Analysis of xx-mith-te3-00157878-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 12....78..567.....79813....2...7.3.88...21.47...8.321..4..1.87.....4..32......... initial

Autosolve

position: 12....78..567.....79813....2...7.3.88...21.47...8.321..4..1.87.....4..32......... 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: 0:00:20.159509

The following important HDP chains were detected:

* DIS # I1: 3,4 # B9: 1,6 => CTR => B9: 3,7,8
* DIS # I1: 5,6,9 # F2: 8 => CTR => F2: 2,9
* DIS # I1: 5,6,9 + F2: 2,9 # C4: 5,9 => CTR => C4: 1
* DIS # I1: 5,6,9 + F2: 2,9 + C4: 1 # G8: 5,6 => CTR => G8: 9
* DIS # I1: 5,6,9 + F2: 2,9 + C4: 1 + G8: 9 # I1: 5,6 => CTR => I1: 9
* PRF # I1: 5,6,9 + F2: 2,9 + C4: 1 + G8: 9 + I1: 9 => SOL
* STA I1: 5,6,9
* CNT   6 HDP CHAINS /  82 HYP OPENED

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

Details

Positions

12....78..567.....79813....2...7.3.88...21.47...8.321..4..1.87.....4..32......... initial
12....78..567.....79813....2...7.3.88...21.47...8.321..4..1.87.....4..32......... autosolve
123456789456789123798132564261574398835921647974863215349215876517648932682397451 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
C1: 3,4
A2: 3,4
E2: 8,9
H2: 2,9
B4: 1,6
B5: 3,6
B6: 6,7
D7: 2,3
D9: 2,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G2,I2: 1.. / G2 = 1  => 12 pairs (_) / I2 = 1  => 14 pairs (_)
B4,C4: 1.. / B4 = 1  =>  9 pairs (_) / C4 = 1  => 10 pairs (_)
I2,I9: 1.. / I2 = 1  => 14 pairs (_) / I9 = 1  => 12 pairs (_)
F2,F3: 2.. / F2 = 2  => 12 pairs (_) / F3 = 2  => 11 pairs (_)
H2,H3: 2.. / H2 = 2  => 11 pairs (_) / H3 = 2  => 12 pairs (_)
C7,C9: 2.. / C7 = 2  =>  7 pairs (_) / C9 = 2  =>  8 pairs (_)
D7,D9: 2.. / D7 = 2  =>  8 pairs (_) / D9 = 2  =>  7 pairs (_)
F2,H2: 2.. / F2 = 2  => 12 pairs (_) / H2 = 2  => 11 pairs (_)
F3,H3: 2.. / F3 = 2  => 11 pairs (_) / H3 = 2  => 12 pairs (_)
C7,D7: 2.. / C7 = 2  =>  7 pairs (_) / D7 = 2  =>  8 pairs (_)
C9,D9: 2.. / C9 = 2  =>  8 pairs (_) / D9 = 2  =>  7 pairs (_)
C1,A2: 3.. / C1 = 3  => 11 pairs (_) / A2 = 3  => 14 pairs (_)
I1,I2: 3.. / I1 = 3  => 14 pairs (_) / I2 = 3  => 11 pairs (_)
B5,C5: 3.. / B5 = 3  =>  9 pairs (_) / C5 = 3  =>  9 pairs (_)
D7,D9: 3.. / D7 = 3  =>  7 pairs (_) / D9 = 3  =>  8 pairs (_)
C1,I1: 3.. / C1 = 3  => 11 pairs (_) / I1 = 3  => 14 pairs (_)
A2,I2: 3.. / A2 = 3  => 14 pairs (_) / I2 = 3  => 11 pairs (_)
B5,B9: 3.. / B5 = 3  =>  9 pairs (_) / B9 = 3  =>  9 pairs (_)
C1,A2: 4.. / C1 = 4  => 14 pairs (_) / A2 = 4  => 11 pairs (_)
A6,C6: 4.. / A6 = 4  => 14 pairs (_) / C6 = 4  => 11 pairs (_)
D4,F4: 4.. / D4 = 4  =>  9 pairs (_) / F4 = 4  => 11 pairs (_)
G9,I9: 4.. / G9 = 4  => 11 pairs (_) / I9 = 4  => 14 pairs (_)
A2,A6: 4.. / A2 = 4  => 11 pairs (_) / A6 = 4  => 14 pairs (_)
C1,C6: 4.. / C1 = 4  => 14 pairs (_) / C6 = 4  => 11 pairs (_)
D1,D4: 4.. / D1 = 4  => 11 pairs (_) / D4 = 4  =>  9 pairs (_)
B6,C6: 7.. / B6 = 7  =>  8 pairs (_) / C6 = 7  => 17 pairs (_)
F8,F9: 7.. / F8 = 7  =>  9 pairs (_) / F9 = 7  =>  9 pairs (_)
E2,F2: 8.. / E2 = 8  => 10 pairs (_) / F2 = 8  =>  0 pairs (X)
B8,B9: 8.. / B8 = 8  =>  9 pairs (_) / B9 = 8  =>  8 pairs (_)
B8,F8: 8.. / B8 = 8  =>  9 pairs (_) / F8 = 8  =>  8 pairs (_)
E2,E9: 8.. / E2 = 8  => 10 pairs (_) / E9 = 8  =>  0 pairs (X)
* DURATION: 0:00:08.118574  START: 15:52:45.558013  END: 15:52:53.676587 2025-04-05
* CP COUNT: (31)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:19.985347  START: 15:52:59.610885  END: 15:53:19.596232 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00157878-base-pr-002.dot
* REASONING
* DIS # I1: 3,4 # B9: 1,6 => CTR => B9: 3,7,8
* DIS # I1: 5,6,9 # F2: 8 => CTR => F2: 2,9
* DIS # I1: 5,6,9 + F2: 2,9 # C4: 5,9 => CTR => C4: 1
* DIS # I1: 5,6,9 + F2: 2,9 + C4: 1 # G8: 5,6 => CTR => G8: 9
* DIS # I1: 5,6,9 + F2: 2,9 + C4: 1 + G8: 9 # I1: 5,6 => CTR => I1: 9
* PRF # I1: 5,6,9 + F2: 2,9 + C4: 1 + G8: 9 + I1: 9 => SOL
* STA I1: 5,6,9
* CNT   6 HDP CHAINS /  82 HYP OPENED

