Analysis of xx-mith-te3-00148361-base.sdk

Contents

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

Original Sudoku

level: hard

position: 12...678..57...2.6..8..7.15...36........786.2..5942.....1....67...6......8671.52. initial

Autosolve

position: 12...678..57...2.66.8..7.15...36........786.2.65942.....1....67...6......8671.52. 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: 0:00:17.551439

The following important HDP chains were detected:

* DIS # A4: 2 # A2: 3,9 => CTR => A2: 4
* PRF # A4: 2 + A2: 4 # C5: 4 => SOL
* STA # A4: 2 + A2: 4 + C5: 4
* CNT   2 HDP CHAINS /  82 HYP OPENED

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

Details

Positions

`12...678..57...2.6..8..7.15...36........786.2..5942.....1....67...6......8671.52.`	initial
`12...678..57...2.66.8..7.15...36........786.2.65942.....1....67...6......8671.52.`	autosolve
`123456789457189236698237415279361854314578692865942371541823967732695148986714523`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
D1: 4,5
D3: 2,4
A6: 7,8
F4: 1,5
D5: 1,5
H6: 3,7
A7: 2,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D2,F2: 1.. / D2 = 1  => 11 pairs (_) / F2 = 1  => 11 pairs (_)
B4,B5: 1.. / B4 = 1  => 11 pairs (_) / B5 = 1  => 11 pairs (_)
F4,D5: 1.. / F4 = 1  => 11 pairs (_) / D5 = 1  => 11 pairs (_)
G6,I6: 1.. / G6 = 1  =>  9 pairs (_) / I6 = 1  =>  8 pairs (_)
G8,I8: 1.. / G8 = 1  =>  8 pairs (_) / I8 = 1  =>  9 pairs (_)
B4,F4: 1.. / B4 = 1  => 11 pairs (_) / F4 = 1  => 11 pairs (_)
B5,D5: 1.. / B5 = 1  => 11 pairs (_) / D5 = 1  => 11 pairs (_)
D2,D5: 1.. / D2 = 1  => 11 pairs (_) / D5 = 1  => 11 pairs (_)
F2,F4: 1.. / F2 = 1  => 11 pairs (_) / F4 = 1  => 11 pairs (_)
G6,G8: 1.. / G6 = 1  =>  9 pairs (_) / G8 = 1  =>  8 pairs (_)
I6,I8: 1.. / I6 = 1  =>  8 pairs (_) / I8 = 1  =>  9 pairs (_)
D3,E3: 2.. / D3 = 2  =>  7 pairs (_) / E3 = 2  =>  9 pairs (_)
A4,C4: 2.. / A4 = 2  => 12 pairs (_) / C4 = 2  =>  9 pairs (_)
C4,C8: 2.. / C4 = 2  =>  9 pairs (_) / C8 = 2  => 12 pairs (_)
D3,D7: 2.. / D3 = 2  =>  7 pairs (_) / D7 = 2  =>  9 pairs (_)
D1,E1: 5.. / D1 = 5  => 12 pairs (_) / E1 = 5  => 10 pairs (_)
F4,D5: 5.. / F4 = 5  => 11 pairs (_) / D5 = 5  => 11 pairs (_)
H4,H5: 5.. / H4 = 5  => 11 pairs (_) / H5 = 5  => 11 pairs (_)
A7,A8: 5.. / A7 = 5  =>  7 pairs (_) / A8 = 5  =>  9 pairs (_)
F4,H4: 5.. / F4 = 5  => 11 pairs (_) / H4 = 5  => 11 pairs (_)
D5,H5: 5.. / D5 = 5  => 11 pairs (_) / H5 = 5  => 11 pairs (_)
H4,H6: 7.. / H4 = 7  => 14 pairs (_) / H6 = 7  =>  8 pairs (_)
A8,B8: 7.. / A8 = 7  => 12 pairs (_) / B8 = 7  =>  9 pairs (_)
A6,H6: 7.. / A6 = 7  => 14 pairs (_) / H6 = 7  =>  8 pairs (_)
B4,B8: 7.. / B4 = 7  => 12 pairs (_) / B8 = 7  =>  9 pairs (_)
D2,E2: 8.. / D2 = 8  => 12 pairs (_) / E2 = 8  => 10 pairs (_)
A4,A6: 8.. / A4 = 8  => 14 pairs (_) / A6 = 8  =>  8 pairs (_)
D2,D7: 8.. / D2 = 8  => 12 pairs (_) / D7 = 8  => 10 pairs (_)
* DURATION: 0:00:09.127533  START: 14:34:52.450292  END: 14:35:01.577825 2025-04-05
* CP COUNT: (28)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:17.283202  START: 14:35:05.398252  END: 14:35:22.681454 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00148361-base-pr-002.dot
* REASONING
* DIS # A4: 2 # A2: 3,9 => CTR => A2: 4
* PRF # A4: 2 + A2: 4 # C5: 4 => SOL
* STA # A4: 2 + A2: 4 + C5: 4
* CNT   2 HDP CHAINS /  82 HYP OPENED

