Analysis of xx-mith-te3-00077028-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: ..34.6.89....8923...932.4....48.....51....89.7.8...62..6.2.8.4..........9....3.6. initial

Autosolve

position: ..34.6.89....8923...932.4....48.....51....89.7.8...62..6.2.8.4..........9....3.6. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A4: 3 => CTR => A4: 2,6
* DIS # B4: 2 => CTR => B4: 3,9
* DIS # A8: 1,3 => CTR => A8: 2,4,8
* DIS # G7: 1,3 => CTR => G7: 5,7,9
* CNT   4 HDP CHAINS /  21 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # A4: 3 => CTR => A4: 2,6
* DIS A4: 2,6 # A8: 1,3 => CTR => A8: 2,4,8
* STA A4: 2,6 + A8: 2,4,8
* CNT   2 HDP CHAINS /  27 HYP OPENED

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

Pair Reduction Position

position: ..34.6.89....8923...932.4....48.....51....89.7.8...62.36.2.894.......3..9....3.6. pair_reduction
Pair Reduction

See section Pair Reduction for the HDP chains leading to this result.

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:22.143586

The following important HDP chains were detected:

* PRF # A8: 2,8 # B8: 5,7 => SOL
* STA # A8: 2,8 + B8: 5,7
* CNT   1 HDP CHAINS / 103 HYP OPENED

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

Details

Positions

..34.6.89....8923...932.4....48.....51....89.7.8...62..6.2.8.4..........9....3.6. initial
..34.6.89....8923...932.4....48.....51....89.7.8...62..6.2.8.4..........9....3.6. autosolve
..34.6.89....8923...932.4....48.....51....89.7.8...62.36.2.894.......3..9....3.6. pair_reduction
123456789457189236689327415294861573516732894738945621365218947871694352942573168 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
A1: 1,2
C5: 2,6
B6: 3,9
D5: 6,7
A7: 1,3
I8: 2,8
I9: 2,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,B1: 2.. / A1 = 2  =>  8 pairs (_) / B1 = 2  => 13 pairs (_)
F4,F5: 2.. / F4 = 2  => 12 pairs (_) / F5 = 2  => 12 pairs (_)
I8,I9: 2.. / I8 = 2  =>  5 pairs (_) / I9 = 2  =>  6 pairs (_)
C5,F5: 2.. / C5 = 2  => 12 pairs (_) / F5 = 2  => 12 pairs (_)
E5,I5: 3.. / E5 = 3  =>  8 pairs (_) / I5 = 3  => 14 pairs (_)
A2,B2: 4.. / A2 = 4  =>  8 pairs (_) / B2 = 4  =>  9 pairs (_)
I5,I6: 4.. / I5 = 4  =>  8 pairs (_) / I6 = 4  => 10 pairs (_)
B9,E9: 4.. / B9 = 4  =>  0 pairs (*) / E9 = 4  =>  0 pairs (X)
A2,A8: 4.. / A2 = 4  =>  8 pairs (_) / A8 = 4  =>  9 pairs (_)
I2,I3: 6.. / I2 = 6  => 10 pairs (_) / I3 = 6  =>  8 pairs (_)
A4,C5: 6.. / A4 = 6  => 12 pairs (_) / C5 = 6  => 12 pairs (_)
D8,E8: 6.. / D8 = 6  => 12 pairs (_) / E8 = 6  => 11 pairs (_)
A3,I3: 6.. / A3 = 6  => 10 pairs (_) / I3 = 6  =>  8 pairs (_)
A4,E4: 6.. / A4 = 6  => 12 pairs (_) / E4 = 6  => 12 pairs (_)
C2,C5: 6.. / C2 = 6  => 12 pairs (_) / C5 = 6  => 12 pairs (_)
D5,D8: 6.. / D5 = 6  => 11 pairs (_) / D8 = 6  => 12 pairs (_)
A3,B3: 8.. / A3 = 8  =>  8 pairs (_) / B3 = 8  =>  7 pairs (_)
I8,I9: 8.. / I8 = 8  =>  6 pairs (_) / I9 = 8  =>  5 pairs (_)
B9,I9: 8.. / B9 = 8  =>  6 pairs (_) / I9 = 8  =>  5 pairs (_)
A3,A8: 8.. / A3 = 8  =>  8 pairs (_) / A8 = 8  =>  7 pairs (_)
B4,B6: 9.. / B4 = 9  =>  7 pairs (_) / B6 = 9  => 11 pairs (_)
G7,G8: 9.. / G7 = 9  =>  9 pairs (_) / G8 = 9  =>  0 pairs (X)
B4,E4: 9.. / B4 = 9  =>  7 pairs (_) / E4 = 9  => 11 pairs (_)
E7,G7: 9.. / E7 = 9  =>  0 pairs (X) / G7 = 9  =>  9 pairs (_)
D6,D8: 9.. / D6 = 9  =>  7 pairs (_) / D8 = 9  => 11 pairs (_)
* DURATION: 0:00:06.411302  START: 20:40:04.644146  END: 20:40:11.055448 2025-04-04
* CP COUNT: (25)
* SOLUTION FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:21.887610  START: 20:40:19.052896  END: 20:40:40.940506 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00077028-base-pr-002.dot
* REASONING
* PRF # A8: 2,8 # B8: 5,7 => SOL
* STA # A8: 2,8 + B8: 5,7
* CNT   1 HDP CHAINS / 103 HYP OPENED

