Analysis of xx-mith-te3-00039382-base.sdk

Contents

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

Original Sudoku

level: hard

position: .234.6.......8..3..8973....2.1...3.5.952.3...83...192..1....8.2.......93......15. initial

Autosolve

position: .234.6.......8..3..8973....2.1...3.5.952.3...83...192..1....8.2.......93......15. 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: 0:00:17.272478

The following important HDP chains were detected:

* DIS # F2: 9 # H7: 4,6 => CTR => H7: 7
* DIS # F2: 9 + H7: 7 # G3: 4,6 => CTR => G3: 5
* DIS # F2: 9 + H7: 7 + G3: 5 # I3: 4,6 => CTR => I3: 1
* DIS # F2: 9 + H7: 7 + G3: 5 + I3: 1 # E6: 5,6 => CTR => E6: 4
* DIS # F2: 9 + H7: 7 + G3: 5 + I3: 1 + E6: 4 # D7: 3,9 => CTR => D7: 6
* PRF # F2: 9 + H7: 7 + G3: 5 + I3: 1 + E6: 4 + D7: 6 # A2: 4,6 => SOL
* STA # F2: 9 + H7: 7 + G3: 5 + I3: 1 + E6: 4 + D7: 6 + A2: 4,6
* CNT   6 HDP CHAINS /  65 HYP OPENED

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

Details

Positions

`.234.6.......8..3..8973....2.1...3.5.952.3...83...192..1....8.2.......93......15.`	initial
`.234.6.......8..3..8973....2.1...3.5.952.3...83...192..1....8.2.......93......15.`	autosolve
`123456789457189236689732541241978365795263418836541927314695872572814693968327154`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
F3: 2,5
G1: 5,7
D6: 5,6
H5: 1,8
I5: 1,8
A7: 3,9
C8: 2,8
A9: 3,9
C9: 2,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E1,D2: 1.. / E1 = 1  => 10 pairs (_) / D2 = 1  =>  9 pairs (_)
H5,I5: 1.. / H5 = 1  =>  8 pairs (_) / I5 = 1  => 12 pairs (_)
D8,E8: 1.. / D8 = 1  => 10 pairs (_) / E8 = 1  =>  9 pairs (_)
D2,D8: 1.. / D2 = 1  =>  9 pairs (_) / D8 = 1  => 10 pairs (_)
E1,E8: 1.. / E1 = 1  => 10 pairs (_) / E8 = 1  =>  9 pairs (_)
F2,F3: 2.. / F2 = 2  => 10 pairs (_) / F3 = 2  =>  9 pairs (_)
G2,G3: 2.. / G2 = 2  =>  9 pairs (_) / G3 = 2  => 10 pairs (_)
C8,C9: 2.. / C8 = 2  =>  7 pairs (_) / C9 = 2  =>  9 pairs (_)
E8,E9: 2.. / E8 = 2  =>  9 pairs (_) / E9 = 2  =>  7 pairs (_)
