Analysis of xx-mith-te3-00157156-base.sdk

Contents

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

Original Sudoku

level: hard

position: 12.4..7.94.....23..........24...8.......14..279.52....3.4.9.1.7.72.4..9391..3.42. initial

Autosolve

position: 12.4..7.94.....23..........24...8.......14..279.52....3.4.9.1.7.72.4..9391..3.42. 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: 0:00:27.342233

The following important HDP chains were detected:

* PRF # F3: 2 # B3: 6,8 => SOL
* STA # F3: 2 + B3: 6,8
* CNT   1 HDP CHAINS / 106 HYP OPENED

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

Details

Positions

`12.4..7.94.....23..........24...8.......14..279.52....3.4.9.1.7.72.4..9391..3.42.`	initial
`12.4..7.94.....23..........24...8.......14..279.52....3.4.9.1.7.72.4..9391..3.42.`	autosolve
`123456789457189236869372514245968371638714952791523648384295167572641893916837425`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (11)
C2: 7,9
C3: 7,9
F1: 3,6
D2: 1,7
H3: 1,4
I3: 1,4
E4: 6,7
F6: 3,6
F7: 2,5
F8: 1,5
F9: 5,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D2,F2: 1.. / D2 = 1  => 11 pairs (_) / F2 = 1  =>  9 pairs (_)
H3,I3: 1.. / H3 = 1  =>  9 pairs (_) / I3 = 1  => 10 pairs (_)
C4,C6: 1.. / C4 = 1  => 16 pairs (_) / C6 = 1  => 11 pairs (_)
D8,F8: 1.. / D8 = 1  =>  9 pairs (_) / F8 = 1  => 11 pairs (_)
D2,D8: 1.. / D2 = 1  => 11 pairs (_) / D8 = 1  =>  9 pairs (_)
F2,F8: 1.. / F2 = 1  =>  9 pairs (_) / F8 = 1  => 11 pairs (_)
D3,F3: 2.. / D3 = 2  => 12 pairs (_) / F3 = 2  => 10 pairs (_)
D7,F7: 2.. / D7 = 2  => 10 pairs (_) / F7 = 2  => 12 pairs (_)
D3,D7: 2.. / D3 = 2  => 12 pairs (_) / D7 = 2  => 10 pairs (_)
F3,F7: 2.. / F3 = 2  => 10 pairs (_) / F7 = 2  => 12 pairs (_)
C1,B3: 3.. / C1 = 3  => 14 pairs (_) / B3 = 3  => 12 pairs (_)
F1,D3: 3.. / F1 = 3  => 12 pairs (_) / D3 = 3  => 14 pairs (_)
C1,F1: 3.. / C1 = 3  => 14 pairs (_) / F1 = 3  => 12 pairs (_)
B3,D3: 3.. / B3 = 3  => 12 pairs (_) / D3 = 3  => 14 pairs (_)
B3,B5: 3.. / B3 = 3  => 12 pairs (_) / B5 = 3  => 14 pairs (_)
F1,F6: 3.. / F1 = 3  => 12 pairs (_) / F6 = 3  => 14 pairs (_)
H3,I3: 4.. / H3 = 4  => 10 pairs (_) / I3 = 4  =>  9 pairs (_)
H6,I6: 4.. / H6 = 4  =>  9 pairs (_) / I6 = 4  => 10 pairs (_)
H3,H6: 4.. / H3 = 4  => 10 pairs (_) / H6 = 4  =>  9 pairs (_)
I3,I6: 4.. / I3 = 4  =>  9 pairs (_) / I6 = 4  => 10 pairs (_)
E4,F6: 6.. / E4 = 6  => 14 pairs (_) / F6 = 6  => 12 pairs (_)
F1,F6: 6.. / F1 = 6  => 14 pairs (_) / F6 = 6  => 12 pairs (_)
C2,C3: 7.. / C2 = 7  =>  9 pairs (_) / C3 = 7  => 10 pairs (_)
H4,H5: 7.. / H4 = 7  => 14 pairs (_) / H5 = 7  => 12 pairs (_)
D9,F9: 7.. / D9 = 7  => 13 pairs (_) / F9 = 7  => 13 pairs (_)
D5,H5: 7.. / D5 = 7  => 14 pairs (_) / H5 = 7  => 12 pairs (_)
E3,E4: 7.. / E3 = 7  => 14 pairs (_) / E4 = 7  => 12 pairs (_)
C2,C3: 9.. / C2 = 9  => 10 pairs (_) / C3 = 9  =>  9 pairs (_)
F2,F3: 9.. / F2 = 9  =>  9 pairs (_) / F3 = 9  => 10 pairs (_)
D4,D5: 9.. / D4 = 9  => 12 pairs (_) / D5 = 9  => 12 pairs (_)
G4,G5: 9.. / G4 = 9  => 12 pairs (_) / G5 = 9  => 12 pairs (_)
C2,F2: 9.. / C2 = 9  => 10 pairs (_) / F2 = 9  =>  9 pairs (_)
C3,F3: 9.. / C3 = 9  =>  9 pairs (_) / F3 = 9  => 10 pairs (_)
D4,G4: 9.. / D4 = 9  => 12 pairs (_) / G4 = 9  => 12 pairs (_)
D5,G5: 9.. / D5 = 9  => 12 pairs (_) / G5 = 9  => 12 pairs (_)
* DURATION: 0:00:13.380124  START: 15:45:29.420395  END: 15:45:42.800519 2025-04-05
* CP COUNT: (35)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:27.092537  START: 15:45:50.058859  END: 15:46:17.151396 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00157156-base-pr-002.dot
* REASONING
* PRF # F3: 2 # B3: 6,8 => SOL
* STA # F3: 2 + B3: 6,8
* CNT   1 HDP CHAINS / 106 HYP OPENED

