Analysis of xx-mith-te3-00007338-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 12.456...4.........98....4....7.4.6.7..62...4....15.72.6..47.15...2......7.56..2. initial

Autosolve

position: 12.456...4.........98....4....7.4.6.7..62...4....15.72.6..47.15...2......7.56.42. 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: 0:00:19.010322

The following important HDP chains were detected:

* DIS # B4: 3,5 # G4: 3,5 => CTR => G4: 1,8,9
* DIS # B4: 3,5 + G4: 1,8,9 # G5: 1,8 => CTR => G5: 3,5,9
* PRF # B4: 3,5 + G4: 1,8,9 + G5: 3,5,9 # B8: 1,8 => SOL
* STA # B4: 3,5 + G4: 1,8,9 + G5: 3,5,9 + B8: 1,8
* CNT   3 HDP CHAINS /  67 HYP OPENED

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

Details

Positions

12.456...4.........98....4....7.4.6.7..62...4....15.72.6..47.15...2......7.56..2. initial
12.456...4.........98....4....7.4.6.7..62...4....15.72.6..47.15...2......7.56.42. autosolve
123456789457189236698372541235794168781623954946815372362947815514238697879561423 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
C1: 3,7
B2: 3,5
C2: 6,7
A3: 5,6
D3: 1,3
E3: 3,7
F3: 2,3
H2: 3,5
G8: 6,7
I8: 6,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D2,D3: 1.. / D2 = 1  => 13 pairs (_) / D3 = 1  => 11 pairs (_)
I2,I3: 1.. / I2 = 1  => 11 pairs (_) / I3 = 1  => 13 pairs (_)
G4,G5: 1.. / G4 = 1  => 10 pairs (_) / G5 = 1  => 10 pairs (_)
F8,F9: 1.. / F8 = 1  => 10 pairs (_) / F9 = 1  =>  0 pairs (*)
D2,I2: 1.. / D2 = 1  => 13 pairs (_) / I2 = 1  => 11 pairs (_)
D3,I3: 1.. / D3 = 1  => 11 pairs (_) / I3 = 1  => 13 pairs (_)
C9,F9: 1.. / C9 = 1  => 10 pairs (_) / F9 = 1  =>  0 pairs (*)
F2,F3: 2.. / F2 = 2  =>  9 pairs (_) / F3 = 2  => 10 pairs (_)
G2,G3: 2.. / G2 = 2  => 10 pairs (_) / G3 = 2  =>  9 pairs (_)
A4,C4: 2.. / A4 = 2  => 10 pairs (_) / C4 = 2  => 11 pairs (_)
A7,C7: 2.. / A7 = 2  => 11 pairs (_) / C7 = 2  => 10 pairs (_)
F2,G2: 2.. / F2 = 2  =>  9 pairs (_) / G2 = 2  => 10 pairs (_)
F3,G3: 2.. / F3 = 2  => 10 pairs (_) / G3 = 2  =>  9 pairs (_)