Header Info

rating: 44062; r2: 836636; index: 157878

Solution

position: 123456789456789123798132564261574398835921647974863215349215876517648932682397451 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 # I1: 3,4 => UNS
* INC # I1: 5,6,9 => UNS
* INC # I2: 3,4 => UNS
* INC # I2: 1,9 => UNS
* INC # F2: 8,9 => UNS
* INC # F2: 2,4 => UNS
* INC # E9: 8,9 => UNS
* INC # E9: 5,6 => UNS
* INC # F2: 2,9 => UNS
* INC # F2: 4,8 => UNS
* INC # B8: 1,6 => UNS
* INC # B9: 1,6 => UNS
* INC # B9: 3,6 => UNS
* INC # B9: 1,7,8 => UNS
* INC # B8: 6,7 => UNS
* INC # B9: 6,7 => UNS
* INC # C7: 2,3 => UNS
* INC # C7: 5,9 => UNS
* INC # C9: 2,3 => UNS
* INC # C9: 1,5,7,9 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # I1: 3,4 => UNS
* INC # I1: 5,6,9 => UNS
* INC # I2: 3,4 => UNS
* INC # I2: 1,9 => UNS
* INC # F2: 8,9 => UNS
* INC # F2: 2,4 => UNS
* INC # E9: 8,9 => UNS
* INC # E9: 5,6 => UNS
* INC # F2: 2,9 => UNS
* INC # F2: 4,8 => UNS
* INC # B8: 1,6 => UNS
* INC # B9: 1,6 => UNS
* INC # B9: 3,6 => UNS
* INC # B9: 1,7,8 => UNS
* INC # B8: 6,7 => UNS
* INC # B9: 6,7 => UNS
* INC # C7: 2,3 => UNS
* INC # C7: 5,9 => UNS
* INC # C9: 2,3 => UNS
* INC # C9: 1,5,7,9 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # I1: 3,4 => UNS
* INC # I1: 5,6,9 => UNS
* INC # I2: 3,4 => UNS
* INC # I2: 1,9 => UNS
* INC # F2: 8,9 => UNS
* INC # F2: 2,4 => UNS
* INC # E9: 8,9 => UNS
* INC # E9: 5,6 => UNS
* INC # F2: 2,9 => UNS
* INC # F2: 4,8 => UNS
* INC # B8: 1,6 => UNS
* INC # B9: 1,6 => UNS
* INC # B9: 3,6 => UNS
* INC # B9: 1,7,8 => UNS
* INC # B8: 6,7 => UNS
* INC # B9: 6,7 => UNS
* INC # C7: 2,3 => UNS
* INC # C7: 5,9 => UNS
* INC # C9: 2,3 => UNS
* INC # C9: 1,5,7,9 => UNS
* INC # I1: 3,4 # I2: 3,4 => UNS
* INC # I1: 3,4 # I2: 1,9 => UNS
* INC # I1: 3,4 # I2: 3,4 => UNS
* INC # I1: 3,4 # I2: 1,9 => UNS
* INC # I1: 3,4 # B8: 1,6 => UNS
* DIS # I1: 3,4 # B9: 1,6 => CTR => B9: 3,7,8
* INC # I1: 3,4 + B9: 3,7,8 # B8: 1,6 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # B8: 7,8 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # B8: 1,6 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # B8: 7,8 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # B8: 6,7 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # B8: 1,8 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # C7: 2,3 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # C7: 5,9 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # B8: 7,8 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # B8: 1,6 