Header Info

rating: 17906; r2: 431634; index: 77028

Solution

position: 123456789457189236689327415294861573516732894738945621365218947871694352942573168 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 # A8: 1,2 => UNS
* INC # A8: 3,4,8 => UNS
* INC # A4: 2,6 => UNS
* DIS # A4: 3 => CTR => A4: 2,6
* INC # B4: 3,9 => UNS
* DIS # B4: 2 => CTR => B4: 3,9
* INC # E6: 3,9 => UNS
* INC # E6: 1,4,5 => UNS
* INC # E4: 6,7 => UNS
* INC # E5: 6,7 => UNS
* INC # D8: 6,7 => UNS
* INC # D8: 1,5,9 => UNS
* DIS # A8: 1,3 => CTR => A8: 2,4,8
* INC # A8: 2,4,8 => UNS
* DIS # G7: 1,3 => CTR => G7: 5,7,9
* INC # G7: 5,7,9 => UNS
* INC # I7: 1,3 => UNS
* INC # A8: 2,8 => UNS
* INC # B8: 2,8 => UNS
* INC # B9: 2,8 => UNS
* INC # B9: 4,5,7 => UNS
* CNT  21 HDP CHAINS /  21 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A8: 1,2 => UNS
* INC # A8: 3,4,8 => UNS
* INC # A4: 2,6 => UNS
* DIS # A4: 3 => CTR => A4: 2,6
* INC A4: 2,6 # E6: 3,9 => UNS
* INC A4: 2,6 # E6: 1,4,5 => UNS
* INC A4: 2,6 # E4: 6,7 => UNS
* INC A4: 2,6 # E5: 6,7 => UNS
* INC A4: 2,6 # D8: 6,7 => UNS
* INC A4: 2,6 # D8: 1,5,9 => UNS
* DIS A4: 2,6 # A8: 1,3 => CTR => A8: 2,4,8
* INC A4: 2,6 + A8: 2,4,8 # A8: 2,8 => UNS
* INC A4: 2,6 + A8: 2,4,8 # B8: 2,8 => UNS
* INC A4: 2,6 + A8: 2,4,8 # B9: 2,8 => UNS
* INC A4: 2,6 + A8: 2,4,8 # B9: 4,5,7 => UNS
* INC A4: 2,6 + A8: 2,4,8 # E4: 3,9 => UNS
* INC A4: 2,6 + A8: 2,4,8 # E4: 1,5,6,7 => UNS
* INC A4: 2,6 + A8: 2,4,8 # E6: 3,9 => UNS
* INC A4: 2,6 + A8: 2,4,8 # E6: 1,4,5 => UNS
* INC A4: 2,6 + A8: 2,4,8 # E4: 6,7 => UNS
* INC A4: 2,6 + A8: 2,4,8 # E5: 6,7 => UNS
* INC A4: 2,6 + A8: 2,4,8 # E4: 6,9 => UNS
* INC A4: 2,6 + A8: 2,4,8 # E4: 1,3,5,7 => UNS
* INC A4: 2,6 + A8: 2,4,8 # A8: 2,8 => UNS
* INC A4: 2,6 + A8: 2,4,8 # B8: 2,8 => UNS