A4,A7: 2.. / A4 = 2  => 10 pairs (_) / A7 = 2  => 11 pairs (_)
C4,C7: 2.. / C4 = 2  => 11 pairs (_) / C7 = 2  => 10 pairs (_)
C1,B2: 3.. / C1 = 3  =>  9 pairs (_) / B2 = 3  => 12 pairs (_)
B2,H2: 3.. / B2 = 3  => 12 pairs (_) / H2 = 3  =>  9 pairs (_)
B6,C6: 4.. / B6 = 4  => 10 pairs (_) / C6 = 4  => 14 pairs (_)
B8,C8: 4.. / B8 = 4  => 14 pairs (_) / C8 = 4  => 10 pairs (_)
B6,B8: 4.. / B6 = 4  => 10 pairs (_) / B8 = 4  => 14 pairs (_)
C6,C8: 4.. / C6 = 4  => 14 pairs (_) / C8 = 4  => 10 pairs (_)
B2,A3: 5.. / B2 = 5  =>  9 pairs (_) / A3 = 5  => 12 pairs (_)
H2,G3: 5.. / H2 = 5  => 12 pairs (_) / G3 = 5  =>  9 pairs (_)
B2,H2: 5.. / B2 = 5  =>  9 pairs (_) / H2 = 5  => 12 pairs (_)
A3,G3: 5.. / A3 = 5  => 12 pairs (_) / G3 = 5  =>  9 pairs (_)
H2,H5: 5.. / H2 = 5  => 12 pairs (_) / H5 = 5  =>  9 pairs (_)
C2,A3: 6.. / C2 = 6  => 12 pairs (_) / A3 = 6  =>  9 pairs (_)
A6,C6: 6.. / A6 = 6  => 12 pairs (_) / C6 = 6  =>  9 pairs (_)
G8,I8: 6.. / G8 = 6  => 11 pairs (_) / I8 = 6  => 10 pairs (_)
A3,A6: 6.. / A3 = 6  =>  9 pairs (_) / A6 = 6  => 12 pairs (_)
C2,C6: 6.. / C2 = 6  => 12 pairs (_) / C6 = 6  =>  9 pairs (_)
C1,C2: 7.. / C1 = 7  => 12 pairs (_) / C2 = 7  =>  9 pairs (_)
E2,E3: 7.. / E2 = 7  => 13 pairs (_) / E3 = 7  => 11 pairs (_)
G8,I8: 7.. / G8 = 7  => 10 pairs (_) / I8 = 7  => 11 pairs (_)
C1,G1: 7.. / C1 = 7  => 12 pairs (_) / G1 = 7  =>  9 pairs (_)
* DURATION: 0:00:13.019945  START: 05:59:00.135986  END: 05:59:13.155931 2025-04-04
* CP COUNT: (35)
* SOLUTION FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:18.823224  START: 05:59:19.133854  END: 05:59:37.957078 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00007338-base-pr-002.dot
* REASONING
* DIS # B4: 3,5 # G4: 3,5 => CTR => G4: 1,8,9
* DIS # B4: 3,5 + G4: 1,8,9 # G5: 1,8 => CTR => G5: 3,5,9
* PRF # B4: 3,5 + G4: 1,8,9 + G5: 3,5,9 # B8: 1,8 => SOL
* STA # B4: 3,5 + G4: 1,8,9 + G5: 3,5,9 + B8: 1,8
* CNT   3 HDP CHAINS /  67 HYP OPENED

