Analysis of xx-mith-te3-00055696-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 12.....89...18.2.6......1..2..5......38....6.7.6....9...5.21..8..269..15..18.5.2. initial

Autosolve

position: 12..56.89...18.2.6......15.2..56.....38....6.7.6....9...5.21..8..269..15..18.5.2. 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: 0:00:08.652585

The following important HDP chains were detected:

* DIS # B4: 4,9 # F3: 3,7 => CTR => F3: 2,4,9
* DIS # B4: 4,9 + F3: 2,4,9 # F8: 3,7 => CTR => F8: 4
* PRF # B4: 4,9 + F3: 2,4,9 + F8: 4 # F2: 9 => SOL
* STA # B4: 4,9 + F3: 2,4,9 + F8: 4 + F2: 9
* CNT   3 HDP CHAINS /  26 HYP OPENED

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

Details

Positions

12.....89...18.2.6......1..2..5......38....6.7.6....9...5.21..8..269..15..18.5.2. initial
12..56.89...18.2.6......15.2..56.....38....6.7.6....9...5.21..8..269..15..18.5.2. autosolve
123456789457189236689372154294563871538917462716248593365721948872694315941835627 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
A3: 6,8
B3: 6,8
C4: 4,9
G7: 6,9
G9: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B4,B6: 1.. / B4 = 1  =>  8 pairs (_) / B6 = 1  => 11 pairs (_)
E5,E6: 1.. / E5 = 1  =>  6 pairs (_) / E6 = 1  => 10 pairs (_)
B4,I4: 1.. / B4 = 1  =>  8 pairs (_) / I4 = 1  => 11 pairs (_)
E5,I5: 1.. / E5 = 1  =>  6 pairs (_) / I5 = 1  => 10 pairs (_)
D3,F3: 2.. / D3 = 2  =>  7 pairs (_) / F3 = 2  =>  5 pairs (_)
I5,I6: 2.. / I5 = 2  =>  6 pairs (_) / I6 = 2  =>  8 pairs (_)
A2,B2: 5.. / A2 = 5  =>  9 pairs (_) / B2 = 5  =>  8 pairs (_)
A5,B6: 5.. / A5 = 5  =>  8 pairs (_) / B6 = 5  =>  9 pairs (_)
G5,G6: 5.. / G5 = 5  =>  9 pairs (_) / G6 = 5  =>  8 pairs (_)
A5,G5: 5.. / A5 = 5  =>  8 pairs (_) / G5 = 5  =>  9 pairs (_)
B6,G6: 5.. / B6 = 5  =>  9 pairs (_) / G6 = 5  =>  8 pairs (_)
A2,A5: 5.. / A2 = 5  =>  9 pairs (_) / A5 = 5  =>  8 pairs (_)
B2,B6: 5.. / B2 = 5  =>  8 pairs (_) / B6 = 5  =>  9 pairs (_)
A3,B3: 6.. / A3 = 6  =>  4 pairs (_) / B3 = 6  =>  4 pairs (_)
G7,G9: 6.. / G7 = 6  =>  3 pairs (_) / G9 = 6  =>  3 pairs (_)
A3,B3: 8.. / A3 = 8  =>  4 pairs (_) / B3 = 8  =>  4 pairs (_)
F4,F6: 8.. / F4 = 8  => 10 pairs (_) / F6 = 8  =>  5 pairs (_)
G4,G6: 8.. / G4 = 8  =>  5 pairs (_) / G6 = 8  => 10 pairs (_)
A8,B8: 8.. / A8 = 8  =>  4 pairs (_) / B8 = 8  =>  4 pairs (_)
F4,G4: 8.. / F4 = 8  => 10 pairs (_) / G4 = 8  =>  5 pairs (_)
F6,G6: 8.. / F6 = 8  =>  5 pairs (_) / G6 = 8  => 10 pairs (_)
A3,A8: 8.. / A3 = 8  =>  4 pairs (_) / A8 = 8  =>  4 pairs (_)
B3,B8: 8.. / B3 = 8  =>  4 pairs (_) / B8 = 8  =>  4 pairs (_)
G7,G9: 9.. / G7 = 9  =>  3 pairs (_) / G9 = 9  =>  3 pairs (_)
D3,D5: 9.. / D3 = 9  =>  5 pairs (_) / D5 = 9  =>  6 pairs (_)
* DURATION: 0:00:07.764958  START: 09:10:13.303457  END: 09:10:21.068415 2025-04-06
* CP COUNT: (25)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:08.517581  START: 09:10:24.688996  END: 09:10:33.206577 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00055696-base-pr-002.dot
* REASONING
* DIS # B4: 4,9 # F3: 3,7 => CTR => F3: 2,4,9
* DIS # B4: 4,9 + F3: 2,4,9 # F8: 3,7 => CTR => F8: 4
* PRF # B4: 4,9 + F3: 2,4,9 + F8: 4 # F2: 9 => SOL
* STA # B4: 4,9 + F3: 2,4,9 + F8: 4 + F2: 9
* CNT   3 HDP CHAINS /  26 HYP OPENED

