Analysis of xx-mith-te3-00073508-base.sdk

Contents

Original Sudoku
Autosolve
Pair Reduction Variants
Details
Solution
Appendix: Full HDP Chains

Original Sudoku

level: hard

position: 1..4.6.8....18....68..37....3......57.....9.2...6...1.3.47.8....7....3.881.36.4.. initial

Autosolve

position: 1..4.6.8....18....68..37....3......57.....9.2...6...1.3.47.8....7....3.881.36.4.. autosolve

Pair Reduction Variants

Pair Reduction Analysis

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

Pair Reduction

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

Deep Pair Reduction

Time used: 0:00:08.174213

The following important HDP chains were detected:

* PRF # I1: 9 # B2: 2,5 => SOL
* STA # I1: 9 + B2: 2,5
* CNT   1 HDP CHAINS /  46 HYP OPENED

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

Details

Positions

`1..4.6.8....18....68..37....3......57.....9.2...6...1.3.47.8....7....3.881.36.4..`	initial
`1..4.6.8....18....68..37....3......57.....9.2...6...1.3.47.8....7....3.881.36.4..`	autosolve
`123456789457189236689237154231894675768513942945672813394728561576941328812365497`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
C1: 3,7
C2: 3,7
D5: 5,8
G6: 7,8
E8: 1,4
F8: 1,4
I9: 7,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G3,I3: 1.. / G3 = 1  =>  8 pairs (_) / I3 = 1  => 10 pairs (_)
C4,C5: 1.. / C4 = 1  =>  8 pairs (_) / C5 = 1  =>  8 pairs (_)
E8,F8: 1.. / E8 = 1  =>  6 pairs (_) / F8 = 1  =>  6 pairs (_)
G7,I7: 1.. / G7 = 1  => 10 pairs (_) / I7 = 1  =>  8 pairs (_)
G3,G7: 1.. / G3 = 1  =>  8 pairs (_) / G7 = 1  => 10 pairs (_)
I3,I7: 1.. / I3 = 1  => 10 pairs (_) / I7 = 1  =>  8 pairs (_)
C1,C2: 3.. / C1 = 3  => 10 pairs (_) / C2 = 3  =>  7 pairs (_)
F5,F6: 3.. / F5 = 3  =>  8 pairs (_) / F6 = 3  =>  8 pairs (_)
H5,I6: 3.. / H5 = 3  =>  8 pairs (_) / I6 = 3  =>  8 pairs (_)
C1,I1: 3.. / C1 = 3  => 10 pairs (_) / I1 = 3  =>  7 pairs (_)
F5,H5: 3.. / F5 = 3  =>  8 pairs (_) / H5 = 3  =>  8 pairs (_)
F6,I6: 3.. / F6 = 3  =>  8 pairs (_) / I6 = 3  =>  8 pairs (_)
H2,H5: 3.. / H2 = 3  =>  8 pairs (_) / H5 = 3  =>  8 pairs (_)
A2,B2: 4.. / A2 = 4  =>  8 pairs (_) / B2 = 4  =>  8 pairs (_)
H3,I3: 4.. / H3 = 4  =>  9 pairs (_) / I3 = 4  =>  8 pairs (_)
E8,F8: 4.. / E8 = 4  =>  6 pairs (_) / F8 = 4  =>  6 pairs (_)
I3,I6: 4.. / I3 = 4  =>  8 pairs (_) / I6 = 4  =>  9 pairs (_)
B7,C8: 6.. / B7 = 6  =>  0 pairs (X) / C8 = 6  =>  8 pairs (_)
C8,H8: 6.. / C8 = 6  =>  8 pairs (_) / H8 = 6  =>  0 pairs (X)
B5,B7: 6.. / B5 = 6  =>  8 pairs (_) / B7 = 6  =>  0 pairs (X)
I2,I7: 6.. / I2 = 6  =>  8 pairs (_) / I7 = 6  =>  9 pairs (_)
C1,C2: 7.. / C1 = 7  =>  7 pairs (_) / C2 = 7  => 10 pairs (_)
E4,E6: 7.. / E4 = 7  =>  9 pairs (_) / E6 = 7  => 12 pairs (_)
H9,I9: 7.. / H9 = 7  => 13 pairs (_) / I9 = 7  =>  8 pairs (_)
D4,D5: 8.. / D4 = 8  => 10 pairs (_) / D5 = 8  =>  7 pairs (_)
G4,G6: 8.. / G4 = 8  => 14 pairs (_) / G6 = 8  => 10 pairs (_)
C5,D5: 8.. / C5 = 8  => 10 pairs (_) / D5 = 8  =>  7 pairs (_)
C6,G6: 8.. / C6 = 8  => 14 pairs (_) / G6 = 8  => 10 pairs (_)
* DURATION: 0:00:07.043194  START: 19:16:21.222464  END: 19:16:28.265658 2025-04-04
* CP COUNT: (28)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:08.022973  START: 19:16:33.119939  END: 19:16:41.142912 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00073508-base-pr-002.dot
* REASONING
* PRF # I1: 9 # B2: 2,5 => SOL
* STA # I1: 9 + B2: 2,5
* CNT   1 HDP CHAINS /  46 HYP OPENED