F2,G2: 2.. / F2 = 2  => 10 pairs (_) / G2 = 2  =>  9 pairs (_)
F3,G3: 2.. / F3 = 2  =>  9 pairs (_) / G3 = 2  => 10 pairs (_)
C8,E8: 2.. / C8 = 2  =>  7 pairs (_) / E8 = 2  =>  9 pairs (_)
C9,E9: 2.. / C9 = 2  =>  9 pairs (_) / E9 = 2  =>  7 pairs (_)
A7,A9: 3.. / A7 = 3  =>  7 pairs (_) / A9 = 3  =>  7 pairs (_)
D7,D9: 3.. / D7 = 3  =>  7 pairs (_) / D9 = 3  =>  7 pairs (_)
A7,D7: 3.. / A7 = 3  =>  7 pairs (_) / D7 = 3  =>  7 pairs (_)
A9,D9: 3.. / A9 = 3  =>  7 pairs (_) / D9 = 3  =>  7 pairs (_)
D6,E6: 5.. / D6 = 5  =>  9 pairs (_) / E6 = 5  => 14 pairs (_)
A8,B8: 5.. / A8 = 5  => 13 pairs (_) / B8 = 5  =>  9 pairs (_)
B2,B8: 5.. / B2 = 5  => 13 pairs (_) / B8 = 5  =>  9 pairs (_)
H1,I1: 8.. / H1 = 8  =>  8 pairs (_) / I1 = 8  => 12 pairs (_)
D4,F4: 8.. / D4 = 8  => 10 pairs (_) / F4 = 8  => 13 pairs (_)
H5,I5: 8.. / H5 = 8  => 12 pairs (_) / I5 = 8  =>  8 pairs (_)
C8,C9: 8.. / C8 = 8  =>  9 pairs (_) / C9 = 8  =>  7 pairs (_)
H1,H5: 8.. / H1 = 8  =>  8 pairs (_) / H5 = 8  => 12 pairs (_)
I1,I5: 8.. / I1 = 8  => 12 pairs (_) / I5 = 8  =>  8 pairs (_)
I1,I2: 9.. / I1 = 9  =>  9 pairs (_) / I2 = 9  => 12 pairs (_)
A7,A9: 9.. / A7 = 9  =>  7 pairs (_) / A9 = 9  =>  7 pairs (_)
E1,I1: 9.. / E1 = 9  => 12 pairs (_) / I1 = 9  =>  9 pairs (_)
* DURATION: 0:00:08.534109  START: 13:22:45.034792  END: 13:22:53.568901 2025-04-04
* CP COUNT: (29)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:17.058988  START: 13:23:00.114566  END: 13:23:17.173554 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00039382-base-pr-002.dot
* REASONING
* DIS # F2: 9 # H7: 4,6 => CTR => H7: 7
* DIS # F2: 9 + H7: 7 # G3: 4,6 => CTR => G3: 5
* DIS # F2: 9 + H7: 7 + G3: 5 # I3: 4,6 => CTR => I3: 1
* DIS # F2: 9 + H7: 7 + G3: 5 + I3: 1 # E6: 5,6 => CTR => E6: 4
* DIS # F2: 9 + H7: 7 + G3: 5 + I3: 1 + E6: 4 # D7: 3,9 => CTR => D7: 6
* PRF # F2: 9 + H7: 7 + G3: 5 + I3: 1 + E6: 4 + D7: 6 # A2: 4,6 => SOL
* STA # F2: 9 + H7: 7 + G3: 5 + I3: 1 + E6: 4 + D7: 6 + A2: 4,6
* CNT   6 HDP CHAINS /  65 HYP OPENED

