Analysis of xx-mith-te3-00134325-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: ...45..8.4.......6...23.1.42.9......34..2.....659........3.2...6.2.45.9..34.9.52. initial

Autosolve

position: ...45..8.4.......6...23.1.42.9.6....34..2.....659........3.2...6.2.45.9..3469.52. 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: 0:00:29.467476

The following important HDP chains were detected:

* DIS # H2: 3 # G6: 8 => CTR => G6: 3,4
* DIS # H2: 3 + G6: 3,4 # E6: 8 => CTR => E6: 1,7
* DIS # H2: 3 + G6: 3,4 + E6: 1,7 # H5: 1,7 => CTR => H5: 6
* DIS # H2: 3 + G6: 3,4 + E6: 1,7 + H5: 6 # D2: 7,8 => CTR => D2: 1
* PRF # H2: 3 + G6: 3,4 + E6: 1,7 + H5: 6 + D2: 1 # F5: 7,8 => SOL
* STA # H2: 3 + G6: 3,4 + E6: 1,7 + H5: 6 + D2: 1 + F5: 7,8
* CNT   5 HDP CHAINS /  74 HYP OPENED

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

Details

Positions

...45..8.4.......6...23.1.42.9......34..2.....659........3.2...6.2.45.9..34.9.52. initial
...45..8.4.......6...23.1.42.9.6....34..2.....659........3.2...6.2.45.9..3469.52. autosolve
123456789457189236986237154279564813341728965865913472598372641612845397734691528 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
H3: 5,7
F4: 3,4
F6: 3,4
A7: 5,9
B7: 5,9
G7: 4,6
H7: 4,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B1,B2: 2.. / B1 = 2  =>  9 pairs (_) / B2 = 2  =>  9 pairs (_)
G6,I6: 2.. / G6 = 2  => 13 pairs (_) / I6 = 2  =>  7 pairs (_)
B2,G2: 2.. / B2 = 2  =>  9 pairs (_) / G2 = 2  =>  9 pairs (_)
I1,I6: 2.. / I1 = 2  => 13 pairs (_) / I6 = 2  =>  7 pairs (_)
C1,C2: 3.. / C1 = 3  => 14 pairs (_) / C2 = 3  => 10 pairs (_)
F4,F6: 3.. / F4 = 3  =>  5 pairs (_) / F6 = 3  =>  5 pairs (_)
G8,I8: 3.. / G8 = 3  => 10 pairs (_) / I8 = 3  =>  8 pairs (_)
F4,F6: 4.. / F4 = 4  =>  5 pairs (_) / F6 = 4  =>  5 pairs (_)
G7,H7: 4.. / G7 = 4  =>  6 pairs (_) / H7 = 4  =>  5 pairs (_)
H2,H3: 5.. / H2 = 5  =>  8 pairs (_) / H3 = 5  =>  7 pairs (_)
D4,D5: 5.. / D4 = 5  =>  7 pairs (_) / D5 = 5  =>  7 pairs (_)
I4,I5: 5.. / I4 = 5  =>  7 pairs (_) / I5 = 5  =>  7 pairs (_)
A7,B7: 5.. / A7 = 5  =>  5 pairs (_) / B7 = 5  =>  8 pairs (_)
B2,H2: 5.. / B2 = 5  =>  7 pairs (_) / H2 = 5  =>  8 pairs (_)
D4,I4: 5.. / D4 = 5  =>  7 pairs (_) / I4 = 5  =>  7 pairs (_)
D5,I5: 5.. / D5 = 5  =>  7 pairs (_) / I5 = 5  =>  7 pairs (_)
A3,A7: 5.. / A3 = 5  =>  8 pairs (_) / A7 = 5  =>  5 pairs (_)
C1,C3: 6.. / C1 = 6  => 13 pairs (_) / C3 = 6  =>  7 pairs (_)
F1,F3: 6.. / F1 = 6  =>  7 pairs (_) / F3 = 6  => 13 pairs (_)
G5,H5: 6.. / G5 = 6  =>  6 pairs (_) / H5 = 6  =>  5 pairs (_)
G7,H7: 6.. / G7 = 6  =>  5 pairs (_) / H7 = 6  =>  6 pairs (_)
C1,F1: 6.. / C1 = 6  => 13 pairs (_) / F1 = 6  =>  7 pairs (_)
C3,F3: 6.. / C3 = 6  =>  7 pairs (_) / F3 = 6  => 13 pairs (_)
G5,G7: 6.. / G5 = 6  =>  6 pairs (_) / G7 = 6  =>  5 pairs (_)
H5,H7: 6.. / H5 = 6  =>  5 pairs (_) / H7 = 6  =>  6 pairs (_)
G5,I5: 9.. / G5 = 9  =>  7 pairs (_) / I5 = 9  =>  7 pairs (_)
A7,B7: 9.. / A7 = 9  =>  8 pairs (_) / B7 = 9  =>  5 pairs (_)
I1,I5: 9.. / I1 = 9  =>  7 pairs (_) / I5 = 9  =>  7 pairs (_)
* DURATION: 0:00:09.403309  START: 20:15:27.042795  END: 20:15:36.446104 2025-04-06
* CP COUNT: (28)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:29.302175  START: 20:15:41.169964  END: 20:16:10.472139 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00134325-base-pr-002.dot
* REASONING
* DIS # H2: 3 # G6: 8 => CTR => G6: 3,4
* DIS # H2: 3 + G6: 3,4 # E6: 8 => CTR => E6: 1,7
* DIS # H2: 3 + G6: 3,4 + E6: 1,7 # H5: 1,7 => CTR => H5: 6
* DIS # H2: 3 + G6: 3,4 + E6: 1,7 + H5: 6 # D2: 7,8 => CTR => D2: 1
* PRF # H2: 3 + G6: 3,4 + E6: 1,7 + H5: 6 + D2: 1 # F5: 7,8 => SOL
* STA # H2: 3 + G6: 3,4 + E6: 1,7 + H5: 6 + D2: 1 + F5: 7,8
* CNT   5 HDP CHAINS /  74 HYP OPENED