* INC A4: 2,6 + A8: 2,4,8 # B9: 2,8 => UNS
* INC A4: 2,6 + A8: 2,4,8 # B9: 4,5,7 => UNS
* STA A4: 2,6 + A8: 2,4,8
* CNT  27 HDP CHAINS /  27 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # E4: 3,9 => UNS
* INC # E4: 1,5,6,7 => UNS
* INC # E6: 3,9 => UNS
* INC # E6: 1,4,5 => UNS
* INC # E4: 6,7 => UNS
* INC # E5: 6,7 => UNS
* INC # E4: 6,9 => UNS
* INC # E4: 1,3,5,7 => UNS
* INC # A8: 2,8 => UNS
* INC # B8: 2,8 => UNS
* INC # B9: 2,8 => UNS
* INC # B9: 4,5,7 => UNS
* INC # E4: 3,9 # E6: 3,9 => UNS
* INC # E4: 3,9 # E6: 1,5 => UNS
* INC # E4: 3,9 # E6: 3,9 => UNS
* INC # E4: 3,9 # E6: 1,5 => UNS
* INC # E4: 3,9 # E5: 6,7 => UNS
* INC # E4: 3,9 # E5: 3 => UNS
* INC # E4: 3,9 # A8: 2,8 => UNS
* INC # E4: 3,9 # B8: 2,8 => UNS
* INC # E4: 3,9 # A8: 2,8 => UNS
* INC # E4: 3,9 # B8: 2,8 => UNS
* INC # E4: 3,9 => UNS
* INC # E4: 1,5,6,7 # E4: 6,7 => UNS
* INC # E4: 1,5,6,7 # E4: 1,5 => UNS
* INC # E4: 1,5,6,7 # F5: 4,7 => UNS
* INC # E4: 1,5,6,7 # F5: 2 => UNS
* INC # E4: 1,5,6,7 # A8: 2,8 => UNS
* INC # E4: 1,5,6,7 # B8: 2,8 => UNS
* INC # E4: 1,5,6,7 # B9: 2,8 => UNS
* INC # E4: 1,5,6,7 # B9: 4,5,7 => UNS
* INC # E4: 1,5,6,7 => UNS
* INC # E6: 3,9 # E4: 3,9 => UNS
* INC # E6: 3,9 # E4: 1,5,7 => UNS
* INC # E6: 3,9 # E4: 3,7 => UNS
* INC # E6: 3,9 # E4: 1,5,9 => UNS
* INC # E6: 3,9 # I5: 3,7 => UNS
* INC # E6: 3,9 # I5: 4 => UNS
* INC # E6: 3,9 # I5: 4,7 => UNS
* INC # E6: 3,9 # I5: 3 => UNS
* INC # E6: 3,9 # E4: 1,5 => UNS
* INC # E6: 3,9 # F6: 1,5 => UNS
* INC # E6: 3,9 # I6: 1,5 => UNS
* INC # E6: 3,9 # I6: 4 => UNS
* INC # E6: 3,9 # D2: 1,5 => UNS
* INC # E6: 3,9 # D9: 1,5 => UNS
* INC # E6: 3,9 # E4: 3,9 => UNS
* INC # E6: 3,9 # E4: 1,5,7 => UNS
* INC # E6: 3,9 # A8: 2,8 => UNS
* INC # E6: 3,9 # B8: 2,8 => UNS