Header Info

rating: 16648; r2: 437986; index: 73508

Solution

position: 123456789457189236689237154231894675768513942945672813394728561576941328812365497 solved

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: 3,7 => UNS
* INC # I1: 9 => UNS
* INC # H2: 3,7 => UNS
* INC # I2: 3,7 => UNS
* INC # C5: 5,8 => UNS
* INC # C5: 1,6 => UNS
* INC # G4: 7,8 => UNS
* INC # G4: 6 => UNS
* INC # E4: 1,4 => UNS
* INC # E5: 1,4 => UNS
* INC # F4: 1,4 => UNS
* INC # F5: 1,4 => UNS
* INC # H9: 7,9 => UNS
* INC # H9: 2,5 => UNS
* INC # I1: 7,9 => UNS
* INC # I2: 7,9 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # I1: 3,7 => UNS
* INC # I1: 9 => UNS
* INC # H2: 3,7 => UNS
* INC # I2: 3,7 => UNS
* INC # C5: 5,8 => UNS
* INC # C5: 1,6 => UNS
* INC # G4: 7,8 => UNS
* INC # G4: 6 => UNS
* INC # E4: 1,4 => UNS
* INC # E5: 1,4 => UNS
* INC # F4: 1,4 => UNS
* INC # F5: 1,4 => UNS
* INC # H9: 7,9 => UNS
* INC # H9: 2,5 => UNS
* INC # I1: 7,9 => UNS
* INC # I2: 7,9 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # I1: 3,7 => UNS
* INC # I1: 9 => UNS
* INC # H2: 3,7 => UNS
* INC # I2: 3,7 => UNS
* INC # C5: 5,8 => UNS
* INC # C5: 1,6 => UNS
* INC # G4: 7,8 => UNS
* INC # G4: 6 => UNS
* INC # E4: 1,4 => UNS
* INC # E5: 1,4 => UNS
* INC # F4: 1,4 => UNS
* INC # F5: 1,4 => UNS
* INC # H9: 7,9 => UNS
* INC # H9: 2,5 => UNS
* INC # I1: 7,9 => UNS
* INC # I2: 7,9 => UNS
* INC # I1: 3,7 # H2: 3,7 => UNS
* INC # I1: 3,7 # I2: 3,7 => UNS
* INC # I1: 3,7 # G2: 2,5 => UNS
* INC # I1: 3,7 # H2: 2,5 => UNS
* INC # I1: 3,7 # G3: 2,5 => UNS
* INC # I1: 3,7 # H3: 2,5 => UNS
* INC # I1: 3,7 # B1: 2,5 => UNS
* INC # I1: 3,7 # E1: 2,5 => UNS
* INC # I1: 3,7 # G7: 2,5 => UNS
* INC # I1: 3,7 # G7: 1,6 => UNS
* INC # I1: 3,7 # H2: 3,7 => UNS
* INC # I1: 3,7 # I2: 3,7 => UNS
* INC # I1: 3,7 # I6: 3,7 => UNS
* INC # I1: 3,7 # I6: 4 => UNS
* INC # I1: 3,7 # C5: 5,8 => UNS
* INC # I1: 3,7 # C5: 1,6 => UNS
* INC # I1: 3,7 # G4: 7,8 => UNS
* INC # I1: 3,7 # G4: 6 => UNS
* INC # I1: 3,7 # E4: 1,4 => UNS
* INC # I1: 3,7 # E5: 1,4 => UNS
* INC # I1: 3,7 # F4: 1,4 => UNS
* INC # I1: 3,7 # F5: 1,4 => UNS
* INC # I1: 3,7 # H9: 7,9 => UNS
* INC # I1: 3,7 # H9: 2,5 => UNS
* INC # I1: 3,7 # I2: 7,9 => UNS
* INC # I1: 3,7 # I2: 3,6 => UNS
* INC # I1: 3,7 => UNS
* INC # I1: 9 # A2: 2,5 => UNS
* PRF # I1: 9 # B2: 2,5 => SOL
* STA # I1: 9 + B2: 2,5
* CNT  45 HDP CHAINS /  46 HYP OPENED