Header Info

rating: 8167; r2: 170184; index: 39382

Solution

position: 123456789457189236689732541241978365795263418836541927314695872572814693968327154 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 # F2: 2,5 => UNS
* INC # F2: 9 => UNS
* INC # G3: 2,5 => UNS
* INC # G3: 4,6 => UNS
* INC # G2: 5,7 => UNS
* INC # G2: 2,4,6 => UNS
* INC # A1: 5,7 => UNS
* INC # A1: 1 => UNS
* INC # E6: 5,6 => UNS
* INC # E6: 4,7 => UNS
* INC # D7: 5,6 => UNS
* INC # D7: 3,9 => UNS
* INC # H1: 1,8 => UNS
* INC # H1: 7 => UNS
* INC # I1: 1,8 => UNS
* INC # I1: 7,9 => UNS
* INC # D7: 3,9 => UNS
* INC # D7: 5,6 => UNS
* INC # D9: 3,9 => UNS
* INC # D9: 6,8 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F2: 2,5 => UNS
* INC # F2: 9 => UNS
* INC # G3: 2,5 => UNS
* INC # G3: 4,6 => UNS
* INC # G2: 5,7 => UNS
* INC # G2: 2,4,6 => UNS
* INC # A1: 5,7 => UNS
* INC # A1: 1 => UNS
* INC # E6: 5,6 => UNS
* INC # E6: 4,7 => UNS
* INC # D7: 5,6 => UNS
* INC # D7: 3,9 => UNS
* INC # H1: 1,8 => UNS
* INC # H1: 7 => UNS
* INC # I1: 1,8 => UNS
* INC # I1: 7,9 => UNS
* INC # D7: 3,9 => UNS
* INC # D7: 5,6 => UNS
* INC # D9: 3,9 => UNS
* INC # D9: 6,8 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # F2: 2,5 => UNS
* INC # F2: 9 => UNS
* INC # G3: 2,5 => UNS
* INC # G3: 4,6 => UNS
* INC # G2: 5,7 => UNS
* INC # G2: 2,4,6 => UNS
* INC # A1: 5,7 => UNS
* INC # A1: 1 => UNS
* INC # E6: 5,6 => UNS
* INC # E6: 4,7 => UNS
* INC # D7: 5,6 => UNS
* INC # D7: 3,9 => UNS
* INC # H1: 1,8 => UNS
* INC # H1: 7 => UNS
* INC # I1: 1,8 => UNS
* INC # I1: 7,9 => UNS
* INC # D7: 3,9 => UNS
* INC # D7: 5,6 => UNS
* INC # D9: 3,9 => UNS
* INC # D9: 6,8 => UNS
* INC # F2: 2,5 # I1: 1,9 => UNS
* INC # F2: 2,5 # I1: 7,8 => UNS
* INC # F2: 2,5 # I2: 1,9 => UNS
* INC # F2: 2,5 # I2: 4,6,7 => UNS
* INC # F2: 2,5 # G2: 2,5 => UNS
* INC # F2: 2,5 # G2: 4,6,7 => UNS
* INC # F2: 2,5 # G3: 2,5 => UNS
* INC # F2: 2,5 # G3: 4,6 => UNS
* INC # F2: 2,5 # G2: 5,7 => UNS
* INC # F2: 2,5 # G2: 2,4,6 => UNS
* INC # F2: 2,5 # A1: 5,7 => UNS
* INC # F2: 2,5 # A1: 1 => UNS
* INC # F2: 2,5 # E6: 5,6 => UNS
* INC # F2: 2,5 # E6: 4,7 => UNS
* INC # F2: 2,5 # D7: 5,6 => UNS
* INC # F2: 2,5 # D7: 3,9 => UNS
* INC # F2: 2,5 # H1: 1,8 => UNS
* INC # F2: 2,5 # H1: 7 => UNS
* INC # F2: 2,5 # I1: 1,8 => UNS
* INC # F2: 2,5 # I1: 7,9 => UNS
* INC # F2: 2,5 # D7: 3,9 => UNS
* INC # F2: 2,5 # D7: 5,6 => UNS
* INC # F2: 2,5 # D9: 3,9 => UNS
* INC # F2: 2,5 # D9: 6,8 => UNS
* INC # F2: 2,5 => UNS
* INC # F2: 9 # A1: 1,5 => UNS
* INC # F2: 9 # A1: 7 => UNS
* INC # F2: 9 # A2: 1,5 => UNS
* INC # F2: 9 # A2: 4,6,7 => UNS
* INC # F2: 9 # A1: 5,7 => UNS
* INC # F2: 9 # A1: 1 => UNS
* INC # F2: 9 # I2: 4,6 => UNS
* INC # F2: 9 # G3: 4,6 => UNS
* INC # F2: 9 # I3: 4,6 => UNS
* INC # F2: 9 # A3: 4,6 => UNS
* INC # F2: 9 # A3: 1,5 => UNS
* INC # F2: 9 # H4: 4,6 => UNS
* DIS # F2: 9 # H7: 4,6 => CTR => H7: 7
* INC # F2: 9 + H7: 7 # I2: 4,6 => UNS
* DIS # F2: 9 + H7: 7 # G3: 4,6 => CTR => G3: 5
* DIS # F2: 9 + H7: 7 + G3: 5 # I3: 4,6 => CTR => I3: 1
* DIS # F2: 9 + H7: 7 + G3: 5 + I3: 1 # E6: 5,6 => CTR => E6: 4
* DIS # F2: 9 + H7: 7 + G3: 5 + I3: 1 + E6: 4 # D7: 3,9 => CTR => D7: 6
* PRF # F2: 9 + H7: 7 + G3: 5 + I3: 1 + E6: 4 + D7: 6 # A2: 4,6 => SOL
* STA # F2: 9 + H7: 7 + G3: 5 + I3: 1 + E6: 4 + D7: 6 + A2: 4,6
* CNT  64 HDP CHAINS /  65 HYP OPENED