Analysis of xx-mith-te3-00033365-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: ..34.6...4.7.89..669.73......6..8.9.8........9.43.7.....9...82......3..47.....51. initial

Autosolve

position: ..34.6..94.7.89..669.73......6.48.9.8........9.43.76..3.9...827....739647.....513 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: 0:00:07.835199

The following important HDP chains were detected:

* PRF # H1: 5,8 # B1: 1,2 => SOL
* STA # H1: 5,8 + B1: 1,2
* CNT   1 HDP CHAINS /  31 HYP OPENED

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

Details

Positions

..34.6...4.7.89..669.73......6..8.9.8........9.43.7.....9...82......3..47.....51. initial
..34.6..94.7.89..669.73......6.48.9.8........9.43.76..3.9...827....739647.....513 autosolve
123456789457189236698732145276548391835961472914327658349615827581273964762894513 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
H2: 3,5
I3: 5,8
B4: 3,7
B5: 3,7
D5: 6,9
E5: 6,9
G4: 3,7
H6: 5,8
B7: 4,6
B9: 4,6
C9: 2,8
D8: 2,8
F9: 2,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G2,H2: 3.. / G2 = 3  => 11 pairs (_) / H2 = 3  => 14 pairs (_)
B4,B5: 3.. / B4 = 3  => 13 pairs (_) / B5 = 3  => 12 pairs (_)
B4,G4: 3.. / B4 = 3  => 13 pairs (_) / G4 = 3  => 12 pairs (_)
H2,H5: 3.. / H2 = 3  => 14 pairs (_) / H5 = 3  => 11 pairs (_)
G3,H3: 4.. / G3 = 4  => 18 pairs (_) / H3 = 4  => 15 pairs (_)
G5,H5: 4.. / G5 = 4  => 15 pairs (_) / H5 = 4  => 18 pairs (_)
B7,B9: 4.. / B7 = 4  => 12 pairs (_) / B9 = 4  => 15 pairs (_)
F7,F9: 4.. / F7 = 4  => 15 pairs (_) / F9 = 4  => 12 pairs (_)
B7,F7: 4.. / B7 = 4  => 12 pairs (_) / F7 = 4  => 15 pairs (_)
B9,F9: 4.. / B9 = 4  => 15 pairs (_) / F9 = 4  => 12 pairs (_)
G3,G5: 4.. / G3 = 4  => 18 pairs (_) / G5 = 4  => 15 pairs (_)
H3,H5: 4.. / H3 = 4  => 15 pairs (_) / H5 = 4  => 18 pairs (_)
D5,E5: 6.. / D5 = 6  => 12 pairs (_) / E5 = 6  => 12 pairs (_)
B7,B9: 6.. / B7 = 6  => 15 pairs (_) / B9 = 6  => 12 pairs (_)
G1,H1: 7.. / G1 = 7  => 12 pairs (_) / H1 = 7  => 15 pairs (_)
B4,B5: 7.. / B4 = 7  => 12 pairs (_) / B5 = 7  => 13 pairs (_)
B4,G4: 7.. / B4 = 7  => 12 pairs (_) / G4 = 7  => 13 pairs (_)
H1,H5: 7.. / H1 = 7  => 15 pairs (_) / H5 = 7  => 12 pairs (_)
B1,C3: 8.. / B1 = 8  => 14 pairs (_) / C3 = 8  => 15 pairs (_)
H6,I6: 8.. / H6 = 8  => 13 pairs (_) / I6 = 8  => 19 pairs (_)
D8,D9: 8.. / D8 = 8  => 12 pairs (_) / D9 = 8  => 12 pairs (_)
B1,H1: 8.. / B1 = 8  => 14 pairs (_) / H1 = 8  => 15 pairs (_)
C9,D9: 8.. / C9 = 8  => 12 pairs (_) / D9 = 8  => 12 pairs (_)
B1,B8: 8.. / B1 = 8  => 14 pairs (_) / B8 = 8  => 15 pairs (_)
I3,I6: 8.. / I3 = 8  => 13 pairs (_) / I6 = 8  => 19 pairs (_)
D5,E5: 9.. / D5 = 9  => 12 pairs (_) / E5 = 9  => 12 pairs (_)
D9,E9: 9.. / D9 = 9  => 12 pairs (_) / E9 = 9  => 12 pairs (_)
D5,D9: 9.. / D5 = 9  => 12 pairs (_) / D9 = 9  => 12 pairs (_)
E5,E9: 9.. / E5 = 9  => 12 pairs (_) / E9 = 9  => 12 pairs (_)
* DURATION: 0:00:12.031951  START: 12:03:06.262135  END: 12:03:18.294086 2025-04-04
* CP COUNT: (29)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:07.706429  START: 12:03:30.593944  END: 12:03:38.300373 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00033365-base-pr-002.dot
* REASONING
* PRF # H1: 5,8 # B1: 1,2 => SOL
* STA # H1: 5,8 + B1: 1,2
* CNT   1 HDP CHAINS /  31 HYP OPENED