Header Info

rating: 43730; r2: 822829; index: 157156

Solution

position: 123456789457189236869372514245968371638714952791523648384295167572641893916837425 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 # F2: 7,9 => UNS
* INC # F2: 1 => UNS
* INC # F3: 7,9 => UNS
* INC # F3: 2 => UNS
* INC # C1: 3,6 => UNS
* INC # C1: 5,8 => UNS
* INC # F2: 1,7 => UNS
* INC # F2: 9 => UNS
* INC # H6: 1,4 => UNS
* INC # H6: 6,8 => UNS
* INC # I6: 1,4 => UNS
* INC # I6: 6,8 => UNS
* INC # H4: 6,7 => UNS
* INC # H4: 1,5 => UNS
* INC # E3: 6,7 => UNS
* INC # E3: 5,8 => UNS
* INC # C6: 3,6 => UNS
* INC # G6: 3,6 => UNS
* CNT  18 HDP CHAINS /  18 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F2: 7,9 => UNS
* INC # F2: 1 => UNS
* INC # F3: 7,9 => UNS
* INC # F3: 2 => UNS
* INC # C1: 3,6 => UNS
* INC # C1: 5,8 => UNS
* INC # F2: 1,7 => UNS
* INC # F2: 9 => UNS
* INC # H6: 1,4 => UNS
* INC # H6: 6,8 => UNS
* INC # I6: 1,4 => UNS
* INC # I6: 6,8 => UNS
* INC # H4: 6,7 => UNS
* INC # H4: 1,5 => UNS
* INC # E3: 6,7 => UNS
* INC # E3: 5,8 => UNS
* INC # C6: 3,6 => UNS
* INC # G6: 3,6 => UNS
* CNT  18 HDP CHAINS /  18 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # F2: 7,9 => UNS
* INC # F2: 1 => UNS
* INC # F3: 7,9 => UNS
* INC # F3: 2 => UNS
* INC # C1: 3,6 => UNS
* INC # C1: 5,8 => UNS
* INC # F2: 1,7 => UNS
* INC # F2: 9 => UNS
* INC # H6: 1,4 => UNS
* INC # H6: 6,8 => UNS
* INC # I6: 1,4 => UNS
* INC # I6: 6,8 => UNS
* INC # H4: 6,7 => UNS
* INC # H4: 1,5 => UNS
* INC # E3: 6,7 => UNS
* INC # E3: 5,8 => UNS
* INC # C6: 3,6 => UNS
* INC # G6: 3,6 => UNS
* INC # F2: 7,9 # F3: 7,9 => UNS
* INC # F2: 7,9 # F3: 2 => UNS
* INC # F2: 7,9 # C1: 3,6 => UNS
* INC # F2: 7,9 # C1: 5,8 => UNS
* INC # F2: 7,9 # F3: 7,9 => UNS
* INC # F2: 7,9 # F3: 2 => UNS
* INC # F2: 7,9 # H6: 1,4 => UNS
* INC # F2: 7,9 # H6: 6,8 => UNS
* INC # F2: 7,9 # I6: 1,4 => UNS
* INC # F2: 7,9 # I6: 6,8 => UNS
* INC # F2: 7,9 # H4: 6,7 => UNS
* INC # F2: 7,9 # H4: 1,5 => UNS
* INC # F2: 7,9 # E3: 6,7 => UNS
* INC # F2: 7,9 # E3: 5,8 => UNS
* INC # F2: 7,9 # C6: 3,6 => UNS
* INC # F2: 7,9 # G6: 3,6 => UNS
* INC # F2: 7,9 # D7: 6,8 => UNS
* INC # F2: 7,9 # D9: 6,8 => UNS
* INC # F2: 7,9 # A8: 6,8 => UNS