Header Info

rating: 1633; r2: 26289; index: 7338

Solution

position: 123456789457189236698372541235794168781623954946815372362947815514238697879561423 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 # G1: 3,7 => UNS
* INC # G1: 8,9 => UNS
* INC # B4: 3,5 => UNS
* INC # B5: 3,5 => UNS
* INC # B8: 3,5 => UNS
* INC # G2: 6,7 => UNS
* INC # I2: 6,7 => UNS
* INC # G3: 5,6 => UNS
* INC # G3: 2,7 => UNS
* INC # H5: 3,5 => UNS
* INC # H5: 8,9 => UNS
* INC # G2: 6,7 => UNS
* INC # G3: 6,7 => UNS
* INC # I2: 6,7 => UNS
* INC # I3: 6,7 => UNS
* CNT  15 HDP CHAINS /  15 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G1: 3,7 => UNS
* INC # G1: 8,9 => UNS
* INC # B4: 3,5 => UNS
* INC # B5: 3,5 => UNS
* INC # B8: 3,5 => UNS
* INC # G2: 6,7 => UNS
* INC # I2: 6,7 => UNS
* INC # G3: 5,6 => UNS
* INC # G3: 2,7 => UNS
* INC # H5: 3,5 => UNS
* INC # H5: 8,9 => UNS
* INC # G2: 6,7 => UNS
* INC # G3: 6,7 => UNS
* INC # I2: 6,7 => UNS
* INC # I3: 6,7 => UNS
* CNT  15 HDP CHAINS /  15 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # G1: 3,7 => UNS
* INC # G1: 8,9 => UNS
* INC # B4: 3,5 => UNS
* INC # B5: 3,5 => UNS
* INC # B8: 3,5 => UNS
* INC # G2: 6,7 => UNS
* INC # I2: 6,7 => UNS
* INC # G3: 5,6 => UNS
* INC # G3: 2,7 => UNS
* INC # H5: 3,5 => UNS
* INC # H5: 8,9 => UNS
* INC # G2: 6,7 => UNS
* INC # G3: 6,7 => UNS
* INC # I2: 6,7 => UNS
* INC # I3: 6,7 => UNS
* INC # G1: 3,7 # B4: 3,5 => UNS
* INC # G1: 3,7 # B5: 3,5 => UNS
* INC # G1: 3,7 # B8: 3,5 => UNS
* INC # G1: 3,7 # G2: 6,7 => UNS
* INC # G1: 3,7 # I2: 6,7 => UNS
* INC # G1: 3,7 # G3: 5,6 => UNS
* INC # G1: 3,7 # G3: 2,7 => UNS
* INC # G1: 3,7 # H5: 8,9 => UNS
* INC # G1: 3,7 # H8: 8,9 => UNS
* INC # G1: 3,7 # I4: 8,9 => UNS
* INC # G1: 3,7 # I9: 8,9 => UNS
* INC # G1: 3,7 # H5: 3,5 => UNS
* INC # G1: 3,7 # H5: 8,9 => UNS
* INC # G1: 3,7 # G2: 6,7 => UNS
* INC # G1: 3,7 # G3: 6,7 => UNS
* INC # G1: 3,7 # I2: 6,7 => UNS
* INC # G1: 3,7 # I3: 6,7 => UNS
* INC # G1: 3,7 => UNS
* INC # G1: 8,9 # H1: 8,9 => UNS
* INC # G1: 8,9 # I1: 8,9 => UNS
* INC # G1: 8,9 # G6: 8,9 => UNS
* INC # G1: 8,9 # G7: 8,9 => UNS
* INC # G1: 8,9 # G3: 2,7 => UNS
* INC # G1: 8,9 # G3: 6 => UNS
* INC # G1: 8,9 # I3: 1,7 => UNS
* INC # G1: 8,9 # I3: 6 => UNS
* INC # G1: 8,9 # B4: 1,5 => UNS
* INC # G1: 8,9 # B4: 8 => UNS
* INC # G1: 8,9 # B5: 1,5 => UNS
* INC # G1: 8,9 # B5: 8 => UNS
* INC # G1: 8,9 # G3: 6,7 => UNS
* INC # G1: 8,9 # G3: 2 => UNS
* INC # G1: 8,9 # I3: 6,7 => UNS
* INC # G1: 8,9 # I3: 1 => UNS
* INC # G1: 8,9 => UNS
* INC # B4: 3,5 # G1: 3,7 => UNS
* INC # B4: 3,5 # G1: 8,9 => UNS
* INC # B4: 3,5 # G2: 6,7 => UNS
* INC # B4: 3,5 # I2: 6,7 => UNS
* INC # B4: 3,5 # G3: 5,6 => UNS
* INC # B4: 3,5 # G3: 2,7 => UNS
* INC # B4: 3,5 # H5: 3,5 => UNS
* INC # B4: 3,5 # H5: 8,9 => UNS
* INC # B4: 3,5 # A4: 3,5 => UNS
* INC # B4: 3,5 # C4: 3,5 => UNS
* INC # B4: 3,5 # C5: 3,5 => UNS
* DIS # B4: 3,5 # G4: 3,5 => CTR => G4: 1,8,9
* INC # B4: 3,5 + G4: 1,8,9 # A4: 3,5 => UNS
* INC # B4: 3,5 + G4: 1,8,9 # C4: 3,5 => UNS
* DIS # B4: 3,5 + G4: 1,8,9 # G5: 1,8 => CTR => G5: 3,5,9
* PRF # B4: 3,5 + G4: 1,8,9 + G5: 3,5,9 # B8: 1,8 => SOL
* STA # B4: 3,5 + G4: 1,8,9 + G5: 3,5,9 + B8: 1,8
* CNT  66 HDP CHAINS /  67 HYP OPENED