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # C9: 2,3 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # C9: 1,5,7,9 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # B9: 7,8 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # B9: 3 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # I2: 3,4 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # I2: 1,9 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # I2: 3,4 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # I2: 1,9 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # B8: 1,6 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # B8: 7,8 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # B8: 6,7 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # B8: 1,8 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # C7: 2,3 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # C7: 5,9 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # B8: 7,8 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # B8: 1,6 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # C9: 2,3 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # C9: 1,5,7,9 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # B9: 7,8 => UNS
* INC # I1: 3,4 + B9: 3,7,8 # B9: 3 => UNS
* INC # I1: 3,4 + B9: 3,7,8 => UNS
* INC # I1: 5,6,9 # F2: 8,9 => UNS
* INC # I1: 5,6,9 # F2: 2 => UNS
* INC # I1: 5,6,9 # E9: 8,9 => UNS
* INC # I1: 5,6,9 # E9: 5,6 => UNS
* INC # I1: 5,6,9 # F2: 2,9 => UNS
* DIS # I1: 5,6,9 # F2: 8 => CTR => F2: 2,9
* INC # I1: 5,6,9 + F2: 2,9 # I1: 5,6 => UNS
* INC # I1: 5,6,9 + F2: 2,9 # H3: 5,6 => UNS
* INC # I1: 5,6,9 + F2: 2,9 # F3: 5,6 => UNS
* INC # I1: 5,6,9 + F2: 2,9 # F3: 2 => UNS
* INC # I1: 5,6,9 + F2: 2,9 # G5: 5,6 => UNS
* INC # I1: 5,6,9 + F2: 2,9 # G8: 5,6 => UNS
* DIS # I1: 5,6,9 + F2: 2,9 # C4: 5,9 => CTR => C4: 1
* INC # I1: 5,6,9 + F2: 2,9 + C4: 1 # D5: 5,9 => UNS
* INC # I1: 5,6,9 + F2: 2,9 + C4: 1 # G5: 5,9 => UNS
* INC # I1: 5,6,9 + F2: 2,9 + C4: 1 # C7: 5,9 => UNS
* INC # I1: 5,6,9 + F2: 2,9 + C4: 1 # C9: 5,9 => UNS
* INC # I1: 5,6,9 + F2: 2,9 + C4: 1 # I1: 5,6 => UNS
* INC # I1: 5,6,9 + F2: 2,9 + C4: 1 # H3: 5,6 => UNS
* INC # I1: 5,6,9 + F2: 2,9 + C4: 1 # F3: 5,6 => UNS
* INC # I1: 5,6,9 + F2: 2,9 + C4: 1 # F3: 2 => UNS
* INC # I1: 5,6,9 + F2: 2,9 + C4: 1 # G5: 5,6 => UNS
* DIS # I1: 5,6,9 + F2: 2,9 + C4: 1 # G8: 5,6 => CTR => G8: 9
* DIS # I1: 5,6,9 + F2: 2,9 + C4: 1 + G8: 9 # I1: 5,6 => CTR => I1: 9
* PRF # I1: 5,6,9 + F2: 2,9 + C4: 1 + G8: 9 + I1: 9 => SOL
* STA I1: 5,6,9
* CNT  82 HDP CHAINS /  82 HYP OPENED