Analysis of xx-mith-te3-00091515-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: ....56..9456.89....9723.....1.......5...7.....7.51..94.4....95..65...4.19.1..5.76 initial

Autosolve

position: ....56..9456.89....9723.....1.......5...7.....7.51..94.4....95..65...4.19.1..5.76 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: 0:00:27.048508

The following important HDP chains were detected:

* PRF # D1: 4 # B5: 2,3 => SOL
* STA # D1: 4 + B5: 2,3
* CNT   1 HDP CHAINS / 127 HYP OPENED

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

Details

Positions

....56..9456.89....9723.....1.......5...7.....7.51..94.4....95..65...4.19.1..5.76 initial
....56..9456.89....9723.....1.......5...7.....7.51..94.4....95..65...4.19.1..5.76 autosolve
123456789456789123897231645214893567539674812678512394342167958765928431981345276 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (11)
A3: 1,8
D2: 1,7
F3: 1,4
I3: 5,8
C4: 4,9
C5: 4,9
G4: 5,7
I4: 5,7
E7: 2,6
E8: 2,9
E9: 2,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,A3: 1.. / A1 = 1  => 14 pairs (_) / A3 = 1  => 15 pairs (_)
G5,H5: 1.. / G5 = 1  => 12 pairs (_) / H5 = 1  => 13 pairs (_)
D7,F7: 1.. / D7 = 1  => 15 pairs (_) / F7 = 1  => 14 pairs (_)
F3,F7: 1.. / F3 = 1  => 15 pairs (_) / F7 = 1  => 14 pairs (_)
D1,F3: 4.. / D1 = 4  => 15 pairs (_) / F3 = 4  => 14 pairs (_)
H1,H3: 4.. / H1 = 4  => 14 pairs (_) / H3 = 4  => 15 pairs (_)
C4,C5: 4.. / C4 = 4  =>  9 pairs (_) / C5 = 4  => 11 pairs (_)
D9,E9: 4.. / D9 = 4  => 12 pairs (_) / E9 = 4  => 11 pairs (_)
D1,H1: 4.. / D1 = 4  => 15 pairs (_) / H1 = 4  => 14 pairs (_)
F3,H3: 4.. / F3 = 4  => 14 pairs (_) / H3 = 4  => 15 pairs (_)
E4,E9: 4.. / E4 = 4  => 12 pairs (_) / E9 = 4  => 11 pairs (_)
G3,I3: 5.. / G3 = 5  => 10 pairs (_) / I3 = 5  =>  9 pairs (_)
G4,I4: 5.. / G4 = 5  =>  9 pairs (_) / I4 = 5  => 10 pairs (_)
G3,G4: 5.. / G3 = 5  => 10 pairs (_) / G4 = 5  =>  9 pairs (_)
I3,I4: 5.. / I3 = 5  =>  9 pairs (_) / I4 = 5  => 10 pairs (_)
G3,H3: 6.. / G3 = 6  =>  9 pairs (_) / H3 = 6  => 13 pairs (_)
A4,A6: 6.. / A4 = 6  =>  0 pairs (X) / A6 = 6  => 11 pairs (_)
D7,E7: 6.. / D7 = 6  => 16 pairs (_) / E7 = 6  => 10 pairs (_)
A6,G6: 6.. / A6 = 6  => 11 pairs (_) / G6 = 6  =>  0 pairs (X)
E4,E7: 6.. / E4 = 6  => 16 pairs (_) / E7 = 6  => 10 pairs (_)
D1,D2: 7.. / D1 = 7  => 15 pairs (_) / D2 = 7  => 11 pairs (_)
G4,I4: 7.. / G4 = 7  => 10 pairs (_) / I4 = 7  =>  9 pairs (_)
A7,A8: 7.. / A7 = 7  => 11 pairs (_) / A8 = 7  => 18 pairs (_)
F7,F8: 7.. / F7 = 7  => 18 pairs (_) / F8 = 7  => 11 pairs (_)
D1,G1: 7.. / D1 = 7  => 15 pairs (_) / G1 = 7  => 11 pairs (_)
A7,F7: 7.. / A7 = 7  => 11 pairs (_) / F7 = 7  => 18 pairs (_)
A8,F8: 7.. / A8 = 7  => 18 pairs (_) / F8 = 7  => 11 pairs (_)
I2,I4: 7.. / I2 = 7  => 10 pairs (_) / I4 = 7  =>  9 pairs (_)
C4,C5: 9.. / C4 = 9  => 11 pairs (_) / C5 = 9  =>  9 pairs (_)
D8,E8: 9.. / D8 = 9  =>  8 pairs (_) / E8 = 9  => 11 pairs (_)
C5,D5: 9.. / C5 = 9  =>  9 pairs (_) / D5 = 9  => 11 pairs (_)
E4,E8: 9.. / E4 = 9  =>  8 pairs (_) / E8 = 9  => 11 pairs (_)
* DURATION: 0:00:10.735234  START: 13:44:34.430027  END: 13:44:45.165261 2025-04-06
* CP COUNT: (32)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:26.749695  START: 13:44:53.920054  END: 13:45:20.669749 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00091515-base-pr-002.dot
* REASONING
* PRF # D1: 4 # B5: 2,3 => SOL
* STA # D1: 4 + B5: 2,3
* CNT   1 HDP CHAINS / 127 HYP OPENED