Header Info

rating: 39905; r2: 782999; index: 148361

Solution

position: 123456789457189236698237415279361854314578692865942371541823967732695148986714523 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 # D7: 4,5 => UNS
* INC # D7: 2,8 => UNS
* INC # D7: 2,4 => UNS
* INC # D7: 5,8 => UNS
* INC # A4: 7,8 => UNS
* INC # A4: 2 => UNS
* INC # A8: 2,5 => UNS
* INC # A8: 7 => UNS
* INC # D7: 2,5 => UNS
* INC # E7: 2,5 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D7: 4,5 => UNS
* INC # D7: 2,8 => UNS
* INC # D7: 2,4 => UNS
* INC # D7: 5,8 => UNS
* INC # A4: 7,8 => UNS
* INC # A4: 2 => UNS
* INC # A8: 2,5 => UNS
* INC # A8: 7 => UNS
* INC # D7: 2,5 => UNS
* INC # E7: 2,5 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # D7: 4,5 => UNS
* INC # D7: 2,8 => UNS
* INC # D7: 2,4 => UNS
* INC # D7: 5,8 => UNS
* INC # A4: 7,8 => UNS
* INC # A4: 2 => UNS
* INC # A8: 2,5 => UNS
* INC # A8: 7 => UNS
* INC # D7: 2,5 => UNS
* INC # E7: 2,5 => UNS
* INC # D7: 4,5 # A2: 3,9 => UNS
* INC # D7: 4,5 # B3: 3,9 => UNS
* INC # D7: 4,5 # C5: 3,9 => UNS
* INC # D7: 4,5 # C8: 3,9 => UNS
* INC # D7: 4,5 # A2: 3,9 => UNS
* INC # D7: 4,5 # H2: 3,9 => UNS
* INC # D7: 4,5 # B3: 3,9 => UNS
* INC # D7: 4,5 # G3: 3,9 => UNS
* INC # D7: 4,5 # H2: 3,9 => UNS
* INC # D7: 4,5 # G3: 3,9 => UNS
* INC # D7: 4,5 # I9: 3,9 => UNS
* INC # D7: 4,5 # I9: 4 => UNS
* INC # D7: 4,5 # G6: 1,8 => UNS
* INC # D7: 4,5 # G6: 3 => UNS
* INC # D7: 4,5 # I6: 1,8 => UNS
* INC # D7: 4,5 # I6: 3 => UNS
* INC # D7: 4,5 => UNS
* INC # D7: 2,8 # A4: 7,8 => UNS
* INC # D7: 2,8 # A4: 2 => UNS
* INC # D7: 2,8 # A8: 2,5 => UNS
* INC # D7: 2,8 # A8: 7 => UNS
* INC # D7: 2,8 # E7: 2,5 => UNS
* INC # D7: 2,8 # E7: 3,8,9 => UNS
* INC # D7: 2,8 # E7: 2,8 => UNS
* INC # D7: 2,8 # E8: 2,8 => UNS
* INC # D7: 2,8 => UNS
* INC # D7: 2,4 # C1: 3,9 => UNS
* INC # D7: 2,4 # A2: 3,9 => UNS
* INC # D7: 2,4 # B5: 3,9 => UNS
* INC # D7: 2,4 # B7: 3,9 => UNS
* INC # D7: 2,4 # C1: 3,9 => UNS
* INC # D7: 2,4 # I1: 3,9 => UNS
* INC # D7: 2,4 # A2: 3,9 => UNS
* INC # D7: 2,4 # H2: 3,9 => UNS
* INC # D7: 2,4 # I1: 3,9 => UNS
* INC # D7: 2,4 # H2: 3,9 => UNS
* INC # D7: 2,4 # G7: 3,9 => UNS
* INC # D7: 2,4 # G7: 4 => UNS
* INC # D7: 2,4 # G6: 1,8 => UNS
* INC # D7: 2,4 # G6: 3 => UNS
* INC # D7: 2,4 # I6: 1,8 => UNS
* INC # D7: 2,4 # I6: 3 => UNS
* INC # D7: 2,4 => UNS
* INC # D7: 5,8 # E1: 3,9 => UNS
* INC # D7: 5,8 # E2: 3,9 => UNS
* INC # D7: 5,8 # F2: 3,9 => UNS
* INC # D7: 5,8 # B3: 3,9 => UNS
* INC # D7: 5,8 # G3: 3,9 => UNS
* INC # D7: 5,8 # E7: 3,9 => UNS
* INC # D7: 5,8 # E8: 3,9 => UNS
* INC # D7: 5,8 # A4: 7,8 => UNS
* INC # D7: 5,8 # A4: 2 => UNS
* INC # D7: 5,8 # A8: 2,5 => UNS
* INC # D7: 5,8 # A8: 7 => UNS
* INC # D7: 5,8 # E7: 2,5 => UNS
* INC # D7: 5,8 # E7: 3,8,9 => UNS
* INC # D7: 5,8 # E7: 5,8 => UNS
* INC # D7: 5,8 # E8: 5,8 => UNS
* INC # D7: 5,8 => UNS
* INC # A4: 7,8 # D7: 4,5 => UNS
* INC # A4: 7,8 # D7: 2,8 => UNS
* INC # A4: 7,8 # D7: 2,4 => UNS
* INC # A4: 7,8 # D7: 5,8 => UNS
* INC # A4: 7,8 # D7: 2,5 => UNS
* INC # A4: 7,8 # E7: 2,5 => UNS
* INC # A4: 7,8 # E8: 2,5 => UNS
* INC # A4: 7,8 # E8: 3,8,9 => UNS
* INC # A4: 7,8 => UNS
* DIS # A4: 2 # A2: 3,9 => CTR => A2: 4
* INC # A4: 2 + A2: 4 # C5: 3,9 => UNS
* PRF # A4: 2 + A2: 4 # C5: 4 => SOL
* STA # A4: 2 + A2: 4 + C5: 4
* CNT  81 HDP CHAINS /  82 HYP OPENED