* INC # E5: 1,2 => UNS
* INC # E5: 4 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A2: 5,7 => UNS
* INC # A2: 4,6 => UNS
* INC # G2: 5,7 => UNS
* INC # I2: 5,7 => UNS
* INC # B7: 5,7 => UNS
* INC # B7: 1,8 => UNS
* INC # I2: 7,9 => UNS
* INC # I2: 2,5,6 => UNS
* INC # G2: 2,5 => UNS
* INC # G2: 6,7 => UNS
* INC # I2: 2,5 => UNS
* INC # I2: 6,7,9 => UNS
* INC # E5: 1,2 => UNS
* INC # E5: 4 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A2: 5,7 => UNS
* INC # A2: 4,6 => UNS
* INC # G2: 5,7 => UNS
* INC # I2: 5,7 => UNS
* INC # B7: 5,7 => UNS
* INC # B7: 1,8 => UNS
* INC # I2: 7,9 => UNS
* INC # I2: 2,5,6 => UNS
* INC # G2: 2,5 => UNS
* INC # G2: 6,7 => UNS
* INC # I2: 2,5 => UNS
* INC # I2: 6,7,9 => UNS
* INC # E5: 1,2 => UNS
* INC # E5: 4 => UNS
* INC # A2: 5,7 # B6: 1,8 => UNS
* INC # A2: 5,7 # B7: 1,8 => UNS
* INC # A2: 5,7 # C4: 1,8 => UNS
* INC # A2: 5,7 # C8: 1,8 => UNS
* INC # A2: 5,7 # C4: 1,8 => UNS
* INC # A2: 5,7 # B6: 1,8 => UNS
* INC # A2: 5,7 # F5: 1,8 => UNS
* INC # A2: 5,7 # G5: 1,8 => UNS
* INC # A2: 5,7 # B7: 1,8 => UNS
* INC # A2: 5,7 # C8: 1,8 => UNS
* INC # A2: 5,7 # I9: 1,8 => UNS
* INC # A2: 5,7 # I9: 7 => UNS
* INC # A2: 5,7 # E7: 4,6 => UNS
* INC # A2: 5,7 # E7: 1 => UNS
* INC # A2: 5,7 # E8: 4,6 => UNS
* INC # A2: 5,7 # E8: 1 => UNS
* INC # A2: 5,7 => UNS
* INC # A2: 4,6 # G2: 5,7 => UNS
* INC # A2: 4,6 # I2: 5,7 => UNS
* INC # A2: 4,6 # B7: 5,7 => UNS
* INC # A2: 4,6 # B7: 1,8 => UNS
* INC # A2: 4,6 # I2: 7,9 => UNS
* INC # A2: 4,6 # I2: 2,5,6 => UNS
* INC # A2: 4,6 # G2: 2,5 => UNS
* INC # A2: 4,6 # G2: 6,7 => UNS
* INC # A2: 4,6 # I2: 2,5 => UNS
* INC # A2: 4,6 # I2: 6,7,9 => UNS
* INC # A2: 4,6 # E5: 1,2 => UNS
* INC # A2: 4,6 # E5: 4 => UNS
* INC # A2: 4,6 => UNS
* INC # G2: 5,7 # A5: 1,8 => UNS
* INC # G2: 5,7 # A9: 1,8 => UNS
* INC # G2: 5,7 # C4: 1,8 => UNS
* INC # G2: 5,7 # C8: 1,8 => UNS
* INC # G2: 5,7 # C4: 1,8 => UNS
* INC # G2: 5,7 # A5: 1,8 => UNS
* INC # G2: 5,7 # F6: 1,8 => UNS
* INC # G2: 5,7 # H6: 1,8 => UNS
* INC # G2: 5,7 # C8: 1,8 => UNS
* INC # G2: 5,7 # A9: 1,8 => UNS
* INC # G2: 5,7 # H7: 1,8 => UNS
* INC # G2: 5,7 # H7: 7 => UNS
* INC # G2: 5,7 # E7: 4,6 => UNS
* INC # G2: 5,7 # E7: 1 => UNS
* INC # G2: 5,7 # E8: 4,6 => UNS
* INC # G2: 5,7 # E8: 1 => UNS
* INC # G2: 5,7 => UNS
* INC # I2: 5,7 # A5: 1,8 => UNS
* INC # I2: 5,7 # A9: 1,8 => UNS
* INC # I2: 5,7 # C4: 1,8 => UNS
* INC # I2: 5,7 # C8: 1,8 => UNS
* INC # I2: 5,7 # C4: 1,8 => UNS
* INC # I2: 5,7 # A5: 1,8 => UNS
* INC # I2: 5,7 # F6: 1,8 => UNS
* INC # I2: 5,7 # H6: 1,8 => UNS
* INC # I2: 5,7 # C8: 1,8 => UNS
* INC # I2: 5,7 # A9: 1,8 => UNS
* INC # I2: 5,7 # H7: 1,8 => UNS
* INC # I2: 5,7 # H7: 7 => UNS
* INC # I2: 5,7 # E7: 4,6 => UNS
* INC # I2: 5,7 # E7: 1 => UNS
* INC # I2: 5,7 # E8: 4,6 => UNS
* INC # I2: 5,7 # E8: 1 => UNS
* INC # I2: 5,7 => UNS
* INC # B7: 5,7 # A2: 5,7 => UNS
* INC # B7: 5,7 # A2: 4,6 => UNS
* DIS # B7: 5,7 # G2: 5,7 => CTR => G2: 2,6
* DIS # B7: 5,7 + G2: 2,6 # I2: 5,7 => CTR => I2: 2,6,9
* INC # B7: 5,7 + G2: 2,6 + I2: 2,6,9 # A2: 5,7 => UNS
* INC # B7: 5,7 + G2: 2,6 + I2: 2,6,9 # A2: 4,6 => UNS
* INC # B7: 5,7 + G2: 2,6 + I2: 2,6,9 # A1: 1,8 => UNS
* INC # B7: 5,7 + G2: 2,6 + I2: 2,6,9 # A3: 1,8 => UNS
* INC # B7: 5,7 + G2: 2,6 + I2: 2,6,9 # C3: 1,8 => UNS
* PRF # B7: 5,7 + G2: 2,6 + I2: 2,6,9 # G3: 1,8 => SOL
* STA # B7: 5,7 + G2: 2,6 + I2: 2,6,9 + G3: 1,8
* CNT  88 HDP CHAINS /  89 HYP OPENED