Header Info

rating: 35621; r2: 652815; index: 134325

Solution

position: 123456789457189236986237154279564813341728965865913472598372641612845397734691528 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: 5,7 => UNS
* INC # H2: 3 => UNS
* INC # A3: 5,7 => UNS
* INC # B3: 5,7 => UNS
* INC # G4: 3,4 => UNS
* INC # H4: 3,4 => UNS
* INC # G6: 3,4 => UNS
* INC # H6: 3,4 => UNS
* INC # A3: 5,9 => UNS
* INC # A3: 7,8 => UNS
* INC # B2: 5,9 => UNS
* INC # B3: 5,9 => UNS
* CNT  12 HDP CHAINS /  12 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # H2: 5,7 => UNS
* INC # H2: 3 => UNS
* INC # A3: 5,7 => UNS
* INC # B3: 5,7 => UNS
* INC # G4: 3,4 => UNS
* INC # H4: 3,4 => UNS
* INC # G6: 3,4 => UNS
* INC # H6: 3,4 => UNS
* INC # A3: 5,9 => UNS
* INC # A3: 7,8 => UNS
* INC # B2: 5,9 => UNS
* INC # B3: 5,9 => UNS
* CNT  12 HDP CHAINS /  12 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # H2: 5,7 => UNS
* INC # H2: 3 => UNS
* INC # A3: 5,7 => UNS
* INC # B3: 5,7 => UNS
* INC # G4: 3,4 => UNS
* INC # H4: 3,4 => UNS
* INC # G6: 3,4 => UNS
* INC # H6: 3,4 => UNS
* INC # A3: 5,9 => UNS
* INC # A3: 7,8 => UNS
* INC # B2: 5,9 => UNS
* INC # B3: 5,9 => UNS
* INC # H2: 5,7 # B2: 5,7 => UNS
* INC # H2: 5,7 # B2: 1,2,8,9 => UNS
* INC # H2: 5,7 # A3: 5,7 => UNS
* INC # H2: 5,7 # B3: 5,7 => UNS
* INC # H2: 5,7 # H4: 3,4 => UNS
* INC # H2: 5,7 # H4: 1 => UNS
* INC # H2: 5,7 # H6: 3,4 => UNS
* INC # H2: 5,7 # H6: 1 => UNS
* INC # H2: 5,7 # A3: 5,9 => UNS
* INC # H2: 5,7 # A3: 7,8 => UNS
* INC # H2: 5,7 # B2: 5,9 => UNS
* INC # H2: 5,7 # B3: 5,9 => UNS
* INC # H2: 5,7 => UNS
* INC # H2: 3 # D2: 7,8 => UNS
* INC # H2: 3 # E2: 7,8 => UNS
* INC # H2: 3 # C5: 7,8 => UNS
* INC # H2: 3 # C7: 7,8 => UNS
* INC # H2: 3 # B4: 7,8 => UNS
* INC # H2: 3 # B8: 7,8 => UNS