Header Info

rating: 6675; r2: 347170; index: 33365

Solution

position: 123456789457189236698732145276548391835961472914327658349615827581273964762894513 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 # H1: 5,8 => UNS
* INC # H3: 5,8 => UNS
* INC # C3: 5,8 => UNS
* INC # C3: 1,2 => UNS
* INC # I6: 5,8 => UNS
* INC # I6: 1,2 => UNS
* INC # G5: 3,7 => UNS
* INC # H5: 3,7 => UNS
* INC # D9: 6,9 => UNS
* INC # D9: 2,8 => UNS
* INC # E9: 6,9 => UNS
* INC # E9: 2 => UNS
* INC # G5: 3,7 => UNS
* INC # H5: 3,7 => UNS
* INC # I6: 5,8 => UNS
* INC # I6: 1,2 => UNS
* INC # H1: 5,8 => UNS
* INC # H3: 5,8 => UNS
* INC # B8: 2,8 => UNS
* INC # C8: 2,8 => UNS
* INC # D9: 2,8 => UNS
* INC # D9: 6,9 => UNS
* INC # C3: 2,8 => UNS
* INC # C3: 1,5 => UNS
* INC # D9: 2,8 => UNS
* INC # D9: 6,9 => UNS
* INC # B8: 2,8 => UNS
* INC # C8: 2,8 => UNS
* CNT  28 HDP CHAINS /  28 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # H1: 5,8 => UNS
* INC # H3: 5,8 => UNS
* INC # C3: 5,8 => UNS
* INC # C3: 1,2 => UNS
* INC # I6: 5,8 => UNS
* INC # I6: 1,2 => UNS
* INC # G5: 3,7 => UNS
* INC # H5: 3,7 => UNS
* INC # D9: 6,9 => UNS
* INC # D9: 2,8 => UNS
* INC # E9: 6,9 => UNS
* INC # E9: 2 => UNS
* INC # G5: 3,7 => UNS
* INC # H5: 3,7 => UNS
* INC # I6: 5,8 => UNS
* INC # I6: 1,2 => UNS
* INC # H1: 5,8 => UNS
* INC # H3: 5,8 => UNS
* INC # B8: 2,8 => UNS
* INC # C8: 2,8 => UNS
* INC # D9: 2,8 => UNS
* INC # D9: 6,9 => UNS
* INC # C3: 2,8 => UNS
* INC # C3: 1,5 => UNS
* INC # D9: 2,8 => UNS
* INC # D9: 6,9 => UNS
* INC # B8: 2,8 => UNS
* INC # C8: 2,8 => UNS
* CNT  28 HDP CHAINS /  28 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # H1: 5,8 => UNS
* INC # H3: 5,8 => UNS
* INC # C3: 5,8 => UNS
* INC # C3: 1,2 => UNS
* INC # I6: 5,8 => UNS
* INC # I6: 1,2 => UNS
* INC # G5: 3,7 => UNS
* INC # H5: 3,7 => UNS
* INC # D9: 6,9 => UNS
* INC # D9: 2,8 => UNS
* INC # E9: 6,9 => UNS
* INC # E9: 2 => UNS
* INC # G5: 3,7 => UNS
* INC # H5: 3,7 => UNS
* INC # I6: 5,8 => UNS
* INC # I6: 1,2 => UNS
* INC # H1: 5,8 => UNS
* INC # H3: 5,8 => UNS
* INC # B8: 2,8 => UNS
* INC # C8: 2,8 => UNS
* INC # D9: 2,8 => UNS
* INC # D9: 6,9 => UNS
* INC # C3: 2,8 => UNS
* INC # C3: 1,5 => UNS
* INC # D9: 2,8 => UNS
* INC # D9: 6,9 => UNS
* INC # B8: 2,8 => UNS
* INC # C8: 2,8 => UNS
* INC # H1: 5,8 # B1: 5,8 => UNS
* PRF # H1: 5,8 # B1: 1,2 => SOL
* STA # H1: 5,8 + B1: 1,2
* CNT  30 HDP CHAINS /  31 HYP OPENED