Header Info

rating: 23012; r2: 462225; index: 91515

Solution

position: 123456789456789123897231645214893567539674812678512394342167958765928431981345276 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 # A1: 1,8 => UNS
* INC # A1: 2,3 => UNS
* INC # G3: 1,8 => UNS
* INC # H3: 1,8 => UNS
* INC # D1: 1,7 => UNS
* INC # D1: 4 => UNS
* INC # G2: 1,7 => UNS
* INC # G2: 2,3 => UNS
* INC # D1: 1,4 => UNS
* INC # D1: 7 => UNS
* INC # H3: 1,4 => UNS
* INC # H3: 6,8 => UNS
* INC # G3: 5,8 => UNS
* INC # G3: 1,6 => UNS
* INC # D4: 4,9 => UNS
* INC # E4: 4,9 => UNS
* INC # D5: 4,9 => UNS
* INC # D5: 3,6,8 => UNS
* INC # E4: 2,6 => UNS
* INC # E4: 4,9 => UNS
* INC # E4: 2,9 => UNS
* INC # E4: 4,6 => UNS
* INC # E4: 2,4 => UNS
* INC # E4: 6,9 => UNS
* CNT  24 HDP CHAINS /  24 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A1: 1,8 => UNS
* INC # A1: 2,3 => UNS
* INC # G3: 1,8 => UNS
* INC # H3: 1,8 => UNS
* INC # D1: 1,7 => UNS
* INC # D1: 4 => UNS
* INC # G2: 1,7 => UNS
* INC # G2: 2,3 => UNS
* INC # D1: 1,4 => UNS
* INC # D1: 7 => UNS
* INC # H3: 1,4 => UNS
* INC # H3: 6,8 => UNS
* INC # G3: 5,8 => UNS
* INC # G3: 1,6 => UNS
* INC # D4: 4,9 => UNS
* INC # E4: 4,9 => UNS
* INC # D5: 4,9 => UNS
* INC # D5: 3,6,8 => UNS
* INC # E4: 2,6 => UNS
* INC # E4: 4,9 => UNS
* INC # E4: 2,9 => UNS
* INC # E4: 4,6 => UNS
* INC # E4: 2,4 => UNS
* INC # E4: 6,9 => UNS
* CNT  24 HDP CHAINS /  24 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A1: 1,8 => UNS
* INC # A1: 2,3 => UNS
* INC # G3: 1,8 => UNS
* INC # H3: 1,8 => UNS
* INC # D1: 1,7 => UNS
* INC # D1: 4 => UNS
* INC # G2: 1,7 => UNS
* INC # G2: 2,3 => UNS
* INC # D1: 1,4 => UNS
* INC # D1: 7 => UNS
* INC # H3: 1,4 => UNS
* INC # H3: 6,8 => UNS
* INC # G3: 5,8 => UNS
* INC # G3: 1,6 => UNS
* INC # D4: 4,9 => UNS
* INC # E4: 4,9 => UNS
* INC # D5: 4,9 => UNS
* INC # D5: 3,6,8 => UNS
* INC # E4: 2,6 => UNS
* INC # E4: 4,9 => UNS
* INC # E4: 2,9 => UNS
* INC # E4: 4,6 => UNS
* INC # E4: 2,4 => UNS
* INC # E4: 6,9 => UNS
* INC # A1: 1,8 # G1: 1,8 => UNS
* INC # A1: 1,8 # H1: 1,8 => UNS
* INC # A1: 1,8 # B5: 2,3 => UNS
* INC # A1: 1,8 # B9: 2,3 => UNS
* INC # A1: 1,8 # C6: 2,3 => UNS
* INC # A1: 1,8 # C7: 2,3 => UNS
* INC # A1: 1,8 # G3: 1,8 => UNS
* INC # A1: 1,8 # H3: 1,8 => UNS
* INC # A1: 1,8 # D1: 1,7 => UNS
* INC # A1: 1,8 # D1: 4 => UNS
* INC # A1: 1,8 # G2: 1,7 => UNS
* INC # A1: 1,8 # G2: 2,3 => UNS
* INC # A1: 1,8 # D1: 1,4 => UNS
* INC # A1: 1,8 # D1: 7 => UNS
* INC # A1: 1,8 # H3: 1,4 => UNS
* INC # A1: 1,8 # H3: 6,8 => UNS
* INC # A1: 1,8 # G3: 5,8 => UNS
* INC # A1: 1,8 # G3: 1,6 => UNS
* INC # A1: 1,8 # D4: 4,9 => UNS
* INC # A1: 1,8 # E4: 4,9 => UNS
* INC # A1: 1,8 # D5: 4,9 => UNS
