Analysis of xx-mith-te3-00029596-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: ...4..7..........368.73.4.5.78.....63.6..7...54...83.7...2..638....75.......1.574 initial

Autosolve

position: ...4..7..........368.73.4.5.78.....63.6..78..54...83.7...2..638....75.......1.574 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: 0:00:12.770229

The following important HDP chains were detected:

* PRF # E1: 2,5,9 # F4: 1,9 => SOL
* STA # E1: 2,5,9 + F4: 1,9
* CNT   1 HDP CHAINS /  53 HYP OPENED

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

Details

Positions

...4..7..........368.73.4.5.78.....63.6..7...54...83.7...2..638....75.......1.574 initial
...4..7..........368.73.4.5.78.....63.6..78..54...83.7...2..638....75.......1.574 autosolve
123456789457189263689732415278341956396527841541968327715294638834675192962813574 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
A2: 4,7
C2: 4,7
H1: 6,8
H2: 6,8
H4: 4,5
H5: 4,5
A7: 1,7
B7: 1,5
A8: 4,8
B8: 3,6
C8: 3,4
E7: 4,9
F7: 4,9
F9: 3,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B1,C1: 3.. / B1 = 3  => 15 pairs (_) / C1 = 3  => 13 pairs (_)
D4,F4: 3.. / D4 = 3  => 17 pairs (_) / F4 = 3  => 17 pairs (_)
F4,F9: 3.. / F4 = 3  => 17 pairs (_) / F9 = 3  => 17 pairs (_)
A2,C2: 4.. / A2 = 4  => 12 pairs (_) / C2 = 4  => 12 pairs (_)
H4,H5: 4.. / H4 = 4  => 13 pairs (_) / H5 = 4  => 12 pairs (_)
A8,C8: 4.. / A8 = 4  => 12 pairs (_) / C8 = 4  => 12 pairs (_)
E7,F7: 4.. / E7 = 4  => 16 pairs (_) / F7 = 4  => 13 pairs (_)
E5,H5: 4.. / E5 = 4  => 13 pairs (_) / H5 = 4  => 12 pairs (_)
A2,A8: 4.. / A2 = 4  => 12 pairs (_) / A8 = 4  => 12 pairs (_)
C2,C8: 4.. / C2 = 4  => 12 pairs (_) / C8 = 4  => 12 pairs (_)
F4,F7: 4.. / F4 = 4  => 16 pairs (_) / F7 = 4  => 13 pairs (_)
H4,H5: 5.. / H4 = 5  => 12 pairs (_) / H5 = 5  => 13 pairs (_)
B7,C7: 5.. / B7 = 5  => 15 pairs (_) / C7 = 5  => 11 pairs (_)
C1,C7: 5.. / C1 = 5  => 15 pairs (_) / C7 = 5  => 11 pairs (_)
H1,H2: 6.. / H1 = 6  => 14 pairs (_) / H2 = 6  => 12 pairs (_)
D6,E6: 6.. / D6 = 6  => 22 pairs (_) / E6 = 6  => 15 pairs (_)
B8,B9: 6.. / B8 = 6  => 14 pairs (_) / B9 = 6  => 10 pairs (_)
B8,D8: 6.. / B8 = 6  => 14 pairs (_) / D8 = 6  => 10 pairs (_)
A2,C2: 7.. / A2 = 7  => 12 pairs (_) / C2 = 7  => 12 pairs (_)
A7,C7: 7.. / A7 = 7  => 12 pairs (_) / C7 = 7  => 12 pairs (_)
A2,A7: 7.. / A2 = 7  => 12 pairs (_) / A7 = 7  => 12 pairs (_)
C2,C7: 7.. / C2 = 7  => 12 pairs (_) / C7 = 7  => 12 pairs (_)
E1,E2: 8.. / E1 = 8  => 14 pairs (_) / E2 = 8  => 12 pairs (_)
H1,H2: 8.. / H1 = 8  => 12 pairs (_) / H2 = 8  => 14 pairs (_)
A8,A9: 8.. / A8 = 8  => 12 pairs (_) / A9 = 8  => 12 pairs (_)
D8,D9: 8.. / D8 = 8  => 12 pairs (_) / D9 = 8  => 12 pairs (_)
E1,H1: 8.. / E1 = 8  => 14 pairs (_) / H1 = 8  => 12 pairs (_)
E2,H2: 8.. / E2 = 8  => 12 pairs (_) / H2 = 8  => 14 pairs (_)
A8,D8: 8.. / A8 = 8  => 12 pairs (_) / D8 = 8  => 12 pairs (_)
A9,D9: 8.. / A9 = 8  => 12 pairs (_) / D9 = 8  => 12 pairs (_)
E7,F7: 9.. / E7 = 9  => 13 pairs (_) / F7 = 9  => 16 pairs (_)
* DURATION: 0:00:12.318456  START: 06:50:47.303416  END: 06:50:59.621872 2025-04-06
* CP COUNT: (31)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:12.606001  START: 06:51:10.871924  END: 06:51:23.477925 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00029596-base-pr-002.dot
* REASONING
* PRF # E1: 2,5,9 # F4: 1,9 => SOL
* STA # E1: 2,5,9 + F4: 1,9
* CNT   1 HDP CHAINS /  53 HYP OPENED

