Analysis of xx-mith-te3-00011019-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: ..34.67.9..7....36..937.54.2.1....73..6.43.....8....5....5.7......96.....9..34... initial

Autosolve

position: ..34.67.94.7....36..937.54.241....73..6.43.....8....5....5.7......96.....9..34... 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: 0:00:09.762864

The following important HDP chains were detected:

* DIS # A5: 5,7 # E1: 1,2 => CTR => E1: 5,8
* PRF # A5: 5,7 + E1: 5,8 => SOL
* STA A5: 5,7
* CNT   2 HDP CHAINS /  28 HYP OPENED

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

Details

Positions

..34.67.9..7....36..937.54.2.1....73..6.43.....8....5....5.7......96.....9..34... initial
..34.67.94.7....36..937.54.241....73..6.43.....8....5....5.7......96.....9..34... autosolve
123456789457189236689372541241695873576843912938721654362517498714968325895234167 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
B5: 5,7
B6: 3,7
D4: 6,8
C7: 2,4
C9: 2,5
I8: 5,7
I9: 5,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A6,B6: 3.. / A6 = 3  => 11 pairs (_) / B6 = 3  =>  7 pairs (_)
G7,G8: 3.. / G7 = 3  =>  7 pairs (_) / G8 = 3  =>  4 pairs (_)
G6,I6: 4.. / G6 = 4  =>  0 pairs (X) / I6 = 4  =>  9 pairs (_)
C7,C8: 4.. / C7 = 4  =>  7 pairs (_) / C8 = 4  =>  4 pairs (_)
C8,G8: 4.. / C8 = 4  =>  4 pairs (_) / G8 = 4  =>  7 pairs (_)
I6,I7: 4.. / I6 = 4  =>  9 pairs (_) / I7 = 4  =>  0 pairs (X)
A5,B5: 5.. / A5 = 5  => 17 pairs (_) / B5 = 5  =>  9 pairs (_)
E4,F4: 5.. / E4 = 5  =>  9 pairs (_) / F4 = 5  =>  8 pairs (_)
C8,C9: 5.. / C8 = 5  =>  7 pairs (_) / C9 = 5  =>  5 pairs (_)
I8,I9: 5.. / I8 = 5  =>  5 pairs (_) / I9 = 5  =>  7 pairs (_)
C8,I8: 5.. / C8 = 5  =>  7 pairs (_) / I8 = 5  =>  5 pairs (_)
C9,I9: 5.. / C9 = 5  =>  5 pairs (_) / I9 = 5  =>  7 pairs (_)
A1,A5: 5.. / A1 = 5  =>  9 pairs (_) / A5 = 5  => 17 pairs (_)
F2,F4: 5.. / F2 = 5  =>  9 pairs (_) / F4 = 5  =>  8 pairs (_)
A3,B3: 6.. / A3 = 6  =>  7 pairs (_) / B3 = 6  =>  8 pairs (_)
D4,D6: 6.. / D4 = 6  => 10 pairs (_) / D6 = 6  => 16 pairs (_)
G4,G6: 6.. / G4 = 6  => 16 pairs (_) / G6 = 6  => 10 pairs (_)
H7,H9: 6.. / H7 = 6  =>  0 pairs (X) / H9 = 6  =>  7 pairs (_)
D4,G4: 6.. / D4 = 6  => 10 pairs (_) / G4 = 6  => 16 pairs (_)
D6,G6: 6.. / D6 = 6  => 16 pairs (_) / G6 = 6  => 10 pairs (_)
A9,H9: 6.. / A9 = 6  =>  0 pairs (X) / H9 = 6  =>  7 pairs (_)
B3,B7: 6.. / B3 = 6  =>  8 pairs (_) / B7 = 6  =>  7 pairs (_)
D5,D6: 7.. / D5 = 7  => 13 pairs (_) / D6 = 7  => 22 pairs (_)
I8,I9: 7.. / I8 = 7  =>  7 pairs (_) / I9 = 7  =>  5 pairs (_)
A9,I9: 7.. / A9 = 7  =>  7 pairs (_) / I9 = 7  =>  5 pairs (_)
E2,F2: 9.. / E2 = 9  =>  9 pairs (_) / F2 = 9  =>  9 pairs (_)
A5,A6: 9.. / A5 = 9  => 13 pairs (_) / A6 = 9  => 22 pairs (_)
G7,H7: 9.. / G7 = 9  =>  0 pairs (X) / H7 = 9  =>  7 pairs (_)
H5,H7: 9.. / H5 = 9  =>  0 pairs (X) / H7 = 9  =>  7 pairs (_)
* DURATION: 0:00:08.521818  START: 06:45:21.661191  END: 06:45:30.183009 2025-04-04
* CP COUNT: (29)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:09.623721  START: 06:45:35.158885  END: 06:45:44.782606 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00011019-base-pr-002.dot
* REASONING
* DIS # A5: 5,7 # E1: 1,2 => CTR => E1: 5,8
* PRF # A5: 5,7 + E1: 5,8 => SOL
* STA A5: 5,7
* CNT   2 HDP CHAINS /  28 HYP OPENED

