Analysis of xx-mith-te3-00146401-base.sdk

Contents

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

Original Sudoku

level: hard

position: ......78..571...3668.3....5.....4.......2...8865..3...5....1..7.3.....51.1...586. initial

Autosolve

position: ......78..571...3668.3..1.5.....4..3....2...8865.13...5....13.7.3.....51.1..3586. 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: 0:00:07.033302

The following important HDP chains were detected:

* PRF # A5: 1,3 # A9: 2,9 => SOL
* STA # A5: 1,3 + A9: 2,9
* CNT   1 HDP CHAINS /  27 HYP OPENED

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

Details

Positions

`......78..571...3668.3....5.....4.......2...8865..3...5....1..7.3.....51.1...586.`	initial
`......78..571...3668.3..1.5.....4..3....2...8865.13...5....13.7.3.....51.1..3586.`	autosolve
`123456789457189236689372145271864593394527618865913472548691327736248951912735864`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
A1: 1,3
C1: 1,3
D6: 7,9
G4: 5,6
G5: 5,6
C7: 6,8
C8: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,C1: 1.. / A1 = 1  =>  6 pairs (_) / C1 = 1  =>  6 pairs (_)
H4,H5: 1.. / H4 = 1  => 14 pairs (_) / H5 = 1  =>  8 pairs (_)
A1,C1: 3.. / A1 = 3  =>  6 pairs (_) / C1 = 3  =>  6 pairs (_)
A5,C5: 3.. / A5 = 3  =>  6 pairs (_) / C5 = 3  =>  6 pairs (_)
A1,A5: 3.. / A1 = 3  =>  6 pairs (_) / A5 = 3  =>  6 pairs (_)
C1,C5: 3.. / C1 = 3  =>  6 pairs (_) / C5 = 3  =>  6 pairs (_)
D1,E1: 5.. / D1 = 5  =>  5 pairs (_) / E1 = 5  =>  8 pairs (_)
G4,G5: 5.. / G4 = 5  =>  8 pairs (_) / G5 = 5  =>  7 pairs (_)
D5,G5: 5.. / D5 = 5  =>  8 pairs (_) / G5 = 5  =>  7 pairs (_)
E1,E4: 5.. / E1 = 5  =>  8 pairs (_) / E4 = 5  =>  5 pairs (_)
G4,G5: 6.. / G4 = 6  =>  7 pairs (_) / G5 = 6  =>  8 pairs (_)
C7,C8: 6.. / C7 = 6  =>  6 pairs (_) / C8 = 6  =>  5 pairs (_)
E3,F3: 7.. / E3 = 7  =>  8 pairs (_) / F3 = 7  =>  9 pairs (_)
B4,B5: 7.. / B4 = 7  =>  9 pairs (_) / B5 = 7  => 10 pairs (_)
A8,A9: 7.. / A8 = 7  => 15 pairs (_) / A9 = 7  =>  7 pairs (_)
B4,H4: 7.. / B4 = 7  =>  9 pairs (_) / H4 = 7  => 10 pairs (_)
D6,H6: 7.. / D6 = 7  => 10 pairs (_) / H6 = 7  => 14 pairs (_)
A9,D9: 7.. / A9 = 7  =>  7 pairs (_) / D9 = 7  => 15 pairs (_)
E3,E8: 7.. / E3 = 7  =>  8 pairs (_) / E8 = 7  =>  9 pairs (_)
E2,F2: 8.. / E2 = 8  =>  7 pairs (_) / F2 = 8  =>  8 pairs (_)
D4,E4: 8.. / D4 = 8  =>  8 pairs (_) / E4 = 8  =>  9 pairs (_)
C7,C8: 8.. / C7 = 8  =>  5 pairs (_) / C8 = 8  =>  6 pairs (_)
F2,F8: 8.. / F2 = 8  =>  8 pairs (_) / F8 = 8  =>  7 pairs (_)
* DURATION: 0:00:07.587841  START: 14:02:06.282305  END: 14:02:13.870146 2025-04-05
* CP COUNT: (23)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:06.907712  START: 14:02:21.083813  END: 14:02:27.991525 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00146401-base-pr-002.dot
* REASONING
* PRF # A5: 1,3 # A9: 2,9 => SOL
* STA # A5: 1,3 + A9: 2,9
* CNT   1 HDP CHAINS /  27 HYP OPENED

Header Info

rating: 39154; r2: 764824; index: 146401

Solution

position: 123456789457189236689372145271864593394527618865913472548691327736248951912735864 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 # A5: 1,3 => UNS
* INC # A5: 4,9 => UNS
* INC # C5: 1,3 => UNS
* INC # C5: 4,9 => UNS
* INC # D5: 7,9 => UNS
* INC # F5: 7,9 => UNS
* INC # H6: 7,9 => UNS
* INC # H6: 2,4 => UNS
* INC # D8: 7,9 => UNS
* INC # D9: 7,9 => UNS
* INC # D4: 5,6 => UNS
* INC # E4: 5,6 => UNS
* INC # D5: 5,6 => UNS
* INC # D5: 7,9 => UNS
* INC # D7: 6,8 => UNS
* INC # E7: 6,8 => UNS
* INC # D8: 6,8 => UNS
* INC # E8: 6,8 => UNS
* INC # F8: 6,8 => UNS
* CNT  19 HDP CHAINS /  19 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A5: 1,3 => UNS
* INC # A5: 4,9 => UNS
* INC # C5: 1,3 => UNS
* INC # C5: 4,9 => UNS
* INC # D5: 7,9 => UNS
* INC # F5: 7,9 => UNS
* INC # H6: 7,9 => UNS
* INC # H6: 2,4 => UNS
* INC # D8: 7,9 => UNS
* INC # D9: 7,9 => UNS
* INC # D4: 5,6 => UNS
* INC # E4: 5,6 => UNS
* INC # D5: 5,6 => UNS
* INC # D5: 7,9 => UNS
* INC # D7: 6,8 => UNS
* INC # E7: 6,8 => UNS
* INC # D8: 6,8 => UNS
* INC # E8: 6,8 => UNS
* INC # F8: 6,8 => UNS
* CNT  19 HDP CHAINS /  19 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A5: 1,3 => UNS
* INC # A5: 4,9 => UNS
* INC # C5: 1,3 => UNS
* INC # C5: 4,9 => UNS
* INC # D5: 7,9 => UNS
* INC # F5: 7,9 => UNS
* INC # H6: 7,9 => UNS
* INC # H6: 2,4 => UNS
* INC # D8: 7,9 => UNS
* INC # D9: 7,9 => UNS
* INC # D4: 5,6 => UNS
* INC # E4: 5,6 => UNS
* INC # D5: 5,6 => UNS
* INC # D5: 7,9 => UNS
* INC # D7: 6,8 => UNS
* INC # E7: 6,8 => UNS
* INC # D8: 6,8 => UNS
* INC # E8: 6,8 => UNS
* INC # F8: 6,8 => UNS
* INC # A5: 1,3 # C5: 1,3 => UNS
* INC # A5: 1,3 # C5: 4,9 => UNS
* INC # A5: 1,3 # B4: 2,9 => UNS
* INC # A5: 1,3 # C4: 2,9 => UNS
* INC # A5: 1,3 # A2: 2,9 => UNS
* INC # A5: 1,3 # A8: 2,9 => UNS
* PRF # A5: 1,3 # A9: 2,9 => SOL
* STA # A5: 1,3 + A9: 2,9
* CNT  26 HDP CHAINS /  27 HYP OPENED