Analysis of xx-mith-te3-00115166-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: ...4....9.57189......2.3..5.85.9..617.6.1.95.......8.7.69...1..5.1....9887.9.15.. initial

Autosolve

position: ...4....9.57189......2.3..5.85.9..617.6.1.95.......8.7.69...17.5.1....9887.9.15.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

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

Pair Reduction

Pair Reduction

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

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:24.353018

The following important HDP chains were detected:

* DIS # G3: 4 # E8: 3,6 => CTR => E8: 2,4
* DIS # G3: 4 + E8: 2,4 # E9: 2,4 => CTR => E9: 3,6
* DIS # G3: 4 + E8: 2,4 + E9: 3,6 # G8: 2 => CTR => G8: 3,6
* DIS # G3: 4 + E8: 2,4 + E9: 3,6 + G8: 3,6 # D6: 5 => CTR => D6: 3,6
* PRF # G3: 4 + E8: 2,4 + E9: 3,6 + G8: 3,6 + D6: 3,6 # C9: 2,3 => SOL
* STA # G3: 4 + E8: 2,4 + E9: 3,6 + G8: 3,6 + D6: 3,6 + C9: 2,3
* CNT   5 HDP CHAINS /  91 HYP OPENED

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

Details

Positions

...4....9.57189......2.3..5.85.9..617.6.1.95.......8.7.69...1..5.1....9887.9.15.. initial
...4....9.57189......2.3..5.85.9..617.6.1.95.......8.7.69...17.5.1....9887.9.15.. autosolve
123456789457189236698273415285794361736812954914635827369548172541327698872961543 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
C3: 4,8
E3: 6,7
H1: 1,8
H3: 1,8
A6: 1,9
B6: 1,9
D4: 3,7
D5: 3,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H1,H3: 1.. / H1 = 1  => 11 pairs (_) / H3 = 1  =>  7 pairs (_)
A6,B6: 1.. / A6 = 1  =>  8 pairs (_) / B6 = 1  =>  7 pairs (_)
E1,F1: 5.. / E1 = 5  => 11 pairs (_) / F1 = 5  => 11 pairs (_)
D6,D7: 5.. / D6 = 5  =>  9 pairs (_) / D7 = 5  =>  9 pairs (_)
G8,I9: 6.. / G8 = 6  => 15 pairs (_) / I9 = 6  =>  8 pairs (_)
E9,I9: 6.. / E9 = 6  => 15 pairs (_) / I9 = 6  =>  8 pairs (_)
D6,D8: 6.. / D6 = 6  =>  9 pairs (_) / D8 = 6  =>  9 pairs (_)
I2,I9: 6.. / I2 = 6  => 15 pairs (_) / I9 = 6  =>  8 pairs (_)
G1,G3: 7.. / G1 = 7  => 11 pairs (_) / G3 = 7  =>  9 pairs (_)
D4,F4: 7.. / D4 = 7  =>  9 pairs (_) / F4 = 7  => 10 pairs (_)
E3,G3: 7.. / E3 = 7  => 11 pairs (_) / G3 = 7  =>  9 pairs (_)
D4,D8: 7.. / D4 = 7  =>  9 pairs (_) / D8 = 7  => 10 pairs (_)
C1,C3: 8.. / C1 = 8  => 11 pairs (_) / C3 = 8  =>  7 pairs (_)
H1,H3: 8.. / H1 = 8  =>  7 pairs (_) / H3 = 8  => 11 pairs (_)
D5,F5: 8.. / D5 = 8  =>  9 pairs (_) / F5 = 8  =>  9 pairs (_)
D7,F7: 8.. / D7 = 8  =>  9 pairs (_) / F7 = 8  =>  9 pairs (_)
C1,H1: 8.. / C1 = 8  => 11 pairs (_) / H1 = 8  =>  7 pairs (_)
C3,H3: 8.. / C3 = 8  =>  7 pairs (_) / H3 = 8  => 11 pairs (_)
D5,D7: 8.. / D5 = 8  =>  9 pairs (_) / D7 = 8  =>  9 pairs (_)
F5,F7: 8.. / F5 = 8  =>  9 pairs (_) / F7 = 8  =>  9 pairs (_)
A3,B3: 9.. / A3 = 9  =>  8 pairs (_) / B3 = 9  =>  7 pairs (_)
A6,B6: 9.. / A6 = 9  =>  7 pairs (_) / B6 = 9  =>  8 pairs (_)
A3,A6: 9.. / A3 = 9  =>  8 pairs (_) / A6 = 9  =>  7 pairs (_)
B3,B6: 9.. / B3 = 9  =>  7 pairs (_) / B6 = 9  =>  8 pairs (_)
* DURATION: 0:00:06.867497  START: 05:40:09.488235  END: 05:40:16.355732 2025-04-05
* CP COUNT: (24)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:24.049777  START: 05:40:20.925731  END: 05:40:44.975508 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00115166-base-pr-002.dot
* REASONING
* DIS # G3: 4 # E8: 3,6 => CTR => E8: 2,4
* DIS # G3: 4 + E8: 2,4 # E9: 2,4 => CTR => E9: 3,6
* DIS # G3: 4 + E8: 2,4 + E9: 3,6 # G8: 2 => CTR => G8: 3,6
* DIS # G3: 4 + E8: 2,4 + E9: 3,6 + G8: 3,6 # D6: 5 => CTR => D6: 3,6
* PRF # G3: 4 + E8: 2,4 + E9: 3,6 + G8: 3,6 + D6: 3,6 # C9: 2,3 => SOL
* STA # G3: 4 + E8: 2,4 + E9: 3,6 + G8: 3,6 + D6: 3,6 + C9: 2,3
* CNT   5 HDP CHAINS /  91 HYP OPENED