* INC # F2: 7,9 # G8: 6,8 => UNS
* INC # F2: 7,9 => UNS
* INC # F2: 1 # H6: 1,4 => UNS
* INC # F2: 1 # H6: 8 => UNS
* INC # F2: 1 # I6: 1,4 => UNS
* INC # F2: 1 # I6: 8 => UNS
* INC # F2: 1 # G4: 3,9 => UNS
* INC # F2: 1 # G4: 5,6 => UNS
* INC # F2: 1 # G5: 3,9 => UNS
* INC # F2: 1 # G5: 5,6,8 => UNS
* INC # F2: 1 # G5: 3,8 => UNS
* INC # F2: 1 # G5: 5,6,9 => UNS
* INC # F2: 1 # C6: 3,8 => UNS
* INC # F2: 1 # C6: 1 => UNS
* INC # F2: 1 # B7: 6,8 => UNS
* INC # F2: 1 # C9: 6,8 => UNS
* INC # F2: 1 # A3: 6,8 => UNS
* INC # F2: 1 # A5: 6,8 => UNS
* INC # F2: 1 # B7: 6,8 => UNS
* INC # F2: 1 # H7: 6,8 => UNS
* INC # F2: 1 # C9: 6,8 => UNS
* INC # F2: 1 # I9: 6,8 => UNS
* INC # F2: 1 # H7: 6,8 => UNS
* INC # F2: 1 # I9: 6,8 => UNS
* INC # F2: 1 # G3: 6,8 => UNS
* INC # F2: 1 # G5: 6,8 => UNS
* INC # F2: 1 => UNS
* INC # F3: 7,9 # F2: 7,9 => UNS
* INC # F3: 7,9 # F2: 1 => UNS
* INC # F3: 7,9 # F2: 1,7 => UNS
* INC # F3: 7,9 # F2: 9 => UNS
* INC # F3: 7,9 # F2: 7,9 => UNS
* INC # F3: 7,9 # F2: 1 => UNS
* INC # F3: 7,9 # H6: 1,4 => UNS
* INC # F3: 7,9 # H6: 8 => UNS
* INC # F3: 7,9 # I6: 1,4 => UNS
* INC # F3: 7,9 # I6: 8 => UNS
* INC # F3: 7,9 # G4: 3,9 => UNS
* INC # F3: 7,9 # G4: 5,6 => UNS
* INC # F3: 7,9 # G5: 3,9 => UNS
* INC # F3: 7,9 # G5: 5,6,8 => UNS
* INC # F3: 7,9 # G5: 3,8 => UNS
* INC # F3: 7,9 # G5: 5,6,9 => UNS
* INC # F3: 7,9 # C6: 3,8 => UNS
* INC # F3: 7,9 # C6: 1 => UNS
* INC # F3: 7,9 # D8: 6,8 => UNS
* INC # F3: 7,9 # D9: 6,8 => UNS
* INC # F3: 7,9 # B7: 6,8 => UNS
* INC # F3: 7,9 # H7: 6,8 => UNS
* INC # F3: 7,9 => UNS
* INC # F3: 2 # C1: 3,6 => UNS
* INC # F3: 2 # C1: 5,8 => UNS
* INC # F3: 2 # D4: 3,7 => UNS
* INC # F3: 2 # D5: 3,7 => UNS
* INC # F3: 2 # H6: 1,4 => UNS
* INC # F3: 2 # H6: 6,8 => UNS
* INC # F3: 2 # I6: 1,4 => UNS
* INC # F3: 2 # I6: 6,8 => UNS
* INC # F3: 2 # H4: 6,7 => UNS
* INC # F3: 2 # H4: 1,5 => UNS
* INC # F3: 2 # E3: 6,7 => UNS
* INC # F3: 2 # E3: 5,8 => UNS
* INC # F3: 2 # C6: 3,6 => UNS
* INC # F3: 2 # G6: 3,6 => UNS
* INC # F3: 2 # A8: 6,8 => UNS
* INC # F3: 2 # C9: 6,8 => UNS
* INC # F3: 2 # B2: 6,8 => UNS
* PRF # F3: 2 # B3: 6,8 => SOL
* STA # F3: 2 + B3: 6,8
* CNT 105 HDP CHAINS / 106 HYP OPENED