Header Info

rating: 6016; r2: 583547; index: 29596

Solution

position: 123456789457189263689732415278341956396527841541968327715294638834675192962813574 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 # E1: 6,8 => UNS
* INC # E1: 2,5,9 => UNS
* INC # E2: 6,8 => UNS
* INC # E2: 2,5,9 => UNS
* INC # E4: 4,5 => UNS
* INC # E4: 2,9 => UNS
* INC # E5: 4,5 => UNS
* INC # E5: 2,9 => UNS
* INC # C7: 1,7 => UNS
* INC # C7: 5 => UNS
* INC # C7: 1,5 => UNS
* INC # C7: 7 => UNS
* INC # B1: 1,5 => UNS
* INC # B2: 1,5 => UNS
* INC # B9: 3,6 => UNS
* INC # B9: 2,9 => UNS
* INC # D8: 3,6 => UNS
* INC # D8: 8 => UNS
* INC # E4: 4,9 => UNS
* INC # E5: 4,9 => UNS
* INC # F4: 4,9 => UNS
* INC # F4: 1,2,3 => UNS
* INC # D8: 3,6 => UNS
* INC # D9: 3,6 => UNS
* INC # B9: 3,6 => UNS
* INC # B9: 2,9 => UNS
* CNT  26 HDP CHAINS /  26 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E1: 6,8 => UNS
* INC # E1: 2,5,9 => UNS
* INC # E2: 6,8 => UNS
* INC # E2: 2,5,9 => UNS
* INC # E4: 4,5 => UNS
* INC # E4: 2,9 => UNS
* INC # E5: 4,5 => UNS
* INC # E5: 2,9 => UNS
* INC # C7: 1,7 => UNS
* INC # C7: 5 => UNS
* INC # C7: 1,5 => UNS
* INC # C7: 7 => UNS
* INC # B1: 1,5 => UNS
* INC # B2: 1,5 => UNS
* INC # B9: 3,6 => UNS
* INC # B9: 2,9 => UNS
* INC # D8: 3,6 => UNS
* INC # D8: 8 => UNS
* INC # E4: 4,9 => UNS
* INC # E5: 4,9 => UNS
* INC # F4: 4,9 => UNS
* INC # F4: 1,2,3 => UNS
* INC # D8: 3,6 => UNS
* INC # D9: 3,6 => UNS
* INC # B9: 3,6 => UNS
* INC # B9: 2,9 => UNS
* CNT  26 HDP CHAINS /  26 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # E1: 6,8 => UNS
* INC # E1: 2,5,9 => UNS
* INC # E2: 6,8 => UNS
* INC # E2: 2,5,9 => UNS
* INC # E4: 4,5 => UNS
* INC # E4: 2,9 => UNS
* INC # E5: 4,5 => UNS
* INC # E5: 2,9 => UNS
* INC # C7: 1,7 => UNS
* INC # C7: 5 => UNS
* INC # C7: 1,5 => UNS
* INC # C7: 7 => UNS
* INC # B1: 1,5 => UNS
* INC # B2: 1,5 => UNS
* INC # B9: 3,6 => UNS
* INC # B9: 2,9 => UNS
* INC # D8: 3,6 => UNS
* INC # D8: 8 => UNS
* INC # E4: 4,9 => UNS
* INC # E5: 4,9 => UNS
* INC # F4: 4,9 => UNS
* INC # F4: 1,2,3 => UNS
* INC # D8: 3,6 => UNS
* INC # D9: 3,6 => UNS
* INC # B9: 3,6 => UNS
* INC # B9: 2,9 => UNS
* INC # E1: 6,8 # E2: 6,8 => UNS
* INC # E1: 6,8 # E2: 2,5,9 => UNS
* INC # E1: 6,8 # E2: 6,8 => UNS
* INC # E1: 6,8 # E2: 2,5,9 => UNS
* INC # E1: 6,8 # E4: 4,5 => UNS
* INC # E1: 6,8 # E4: 2,9 => UNS
* INC # E1: 6,8 # E5: 4,5 => UNS
* INC # E1: 6,8 # E5: 2,9 => UNS
* INC # E1: 6,8 # C7: 1,7 => UNS
* INC # E1: 6,8 # C7: 5 => UNS
* INC # E1: 6,8 # C7: 1,5 => UNS
* INC # E1: 6,8 # C7: 7 => UNS
* INC # E1: 6,8 # B9: 3,6 => UNS
* INC # E1: 6,8 # B9: 2,9 => UNS
* INC # E1: 6,8 # D8: 3,6 => UNS
* INC # E1: 6,8 # D8: 8 => UNS
* INC # E1: 6,8 # E4: 4,9 => UNS
* INC # E1: 6,8 # E5: 4,9 => UNS
* INC # E1: 6,8 # F4: 4,9 => UNS
* INC # E1: 6,8 # F4: 1,2,3 => UNS
* INC # E1: 6,8 # D8: 3,6 => UNS
* INC # E1: 6,8 # D9: 3,6 => UNS
* INC # E1: 6,8 # B9: 3,6 => UNS
* INC # E1: 6,8 # B9: 2,9 => UNS
* INC # E1: 6,8 => UNS
* PRF # E1: 2,5,9 # F4: 1,9 => SOL
* STA # E1: 2,5,9 + F4: 1,9
* CNT  52 HDP CHAINS /  53 HYP OPENED