Header Info

rating: 29342; r2: 551548; index: 115166

Solution

position: 123456789457189236698273415285794361736812954914635827369548172541327698872961543 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 # E1: 6,7 => UNS
* INC # F1: 6,7 => UNS
* INC # G3: 6,7 => UNS
* INC # G3: 4 => UNS
* INC # E8: 6,7 => UNS
* INC # E8: 2,3,4 => UNS
* INC # A3: 1,9 => UNS
* INC # A3: 4,6 => UNS
* INC # B3: 1,9 => UNS
* INC # B3: 4 => UNS
* INC # D8: 3,7 => UNS
* INC # D8: 6 => UNS
* INC # D7: 3,8 => UNS
* INC # D7: 5 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E1: 6,7 => UNS
* INC # F1: 6,7 => UNS
* INC # G3: 6,7 => UNS
* INC # G3: 4 => UNS
* INC # E8: 6,7 => UNS
* INC # E8: 2,3,4 => UNS
* INC # A3: 1,9 => UNS
* INC # A3: 4,6 => UNS
* INC # B3: 1,9 => UNS
* INC # B3: 4 => UNS
* INC # D8: 3,7 => UNS
* INC # D8: 6 => UNS
* INC # D7: 3,8 => UNS
* INC # D7: 5 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # E1: 6,7 => UNS
* INC # F1: 6,7 => UNS
* INC # G3: 6,7 => UNS
* INC # G3: 4 => UNS
* INC # E8: 6,7 => UNS
* INC # E8: 2,3,4 => UNS
* INC # A3: 1,9 => UNS
* INC # A3: 4,6 => UNS
* INC # B3: 1,9 => UNS
* INC # B3: 4 => UNS
* INC # D8: 3,7 => UNS
* INC # D8: 6 => UNS
* INC # D7: 3,8 => UNS
* INC # D7: 5 => UNS
* INC # E1: 6,7 # G1: 6,7 => UNS
* INC # E1: 6,7 # G1: 2,3 => UNS
* INC # E1: 6,7 # G3: 6,7 => UNS
* INC # E1: 6,7 # G3: 4 => UNS
* INC # E1: 6,7 # A3: 1,9 => UNS
* INC # E1: 6,7 # A3: 4,6 => UNS
* INC # E1: 6,7 # B3: 1,9 => UNS
* INC # E1: 6,7 # B3: 4 => UNS
* INC # E1: 6,7 # D7: 3,8 => UNS
* INC # E1: 6,7 # D7: 5 => UNS
* INC # E1: 6,7 => UNS
* INC # F1: 6,7 # G1: 6,7 => UNS
* INC # F1: 6,7 # G1: 2,3 => UNS
* INC # F1: 6,7 # F8: 6,7 => UNS
