Analysis of xx-mith-te3-00023293-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: .2......9...1..23..8....4.526.81..7.7..3.2....3..67.2.31....8...726.8...8.6.31..2 initial

Autosolve

position: .2......9...1..23..8....4.526.81..7.7..3.2....3..67.2.31....8...726.8...8.6.31..2 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # H1: 1,6 => CTR => H1: 8
* CNT   1 HDP CHAINS /   9 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 # H1: 1,6 => CTR => H1: 8
* STA H1: 8
* CNT   1 HDP CHAINS /  22 HYP OPENED

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

Pair Reduction Position

position: .2.....89...18.23..8....4.526.81..7.7..3.2....3..67.2.31....8...726.8...8.6.31..2 pair_reduction
Pair Reduction

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

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:15.252809

The following important HDP chains were detected:

* DIS # I7: 4 # F3: 6,9 => CTR => F3: 3
* DIS # I7: 4 + F3: 3 # C4: 5,9 => CTR => C4: 4
* DIS # G1: 7 # A6: 4,5 => CTR => A6: 1,9
* PRF # G1: 7 + A6: 1,9 # B5: 4,5 => SOL
* STA # G1: 7 + A6: 1,9 + B5: 4,5
* CNT   4 HDP CHAINS /  78 HYP OPENED

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

Details

Positions

.2......9...1..23..8....4.526.81..7.7..3.2....3..67.2.31....8...726.8...8.6.31..2 initial
.2......9...1..23..8....4.526.81..7.7..3.2....3..67.2.31....8...726.8...8.6.31..2 autosolve
.2.....89...18.23..8....4.526.81..7.7..3.2....3..67.2.31....8...726.8...8.6.31..2 pair_reduction
123456789457189236689273415265814973741392658938567124314925867572648391896731542 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (2)
H3: 1,6
I4: 3,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D3,E3: 2.. / D3 = 2  =>  4 pairs (_) / E3 = 2  =>  3 pairs (_)
D7,E7: 2.. / D7 = 2  =>  3 pairs (_) / E7 = 2  =>  4 pairs (_)
D3,D7: 2.. / D3 = 2  =>  4 pairs (_) / D7 = 2  =>  3 pairs (_)
E3,E7: 2.. / E3 = 2  =>  3 pairs (_) / E7 = 2  =>  4 pairs (_)
C1,C3: 3.. / C1 = 3  =>  2 pairs (_) / C3 = 3  =>  7 pairs (_)
F1,F3: 3.. / F1 = 3  =>  7 pairs (_) / F3 = 3  =>  2 pairs (_)
G4,I4: 3.. / G4 = 3  =>  6 pairs (_) / I4 = 3  =>  3 pairs (_)
G8,I8: 3.. / G8 = 3  =>  3 pairs (_) / I8 = 3  =>  6 pairs (_)
C1,F1: 3.. / C1 = 3  =>  2 pairs (_) / F1 = 3  =>  7 pairs (_)
C3,F3: 3.. / C3 = 3  =>  7 pairs (_) / F3 = 3  =>  2 pairs (_)
G4,G8: 3.. / G4 = 3  =>  6 pairs (_) / G8 = 3  =>  3 pairs (_)
I4,I8: 3.. / I4 = 3  =>  3 pairs (_) / I8 = 3  =>  6 pairs (_)
H7,I7: 6.. / H7 = 6  =>  9 pairs (_) / I7 = 6  =>  9 pairs (_)
G1,G5: 6.. / G1 = 6  => 13 pairs (_) / G5 = 6  =>  5 pairs (_)
G1,I2: 7.. / G1 = 7  => 19 pairs (_) / I2 = 7  => 10 pairs (_)
I7,G9: 7.. / I7 = 7  => 19 pairs (_) / G9 = 7  => 10 pairs (_)
D9,G9: 7.. / D9 = 7  => 19 pairs (_) / G9 = 7  => 10 pairs (_)
G1,G9: 7.. / G1 = 7  => 19 pairs (_) / G9 = 7  => 10 pairs (_)
I2,I7: 7.. / I2 = 7  => 10 pairs (_) / I7 = 7  => 19 pairs (_)
E1,E2: 8.. / E1 = 8  =>  0 pairs (X) / E2 = 8  =>  3 pairs (_)
H1,I2: 8.. / H1 = 8  =>  3 pairs (_) / I2 = 8  =>  0 pairs (X)
C5,C6: 8.. / C5 = 8  =>  4 pairs (_) / C6 = 8  =>  5 pairs (_)
E1,H1: 8.. / E1 = 8  =>  0 pairs (X) / H1 = 8  =>  3 pairs (_)
E2,I2: 8.. / E2 = 8  =>  3 pairs (_) / I2 = 8  =>  0 pairs (X)
C6,I6: 8.. / C6 = 8  =>  5 pairs (_) / I6 = 8  =>  4 pairs (_)
H1,H5: 8.. / H1 = 8  =>  3 pairs (_) / H5 = 8  =>  0 pairs (X)
* DURATION: 0:00:05.844586  START: 06:31:56.930830  END: 06:32:02.775416 2025-04-06
* CP COUNT: (26)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:15.014677  START: 06:32:07.616427  END: 06:32:22.631104 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00023293-base-pr-002.dot
* REASONING
* DIS # I7: 4 # F3: 6,9 => CTR => F3: 3
* DIS # I7: 4 + F3: 3 # C4: 5,9 => CTR => C4: 4
* DIS # G1: 7 # A6: 4,5 => CTR => A6: 1,9
* PRF # G1: 7 + A6: 1,9 # B5: 4,5 => SOL
* STA # G1: 7 + A6: 1,9 + B5: 4,5
* CNT   4 HDP CHAINS /  78 HYP OPENED

