Analysis of xx-mith-te3-00127068-base.sdk

Contents

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

Original Sudoku

level: hard

position: ...4....9.57..9......237..1.........5.8.6.9..71.8..6.5.81.....767...18..9.5..81.6 initial

Autosolve

position: ...4....9.57..9......237..1.........5.8.6.9..71.8..6.5.81.....767...18..9.5..81.6 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: 0:00:17.447851

The following important HDP chains were detected:

* DIS # A2: 4,8 # C4: 2,3 => CTR => C4: 4,6,9
* PRF # A2: 4,8 + C4: 4,6,9 # F7: 2,3 => SOL
* STA # A2: 4,8 + C4: 4,6,9 + F7: 2,3
* CNT   2 HDP CHAINS /  55 HYP OPENED

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

Details

Positions

`...4....9.57..9......237..1.........5.8.6.9..71.8..6.5.81.....767...18..9.5..81.6`	initial
`...4....9.57..9......237..1.........5.8.6.9..71.8..6.5.81.....767...18..9.5..81.6`	autosolve
`123456789457189263896237451264915378538764912719823645381642597672591834945378126`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
A3: 4,8
F1: 5,6
D2: 1,6
E2: 1,8
G3: 4,5
D5: 1,7
H5: 1,7
D9: 3,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,A2: 1.. / A1 = 1  =>  9 pairs (_) / A2 = 1  => 12 pairs (_)
H4,H5: 1.. / H4 = 1  =>  9 pairs (_) / H5 = 1  =>  8 pairs (_)
A1,E1: 1.. / A1 = 1  =>  9 pairs (_) / E1 = 1  => 12 pairs (_)
D5,H5: 1.. / D5 = 1  =>  9 pairs (_) / H5 = 1  =>  8 pairs (_)
E1,F1: 5.. / E1 = 5  => 15 pairs (_) / F1 = 5  => 10 pairs (_)
G3,H3: 5.. / G3 = 5  =>  9 pairs (_) / H3 = 5  => 21 pairs (_)
G3,G7: 5.. / G3 = 5  =>  9 pairs (_) / G7 = 5  => 21 pairs (_)
F1,D2: 6.. / F1 = 6  => 15 pairs (_) / D2 = 6  => 10 pairs (_)
B4,C4: 6.. / B4 = 6  => 10 pairs (_) / C4 = 6  => 10 pairs (_)
D7,F7: 6.. / D7 = 6  => 15 pairs (_) / F7 = 6  => 10 pairs (_)
D2,H2: 6.. / D2 = 6  => 10 pairs (_) / H2 = 6  => 15 pairs (_)
D2,D7: 6.. / D2 = 6  => 10 pairs (_) / D7 = 6  => 15 pairs (_)
F1,F7: 6.. / F1 = 6  => 15 pairs (_) / F7 = 6  => 10 pairs (_)
G1,H1: 7.. / G1 = 7  =>  9 pairs (_) / H1 = 7  => 14 pairs (_)
D9,E9: 7.. / D9 = 7  =>  9 pairs (_) / E9 = 7  => 10 pairs (_)
D5,H5: 7.. / D5 = 7  =>  8 pairs (_) / H5 = 7  =>  9 pairs (_)
E4,E9: 7.. / E4 = 7  =>  9 pairs (_) / E9 = 7  => 10 pairs (_)
G1,G4: 7.. / G1 = 7  =>  9 pairs (_) / G4 = 7  => 14 pairs (_)
E1,E2: 8.. / E1 = 8  =>  8 pairs (_) / E2 = 8  =>  8 pairs (_)
H4,I4: 8.. / H4 = 8  => 14 pairs (_) / I4 = 8  =>  8 pairs (_)
A3,H3: 8.. / A3 = 8  =>  7 pairs (_) / H3 = 8  => 19 pairs (_)
I2,I4: 8.. / I2 = 8  => 14 pairs (_) / I4 = 8  =>  8 pairs (_)
B3,C3: 9.. / B3 = 9  =>  9 pairs (_) / C3 = 9  => 10 pairs (_)
H7,H8: 9.. / H7 = 9  =>  8 pairs (_) / H8 = 9  =>  9 pairs (_)
C6,E6: 9.. / C6 = 9  => 12 pairs (_) / E6 = 9  => 10 pairs (_)
B3,B4: 9.. / B3 = 9  =>  9 pairs (_) / B4 = 9  => 10 pairs (_)
* DURATION: 0:00:06.735447  START: 09:07:54.008909  END: 09:08:00.744356 2025-04-05
* CP COUNT: (26)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:17.292516  START: 09:08:06.565791  END: 09:08:23.858307 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00127068-base-pr-002.dot
* REASONING
* DIS # A2: 4,8 # C4: 2,3 => CTR => C4: 4,6,9
* PRF # A2: 4,8 + C4: 4,6,9 # F7: 2,3 => SOL
* STA # A2: 4,8 + C4: 4,6,9 + F7: 2,3
* CNT   2 HDP CHAINS /  55 HYP OPENED