* INC # E6: 3,9 # A8: 2,8 => UNS
* INC # E6: 3,9 # B8: 2,8 => UNS
* INC # E6: 3,9 => UNS
* INC # E6: 1,4,5 # E4: 3,9 => UNS
* INC # E6: 1,4,5 # E4: 6 => UNS
* INC # E6: 1,4,5 # E4: 3,6 => UNS
* INC # E6: 1,4,5 # E4: 9 => UNS
* INC # E6: 1,4,5 # E4: 6,9 => UNS
* INC # E6: 1,4,5 # E4: 3 => UNS
* INC # E6: 1,4,5 # A8: 2,8 => UNS
* INC # E6: 1,4,5 # B8: 2,8 => UNS
* INC # E6: 1,4,5 # B9: 2,8 => UNS
* INC # E6: 1,4,5 # B9: 4,5,7 => UNS
* INC # E6: 1,4,5 => UNS
* INC # E4: 6,7 # A8: 2,8 => UNS
* INC # E4: 6,7 # B8: 2,8 => UNS
* INC # E4: 6,7 # B9: 2,8 => UNS
* INC # E4: 6,7 # B9: 4,5,7 => UNS
* INC # E4: 6,7 => UNS
* INC # E5: 6,7 # E6: 3,9 => UNS
* INC # E5: 6,7 # E6: 1,5 => UNS
* INC # E5: 6,7 # E6: 3,9 => UNS
* INC # E5: 6,7 # E6: 1,5 => UNS
* INC # E5: 6,7 # D6: 1,5 => UNS
* INC # E5: 6,7 # E6: 1,5 => UNS
* INC # E5: 6,7 # F3: 1,5 => UNS
* INC # E5: 6,7 # F8: 1,5 => UNS
* INC # E5: 6,7 # A8: 2,8 => UNS
* INC # E5: 6,7 # B8: 2,8 => UNS
* INC # E5: 6,7 # A8: 2,8 => UNS
* INC # E5: 6,7 # B8: 2,8 => UNS
* INC # E5: 6,7 => UNS
* INC # E4: 6,9 # A8: 2,8 => UNS
* INC # E4: 6,9 # B8: 2,8 => UNS
* INC # E4: 6,9 # B9: 2,8 => UNS
* INC # E4: 6,9 # B9: 4,5,7 => UNS
* INC # E4: 6,9 => UNS
* INC # E4: 1,3,5,7 # E5: 6,7 => UNS
* INC # E4: 1,3,5,7 # E5: 3 => UNS
* INC # E4: 1,3,5,7 # I5: 4,7 => UNS
* INC # E4: 1,3,5,7 # I5: 3 => UNS
* INC # E4: 1,3,5,7 # A8: 2,8 => UNS
* INC # E4: 1,3,5,7 # B8: 2,8 => UNS
* INC # E4: 1,3,5,7 # A8: 2,8 => UNS
* INC # E4: 1,3,5,7 # B8: 2,8 => UNS
* INC # E4: 1,3,5,7 => UNS
* INC # A8: 2,8 # B1: 5,7 => UNS
* INC # A8: 2,8 # C2: 5,7 => UNS
* INC # A8: 2,8 # B3: 5,7 => UNS
* INC # A8: 2,8 # D2: 5,7 => UNS
* INC # A8: 2,8 # I2: 5,7 => UNS
* PRF # A8: 2,8 # B8: 5,7 => SOL
* STA # A8: 2,8 + B8: 5,7
* CNT 102 HDP CHAINS / 103 HYP OPENED