Analysis of xx-mith-te3-00113602-base.sdk

Contents

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

Original Sudoku

level: hard

position: 1..4.678....18.2...8..27.1....76......82.1.47..1.4862.5......72.14..2....3.....6. initial

Autosolve

position: 1..4.678....18.2...8..27.1....76......82.1.47..1.4862.5......72.146.2....3.....6. 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: 0:00:12.615883

The following important HDP chains were detected:

* DIS # G7: 1,8 # I9: 4,5,9 => CTR => I9: 1,8
* PRF # G9: 1,8 # F9: 5,9 => SOL
* STA # G9: 1,8 + F9: 5,9
* CNT   2 HDP CHAINS /  55 HYP OPENED

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

Details

Positions

`1..4.678....18.2...8..27.1....76......82.1.47..1.4862.5......72.14..2....3.....6.`	initial
`1..4.678....18.2...8..27.1....76......82.1.47..1.4862.5......72.146.2....3.....6.`	autosolve
`123456789457189236689327415245763891368291547971548623596814372714632958832975164`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
G4: 1,8
I4: 1,8
B7: 6,9
C7: 6,9
A8: 7,8
C9: 2,7
D7: 3,8
E7: 1,3
F7: 3,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G4,I4: 1.. / G4 = 1  =>  8 pairs (_) / I4 = 1  =>  7 pairs (_)
E7,E9: 1.. / E7 = 1  =>  8 pairs (_) / E9 = 1  => 10 pairs (_)
E7,G7: 1.. / E7 = 1  =>  8 pairs (_) / G7 = 1  => 10 pairs (_)
I4,I9: 1.. / I4 = 1  =>  7 pairs (_) / I9 = 1  =>  8 pairs (_)
B1,C1: 2.. / B1 = 2  =>  9 pairs (_) / C1 = 2  => 10 pairs (_)
A9,C9: 2.. / A9 = 2  => 10 pairs (_) / C9 = 2  => 10 pairs (_)
A4,A9: 2.. / A4 = 2  => 10 pairs (_) / A9 = 2  => 10 pairs (_)
B1,B4: 2.. / B1 = 2  =>  9 pairs (_) / B4 = 2  => 10 pairs (_)
A4,B4: 4.. / A4 = 4  =>  9 pairs (_) / B4 = 4  =>  9 pairs (_)
F7,F9: 4.. / F7 = 4  =>  9 pairs (_) / F9 = 4  => 11 pairs (_)
F7,G7: 4.. / F7 = 4  =>  9 pairs (_) / G7 = 4  => 11 pairs (_)
B2,B4: 4.. / B2 = 4  =>  9 pairs (_) / B4 = 4  =>  9 pairs (_)
I2,I3: 6.. / I2 = 6  =>  9 pairs (_) / I3 = 6  =>  9 pairs (_)
A5,B5: 6.. / A5 = 6  => 10 pairs (_) / B5 = 6  => 10 pairs (_)
B7,C7: 6.. / B7 = 6  =>  8 pairs (_) / C7 = 6  => 10 pairs (_)
A6,B6: 7.. / A6 = 7  => 12 pairs (_) / B6 = 7  => 10 pairs (_)
E8,E9: 7.. / E8 = 7  => 12 pairs (_) / E9 = 7  =>  8 pairs (_)
A8,E8: 7.. / A8 = 7  =>  8 pairs (_) / E8 = 7  => 12 pairs (_)
B2,B6: 7.. / B2 = 7  => 12 pairs (_) / B6 = 7  => 10 pairs (_)
C2,C9: 7.. / C2 = 7  => 10 pairs (_) / C9 = 7  => 10 pairs (_)
G4,I4: 8.. / G4 = 8  =>  7 pairs (_) / I4 = 8  =>  8 pairs (_)
A8,A9: 8.. / A8 = 8  => 12 pairs (_) / A9 = 8  =>  8 pairs (_)
D7,D9: 8.. / D7 = 8  =>  9 pairs (_) / D9 = 8  => 10 pairs (_)
D7,G7: 8.. / D7 = 8  =>  9 pairs (_) / G7 = 8  => 10 pairs (_)
B7,C7: 9.. / B7 = 9  => 10 pairs (_) / C7 = 9  =>  8 pairs (_)
* DURATION: 0:00:07.061549  START: 04:07:18.485502  END: 04:07:25.547051 2025-04-05
* CP COUNT: (25)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:12.458258  START: 04:07:31.346005  END: 04:07:43.804263 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00113602-base-pr-002.dot
* REASONING
* DIS # G7: 1,8 # I9: 4,5,9 => CTR => I9: 1,8
* PRF # G9: 1,8 # F9: 5,9 => SOL
* STA # G9: 1,8 + F9: 5,9
* CNT   2 HDP CHAINS /  55 HYP OPENED