* INC # H2: 3 # D2: 7,8 => UNS
* INC # H2: 3 # E2: 7,8 => UNS
* INC # H2: 3 # F5: 7,8 => UNS
* INC # H2: 3 # F9: 7,8 => UNS
* INC # H2: 3 # B4: 7,8 => UNS
* INC # H2: 3 # C5: 7,8 => UNS
* INC # H2: 3 # E6: 7,8 => UNS
* INC # H2: 3 # E6: 1 => UNS
* INC # H2: 3 # G4: 3,4 => UNS
* INC # H2: 3 # G4: 8 => UNS
* INC # H2: 3 # G6: 3,4 => UNS
* DIS # H2: 3 # G6: 8 => CTR => G6: 3,4
* INC # H2: 3 + G6: 3,4 # C7: 7,8 => UNS
* INC # H2: 3 + G6: 3,4 # B8: 7,8 => UNS
* INC # H2: 3 + G6: 3,4 # F9: 7,8 => UNS
* INC # H2: 3 + G6: 3,4 # I9: 7,8 => UNS
* INC # H2: 3 + G6: 3,4 # D2: 7,8 => UNS
* INC # H2: 3 + G6: 3,4 # E2: 7,8 => UNS
* INC # H2: 3 + G6: 3,4 # C5: 7,8 => UNS
* INC # H2: 3 + G6: 3,4 # C7: 7,8 => UNS
* INC # H2: 3 + G6: 3,4 # B4: 7,8 => UNS
* INC # H2: 3 + G6: 3,4 # B8: 7,8 => UNS
* INC # H2: 3 + G6: 3,4 # D2: 7,8 => UNS
* INC # H2: 3 + G6: 3,4 # E2: 7,8 => UNS
* INC # H2: 3 + G6: 3,4 # F5: 7,8 => UNS
* INC # H2: 3 + G6: 3,4 # F9: 7,8 => UNS
* INC # H2: 3 + G6: 3,4 # B4: 7,8 => UNS
* INC # H2: 3 + G6: 3,4 # C5: 7,8 => UNS
* INC # H2: 3 + G6: 3,4 # E6: 7,8 => UNS
* INC # H2: 3 + G6: 3,4 # E6: 1 => UNS
* INC # H2: 3 + G6: 3,4 # G4: 3,4 => UNS
* INC # H2: 3 + G6: 3,4 # G4: 8 => UNS
* INC # H2: 3 + G6: 3,4 # G4: 3,4 => UNS
* INC # H2: 3 + G6: 3,4 # G4: 8 => UNS
* INC # H2: 3 + G6: 3,4 # H4: 1,7 => UNS
* INC # H2: 3 + G6: 3,4 # H5: 1,7 => UNS
* INC # H2: 3 + G6: 3,4 # E6: 1,7 => UNS
* DIS # H2: 3 + G6: 3,4 # E6: 8 => CTR => E6: 1,7
* INC # H2: 3 + G6: 3,4 + E6: 1,7 # H4: 1,7 => UNS
* DIS # H2: 3 + G6: 3,4 + E6: 1,7 # H5: 1,7 => CTR => H5: 6
* DIS # H2: 3 + G6: 3,4 + E6: 1,7 + H5: 6 # D2: 7,8 => CTR => D2: 1
* PRF # H2: 3 + G6: 3,4 + E6: 1,7 + H5: 6 + D2: 1 # F5: 7,8 => SOL
* STA # H2: 3 + G6: 3,4 + E6: 1,7 + H5: 6 + D2: 1 + F5: 7,8
* CNT  73 HDP CHAINS /  74 HYP OPENED