Header Info

rating: 33340; r2: 615459; index: 127068

Solution

position: 123456789457189263896237451264915378538764912719823645381642597672591834945378126 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 # A2: 4,8 => UNS
* INC # A2: 1,2,3 => UNS
* INC # H3: 4,8 => UNS
* INC # H3: 5,6 => UNS
* INC # F7: 5,6 => UNS
* INC # F7: 2,3,4 => UNS
* INC # E1: 1,8 => UNS
* INC # E1: 5 => UNS
* INC # A2: 1,8 => UNS
* INC # A2: 2,3,4 => UNS
* INC # H3: 4,5 => UNS
* INC # H3: 6,8 => UNS
* INC # G7: 4,5 => UNS
* INC # G7: 2,3 => UNS
* INC # D4: 1,7 => UNS
* INC # E4: 1,7 => UNS
* INC # H4: 1,7 => UNS
* INC # H4: 2,3,4,8 => UNS
* INC # D4: 3,7 => UNS
* INC # D4: 1,5,9 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A2: 4,8 => UNS
* INC # A2: 1,2,3 => UNS
* INC # H3: 4,8 => UNS
* INC # H3: 5,6 => UNS
* INC # F7: 5,6 => UNS
* INC # F7: 2,3,4 => UNS
* INC # E1: 1,8 => UNS
* INC # E1: 5 => UNS
* INC # A2: 1,8 => UNS
* INC # A2: 2,3,4 => UNS
* INC # H3: 4,5 => UNS
* INC # H3: 6,8 => UNS
* INC # G7: 4,5 => UNS
* INC # G7: 2,3 => UNS
* INC # D4: 1,7 => UNS
* INC # E4: 1,7 => UNS
* INC # H4: 1,7 => UNS
* INC # H4: 2,3,4,8 => UNS
* INC # D4: 3,7 => UNS
* INC # D4: 1,5,9 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A2: 4,8 => UNS
* INC # A2: 1,2,3 => UNS
* INC # H3: 4,8 => UNS
* INC # H3: 5,6 => UNS
* INC # F7: 5,6 => UNS
* INC # F7: 2,3,4 => UNS
* INC # E1: 1,8 => UNS
* INC # E1: 5 => UNS
* INC # A2: 1,8 => UNS
* INC # A2: 2,3,4 => UNS
* INC # H3: 4,5 => UNS
* INC # H3: 6,8 => UNS
* INC # G7: 4,5 => UNS
* INC # G7: 2,3 => UNS
* INC # D4: 1,7 => UNS
* INC # E4: 1,7 => UNS
* INC # H4: 1,7 => UNS
* INC # H4: 2,3,4,8 => UNS
* INC # D4: 3,7 => UNS
* INC # D4: 1,5,9 => UNS
* INC # A2: 4,8 # B5: 2,3 => UNS
* INC # A2: 4,8 # B9: 2,3 => UNS
* DIS # A2: 4,8 # C4: 2,3 => CTR => C4: 4,6,9
* INC # A2: 4,8 + C4: 4,6,9 # C6: 2,3 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # C8: 2,3 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # C6: 2,3 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # C8: 2,3 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # H2: 4,8 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # H2: 2,3,6 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # H3: 4,8 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # H3: 5 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # C4: 6,9 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # C4: 4 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # F7: 5,6 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # F7: 2,3,4 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # H2: 6,8 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # H2: 2,3,4 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # H3: 4,5 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # H3: 8 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # G7: 4,5 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # G7: 2,3 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # B5: 2,3 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # C6: 2,3 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # F4: 2,3 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # G4: 2,3 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # C4: 6,9 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # C4: 4 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # D4: 1,7 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # E4: 1,7 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # D4: 1,7 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # E4: 1,7 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # C8: 2,3 => UNS
* INC # A2: 4,8 + C4: 4,6,9 # B9: 2,3 => UNS
* PRF # A2: 4,8 + C4: 4,6,9 # F7: 2,3 => SOL
* STA # A2: 4,8 + C4: 4,6,9 + F7: 2,3
* CNT  54 HDP CHAINS /  55 HYP OPENED