Header Info

rating: 28937; r2: 565901; index: 113602

Solution

position: 123456789457189236689327415245763891368291547971548623596814372714632958832975164 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 # G7: 1,8 => UNS
* INC # G9: 1,8 => UNS
* INC # I9: 1,8 => UNS
* INC # I9: 4,5,9 => UNS
* INC # B2: 6,9 => UNS
* INC # B5: 6,9 => UNS
* INC # C2: 6,9 => UNS
* INC # C3: 6,9 => UNS
* INC # A9: 7,8 => UNS
* INC # A9: 2 => UNS
* INC # A9: 2,7 => UNS
* INC # A9: 8 => UNS
* INC # G7: 3,8 => UNS
* INC # G7: 1,4 => UNS
* INC # G7: 1,3 => UNS
* INC # G7: 4,8 => UNS
* INC # G7: 3,4 => UNS
* INC # G7: 1,8 => UNS
* CNT  18 HDP CHAINS /  18 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G7: 1,8 => UNS
* INC # G9: 1,8 => UNS
* INC # I9: 1,8 => UNS
* INC # I9: 4,5,9 => UNS
* INC # B2: 6,9 => UNS
* INC # B5: 6,9 => UNS
* INC # C2: 6,9 => UNS
* INC # C3: 6,9 => UNS
* INC # A9: 7,8 => UNS
* INC # A9: 2 => UNS
* INC # A9: 2,7 => UNS
* INC # A9: 8 => UNS
* INC # G7: 3,8 => UNS
* INC # G7: 1,4 => UNS
* INC # G7: 1,3 => UNS
* INC # G7: 4,8 => UNS
* INC # G7: 3,4 => UNS
* INC # G7: 1,8 => UNS
* CNT  18 HDP CHAINS /  18 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # G7: 1,8 => UNS
* INC # G9: 1,8 => UNS
* INC # I9: 1,8 => UNS
* INC # I9: 4,5,9 => UNS
* INC # B2: 6,9 => UNS
* INC # B5: 6,9 => UNS
* INC # C2: 6,9 => UNS
* INC # C3: 6,9 => UNS
* INC # A9: 7,8 => UNS
* INC # A9: 2 => UNS
* INC # A9: 2,7 => UNS
* INC # A9: 8 => UNS
* INC # G7: 3,8 => UNS
* INC # G7: 1,4 => UNS
* INC # G7: 1,3 => UNS
* INC # G7: 4,8 => UNS
* INC # G7: 3,4 => UNS
* INC # G7: 1,8 => UNS
* INC # G7: 1,8 # I9: 1,8 => UNS
* DIS # G7: 1,8 # I9: 4,5,9 => CTR => I9: 1,8
* INC # G7: 1,8 + I9: 1,8 # B2: 6,9 => UNS
* INC # G7: 1,8 + I9: 1,8 # B5: 6,9 => UNS
* INC # G7: 1,8 + I9: 1,8 # C2: 6,9 => UNS
* INC # G7: 1,8 + I9: 1,8 # C3: 6,9 => UNS
* INC # G7: 1,8 + I9: 1,8 # D9: 5,9 => UNS
* INC # G7: 1,8 + I9: 1,8 # E9: 5,9 => UNS
* INC # G7: 1,8 + I9: 1,8 # F2: 5,9 => UNS
* INC # G7: 1,8 + I9: 1,8 # F4: 5,9 => UNS
* INC # G7: 1,8 + I9: 1,8 # A2: 4,6 => UNS
* INC # G7: 1,8 + I9: 1,8 # B2: 4,6 => UNS
* INC # G7: 1,8 + I9: 1,8 # A3: 4,6 => UNS
* INC # G7: 1,8 + I9: 1,8 # A3: 3,9 => UNS
* INC # G7: 1,8 + I9: 1,8 # B2: 6,9 => UNS
* INC # G7: 1,8 + I9: 1,8 # B5: 6,9 => UNS
* INC # G7: 1,8 + I9: 1,8 # C2: 6,9 => UNS
* INC # G7: 1,8 + I9: 1,8 # C3: 6,9 => UNS
* INC # G7: 1,8 + I9: 1,8 # D9: 5,9 => UNS
* INC # G7: 1,8 + I9: 1,8 # E9: 5,9 => UNS
* INC # G7: 1,8 + I9: 1,8 # F2: 5,9 => UNS
* INC # G7: 1,8 + I9: 1,8 # F4: 5,9 => UNS
* INC # G7: 1,8 + I9: 1,8 => UNS
* INC # G9: 1,8 # I9: 1,8 => UNS
* INC # G9: 1,8 # I9: 4,5,9 => UNS
* INC # G9: 1,8 # B2: 6,9 => UNS
* INC # G9: 1,8 # B5: 6,9 => UNS
* INC # G9: 1,8 # C2: 6,9 => UNS
* INC # G9: 1,8 # C3: 6,9 => UNS
* INC # G9: 1,8 # A9: 7,8 => UNS
* INC # G9: 1,8 # A9: 2 => UNS
* INC # G9: 1,8 # A9: 2,7 => UNS
* INC # G9: 1,8 # A9: 8 => UNS
* INC # G9: 1,8 # E8: 5,9 => UNS
* INC # G9: 1,8 # E9: 5,9 => UNS
* PRF # G9: 1,8 # F9: 5,9 => SOL
* STA # G9: 1,8 + F9: 5,9
* CNT  54 HDP CHAINS /  55 HYP OPENED