Header Info

rating: 2585; r2: 50507; index: 11019

Solution

position: 123456789457189236689372541241695873576843912938721654362517498714968325895234167 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 # A5: 5,7 => UNS
* INC # A5: 9 => UNS
* INC # A6: 3,7 => UNS
* INC # A6: 9 => UNS
* INC # B8: 3,7 => UNS
* INC # B8: 1,8 => UNS
* INC # G4: 6,8 => UNS
* INC # G4: 9 => UNS
* INC # C8: 2,4 => UNS
* INC # C8: 5 => UNS
* INC # G7: 2,4 => UNS
* INC # I7: 2,4 => UNS
* INC # C8: 2,5 => UNS
* INC # C8: 4 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A5: 5,7 => UNS
* INC # A5: 9 => UNS
* INC # A6: 3,7 => UNS
* INC # A6: 9 => UNS
* INC # B8: 3,7 => UNS
* INC # B8: 1,8 => UNS
* INC # G4: 6,8 => UNS
* INC # G4: 9 => UNS
* INC # C8: 2,4 => UNS
* INC # C8: 5 => UNS
* INC # G7: 2,4 => UNS
* INC # I7: 2,4 => UNS
* INC # C8: 2,5 => UNS
* INC # C8: 4 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A5: 5,7 => UNS
* INC # A5: 9 => UNS
* INC # A6: 3,7 => UNS
* INC # A6: 9 => UNS
* INC # B8: 3,7 => UNS
* INC # B8: 1,8 => UNS
* INC # G4: 6,8 => UNS
* INC # G4: 9 => UNS
* INC # C8: 2,4 => UNS
* INC # C8: 5 => UNS
* INC # G7: 2,4 => UNS
* INC # I7: 2,4 => UNS
* INC # C8: 2,5 => UNS
* INC # C8: 4 => UNS
* INC # A5: 5,7 # B1: 1,5 => UNS
* INC # A5: 5,7 # B1: 2,8 => UNS
* INC # A5: 5,7 # E1: 1,5 => UNS
* INC # A5: 5,7 # E1: 2,8 => UNS
* INC # A5: 5,7 # B1: 5,8 => UNS
* INC # A5: 5,7 # B1: 1,2 => UNS
* INC # A5: 5,7 # E2: 5,8 => UNS
* INC # A5: 5,7 # E2: 9 => UNS
* INC # A5: 5,7 # B3: 1,6 => UNS
* INC # A5: 5,7 # B3: 2,8 => UNS
* INC # A5: 5,7 # A7: 1,6 => UNS
* INC # A5: 5,7 # A7: 3 => UNS
* DIS # A5: 5,7 # E1: 1,2 => CTR => E1: 5,8
* PRF # A5: 5,7 + E1: 5,8 => SOL
* STA A5: 5,7
* CNT  28 HDP CHAINS /  28 HYP OPENED