Header Info

rating: 4745; r2: 119866; index: 23293

Solution

position: 123456789457189236689273415265814973741392658938567124314925867572648391896731542 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 # G1: 1,6 => UNS
* DIS # H1: 1,6 => CTR => H1: 8
* INC # H1: 8 => UNS
* INC # A3: 1,6 => UNS
* INC # A3: 9 => UNS
* INC # H5: 1,6 => UNS
* INC # H5: 4,5,8,9 => UNS
* INC # I8: 3,4 => UNS
* INC # I8: 1 => UNS
* CNT   9 HDP CHAINS /   9 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G1: 1,6 => UNS
* DIS # H1: 1,6 => CTR => H1: 8
* INC H1: 8 # G1: 1,6 => UNS
* INC H1: 8 # G1: 7 => UNS
* INC H1: 8 # A3: 1,6 => UNS
* INC H1: 8 # A3: 9 => UNS
* INC H1: 8 # H5: 1,6 => UNS
* INC H1: 8 # H5: 4,5,9 => UNS
* INC H1: 8 # I8: 3,4 => UNS
* INC H1: 8 # I8: 1 => UNS
* INC H1: 8 # G1: 6,7 => UNS
* INC H1: 8 # G1: 1 => UNS
* INC H1: 8 # I7: 6,7 => UNS
* INC H1: 8 # I7: 4 => UNS
* INC H1: 8 # G1: 1,6 => UNS
* INC H1: 8 # G1: 7 => UNS
* INC H1: 8 # A3: 1,6 => UNS
* INC H1: 8 # A3: 9 => UNS
* INC H1: 8 # H5: 1,6 => UNS
* INC H1: 8 # H5: 4,5,9 => UNS
* INC H1: 8 # I8: 3,4 => UNS
* INC H1: 8 # I8: 1 => UNS
* STA H1: 8
* CNT  22 HDP CHAINS /  22 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # G1: 6,7 => UNS
* INC # G1: 1 => UNS
* INC # I7: 6,7 => UNS
* INC # I7: 4 => UNS
* INC # G1: 1,6 => UNS
* INC # G1: 7 => UNS
* INC # A3: 1,6 => UNS
* INC # A3: 9 => UNS
* INC # H5: 1,6 => UNS
* INC # H5: 4,5,9 => UNS
* INC # I8: 3,4 => UNS
* INC # I8: 1 => UNS
* INC # G1: 6,7 # A2: 6,9 => UNS
* INC # G1: 6,7 # A2: 4,5 => UNS
* INC # G1: 6,7 # F3: 6,9 => UNS
* INC # G1: 6,7 # F3: 3 => UNS
* INC # G1: 6,7 # I7: 6,7 => UNS
* INC # G1: 6,7 # I7: 4 => UNS
* INC # G1: 6,7 => UNS
* INC # G1: 1 # I5: 1,8 => UNS
* INC # G1: 1 # I5: 4 => UNS
* INC # G1: 1 # I8: 3,4 => UNS
* INC # G1: 1 # I8: 1 => UNS