Header Info

rating: 11451; r2: 280577; index: 55696

Solution

position: 123456789457189236689372154294563871538917462716248593365721948872694315941835627 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 # B4: 4,9 => UNS
* INC # A5: 4,9 => UNS
* INC # F4: 4,9 => UNS
* INC # F4: 3,7,8 => UNS
* INC # C2: 4,9 => UNS
* INC # C3: 4,9 => UNS
* INC # A7: 6,9 => UNS
* INC # B7: 6,9 => UNS
* INC # A9: 6,9 => UNS
* INC # B9: 6,9 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B4: 4,9 => UNS
* INC # A5: 4,9 => UNS
* INC # F4: 4,9 => UNS
* INC # F4: 3,7,8 => UNS
* INC # C2: 4,9 => UNS
* INC # C3: 4,9 => UNS
* INC # A7: 6,9 => UNS
* INC # B7: 6,9 => UNS
* INC # A9: 6,9 => UNS
* INC # B9: 6,9 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # B4: 4,9 => UNS
* INC # A5: 4,9 => UNS
* INC # F4: 4,9 => UNS
* INC # F4: 3,7,8 => UNS
* INC # C2: 4,9 => UNS
* INC # C3: 4,9 => UNS
* INC # A7: 6,9 => UNS
* INC # B7: 6,9 => UNS
* INC # A9: 6,9 => UNS
* INC # B9: 6,9 => UNS
* INC # B4: 4,9 # C2: 4,9 => UNS
* INC # B4: 4,9 # C3: 4,9 => UNS
* INC # B4: 4,9 # F2: 4,9 => UNS
* INC # B4: 4,9 # F2: 3,7 => UNS
* INC # B4: 4,9 # A7: 4,9 => UNS
* INC # B4: 4,9 # A9: 4,9 => UNS
* INC # B4: 4,9 # B7: 4,9 => UNS
* INC # B4: 4,9 # B9: 4,9 => UNS
* INC # B4: 4,9 # C2: 4,9 => UNS
* INC # B4: 4,9 # C3: 4,9 => UNS
* INC # B4: 4,9 # F2: 3,7 => UNS
* DIS # B4: 4,9 # F3: 3,7 => CTR => F3: 2,4,9
* DIS # B4: 4,9 + F3: 2,4,9 # F8: 3,7 => CTR => F8: 4
* INC # B4: 4,9 + F3: 2,4,9 + F8: 4 # F2: 3,7 => UNS
* PRF # B4: 4,9 + F3: 2,4,9 + F8: 4 # F2: 9 => SOL
* STA # B4: 4,9 + F3: 2,4,9 + F8: 4 + F2: 9
* CNT  25 HDP CHAINS /  26 HYP OPENED