* INC # A1: 1,8 # D5: 3,6,8 => UNS
* INC # A1: 1,8 # E4: 2,6 => UNS
* INC # A1: 1,8 # E4: 4,9 => UNS
* INC # A1: 1,8 # E4: 2,9 => UNS
* INC # A1: 1,8 # E4: 4,6 => UNS
* INC # A1: 1,8 # E4: 2,4 => UNS
* INC # A1: 1,8 # E4: 6,9 => UNS
* INC # A1: 1,8 => UNS
* INC # A1: 2,3 # B1: 2,3 => UNS
* INC # A1: 2,3 # C1: 2,3 => UNS
* INC # A1: 2,3 # A4: 2,3 => UNS
* INC # A1: 2,3 # A8: 2,3 => UNS
* INC # A1: 2,3 # G2: 1,7 => UNS
* INC # A1: 2,3 # G2: 2,3 => UNS
* INC # A1: 2,3 # G2: 1,7 => UNS
* INC # A1: 2,3 # G2: 2,3 => UNS
* INC # A1: 2,3 # G3: 6,8 => UNS
* INC # A1: 2,3 # G3: 5 => UNS
* INC # A1: 2,3 # G3: 5,8 => UNS
* INC # A1: 2,3 # G3: 6 => UNS
* INC # A1: 2,3 # D4: 4,9 => UNS
* INC # A1: 2,3 # E4: 4,9 => UNS
* INC # A1: 2,3 # D4: 4,9 => UNS
* INC # A1: 2,3 # E4: 4,9 => UNS
* INC # A1: 2,3 => UNS
* INC # G3: 1,8 # A1: 1,8 => UNS
* INC # G3: 1,8 # A1: 2,3 => UNS
* INC # G3: 1,8 # G1: 1,7 => UNS
* INC # G3: 1,8 # G1: 8 => UNS
* INC # G3: 1,8 # G1: 1,7 => UNS
* INC # G3: 1,8 # G1: 8 => UNS
* INC # G3: 1,8 # H4: 2,3 => UNS
* INC # G3: 1,8 # H8: 2,3 => UNS
* INC # G3: 1,8 # I5: 2,3 => UNS
* INC # G3: 1,8 # I7: 2,3 => UNS
* INC # G3: 1,8 # G1: 1,8 => UNS
* INC # G3: 1,8 # G1: 7 => UNS
* INC # G3: 1,8 # D4: 4,9 => UNS
* INC # G3: 1,8 # E4: 4,9 => UNS
* INC # G3: 1,8 # D4: 4,9 => UNS
* INC # G3: 1,8 # E4: 4,9 => UNS
* INC # G3: 1,8 # H4: 2,3 => UNS
* INC # G3: 1,8 # I5: 2,3 => UNS
* INC # G3: 1,8 # C6: 2,3 => UNS
* INC # G3: 1,8 # F6: 2,3 => UNS
* INC # G3: 1,8 # I7: 2,3 => UNS
* INC # G3: 1,8 # H8: 2,3 => UNS
* INC # G3: 1,8 # B9: 2,3 => UNS
* INC # G3: 1,8 # B9: 8 => UNS
* INC # G3: 1,8 => UNS
* INC # H3: 1,8 # A1: 1,8 => UNS
* INC # H3: 1,8 # A1: 2,3 => UNS
* INC # H3: 1,8 # G2: 2,3 => UNS
* INC # H3: 1,8 # H2: 2,3 => UNS
* INC # H3: 1,8 # I5: 2,3 => UNS
* INC # H3: 1,8 # I7: 2,3 => UNS
* INC # H3: 1,8 # D4: 4,9 => UNS
* INC # H3: 1,8 # E4: 4,9 => UNS
* INC # H3: 1,8 # D4: 4,9 => UNS
* INC # H3: 1,8 # E4: 4,9 => UNS
* INC # H3: 1,8 => UNS
* INC # D1: 1,7 # A1: 1,8 => UNS
* INC # D1: 1,7 # A1: 2,3 => UNS
* INC # D1: 1,7 # G3: 1,8 => UNS
* INC # D1: 1,7 # H3: 1,8 => UNS
* INC # D1: 1,7 # G1: 1,7 => UNS
* INC # D1: 1,7 # G1: 8 => UNS
* INC # D1: 1,7 # G2: 1,7 => UNS
* INC # D1: 1,7 # G2: 2,3 => UNS
* INC # D1: 1,7 # G3: 5,8 => UNS
* INC # D1: 1,7 # G3: 1,6 => UNS
* INC # D1: 1,7 # D4: 4,9 => UNS
* INC # D1: 1,7 # E4: 4,9 => UNS
* INC # D1: 1,7 # D4: 4,9 => UNS
* INC # D1: 1,7 # E4: 4,9 => UNS
* INC # D1: 1,7 # G3: 1,6 => UNS
* INC # D1: 1,7 # G3: 5,8 => UNS
* INC # D1: 1,7 # H3: 1,6 => UNS
* INC # D1: 1,7 # H3: 8 => UNS
* INC # D1: 1,7 => UNS
* PRF # D1: 4 # B5: 2,3 => SOL
* STA # D1: 4 + B5: 2,3
* CNT 126 HDP CHAINS / 127 HYP OPENED