* INC # G1: 1 # G4: 5,9 => UNS
* INC # G1: 1 # H5: 5,9 => UNS
* INC # G1: 1 # A6: 5,9 => UNS
* INC # G1: 1 # D6: 5,9 => UNS
* INC # G1: 1 # G8: 5,9 => UNS
* INC # G1: 1 # G8: 3 => UNS
* INC # G1: 1 # I5: 1,8 => UNS
* INC # G1: 1 # I5: 4 => UNS
* INC # G1: 1 # D3: 2,7 => UNS
* INC # G1: 1 # D3: 9 => UNS
* INC # G1: 1 # E3: 2,7 => UNS
* INC # G1: 1 # E3: 9 => UNS
* INC # G1: 1 => UNS
* INC # I7: 6,7 # G1: 6,7 => UNS
* INC # I7: 6,7 # G1: 1 => UNS
* INC # I7: 6,7 # G1: 1,6 => UNS
* INC # I7: 6,7 # G1: 7 => UNS
* INC # I7: 6,7 # A3: 1,6 => UNS
* INC # I7: 6,7 # A3: 9 => UNS
* INC # I7: 6,7 # H5: 1,6 => UNS
* INC # I7: 6,7 # H5: 4,5,9 => UNS
* INC # I7: 6,7 # I8: 3,4 => UNS
* INC # I7: 6,7 # I8: 1 => UNS
* INC # I7: 6,7 => UNS
* INC # I7: 4 # A2: 6,9 => UNS
* INC # I7: 4 # A2: 4,5 => UNS
* DIS # I7: 4 # F3: 6,9 => CTR => F3: 3
* DIS # I7: 4 + F3: 3 # C4: 5,9 => CTR => C4: 4
* INC # I7: 4 + F3: 3 + C4: 4 => UNS
* INC # G1: 1,6 # A1: 1,6 => UNS
* INC # G1: 1,6 # A1: 4,5 => UNS
* INC # G1: 1,6 # G5: 1,6 => UNS
* INC # G1: 1,6 # G5: 5,9 => UNS
* INC # G1: 1,6 # A3: 1,6 => UNS
* INC # G1: 1,6 # A3: 9 => UNS
* INC # G1: 1,6 # H5: 1,6 => UNS
* INC # G1: 1,6 # H5: 4,5,9 => UNS
* INC # G1: 1,6 # I5: 1,8 => UNS
* INC # G1: 1,6 # I5: 4,6 => UNS
* INC # G1: 1,6 # I6: 1,8 => UNS
* INC # G1: 1,6 # I6: 4 => UNS
* INC # G1: 1,6 # I8: 3,4 => UNS
* INC # G1: 1,6 # I8: 1 => UNS
* INC # G1: 1,6 # D3: 2,7 => UNS
* INC # G1: 1,6 # D3: 9 => UNS
* INC # G1: 1,6 # E3: 2,7 => UNS
* INC # G1: 1,6 # E3: 9 => UNS
* INC # G1: 1,6 # H7: 4,6 => UNS
* INC # G1: 1,6 # H7: 5,9 => UNS
* INC # G1: 1,6 # I5: 4,6 => UNS
* INC # G1: 1,6 # I5: 1,8 => UNS
* INC # G1: 1,6 => UNS
* DIS # G1: 7 # A6: 4,5 => CTR => A6: 1,9
* PRF # G1: 7 + A6: 1,9 # B5: 4,5 => SOL
* STA # G1: 7 + A6: 1,9 + B5: 4,5
* CNT  77 HDP CHAINS /  78 HYP OPENED