* INC # F1: 6,7 # F8: 2,4 => UNS
* INC # F1: 6,7 # G3: 6,7 => UNS
* INC # F1: 6,7 # G3: 4 => UNS
* INC # F1: 6,7 # E8: 6,7 => UNS
* INC # F1: 6,7 # E8: 2,3,4 => UNS
* INC # F1: 6,7 # A3: 1,9 => UNS
* INC # F1: 6,7 # A3: 4,6 => UNS
* INC # F1: 6,7 # B3: 1,9 => UNS
* INC # F1: 6,7 # B3: 4 => UNS
* INC # F1: 6,7 # D8: 3,7 => UNS
* INC # F1: 6,7 # D8: 6 => UNS
* INC # F1: 6,7 => UNS
* INC # G3: 6,7 # E1: 6,7 => UNS
* INC # G3: 6,7 # F1: 6,7 => UNS
* INC # G3: 6,7 # E8: 6,7 => UNS
* INC # G3: 6,7 # E8: 2,3,4 => UNS
* INC # G3: 6,7 # G1: 6,7 => UNS
* INC # G3: 6,7 # G1: 2,3 => UNS
* INC # G3: 6,7 # A3: 1,9 => UNS
* INC # G3: 6,7 # A3: 4 => UNS
* INC # G3: 6,7 # B3: 1,9 => UNS
* INC # G3: 6,7 # B3: 4 => UNS
* INC # G3: 6,7 # D8: 3,7 => UNS
* INC # G3: 6,7 # D8: 6 => UNS
* INC # G3: 6,7 # D7: 3,8 => UNS
* INC # G3: 6,7 # D7: 5 => UNS
* INC # G3: 6,7 => UNS
* INC # G3: 4 # B5: 2,3 => UNS
* INC # G3: 4 # B8: 2,3 => UNS
* INC # G3: 4 # C6: 2,3 => UNS
* INC # G3: 4 # C9: 2,3 => UNS
* INC # G3: 4 # E6: 5,6 => UNS
* INC # G3: 4 # E6: 2,3 => UNS
* INC # G3: 4 # F6: 5,6 => UNS
* INC # G3: 4 # F6: 2 => UNS
* INC # G3: 4 # G2: 2,3 => UNS
* INC # G3: 4 # I2: 2,3 => UNS
* INC # G3: 4 # H6: 2,3 => UNS
* INC # G3: 4 # H9: 2,3 => UNS
* INC # G3: 4 # B5: 2,3 => UNS
* INC # G3: 4 # C6: 2,3 => UNS
* INC # G3: 4 # D7: 3,8 => UNS
* INC # G3: 4 # D7: 5 => UNS
* INC # G3: 4 # F7: 2,8 => UNS
* INC # G3: 4 # F7: 5 => UNS
* INC # G3: 4 # I5: 2,3 => UNS
* INC # G3: 4 # H6: 2,3 => UNS
* INC # G3: 4 # G2: 2,3 => UNS
* INC # G3: 4 # G8: 2,3 => UNS
* INC # G3: 4 # B8: 2,3 => UNS
* INC # G3: 4 # C9: 2,3 => UNS
* INC # G3: 4 # E7: 2,3 => UNS
* INC # G3: 4 # I7: 2,3 => UNS
* DIS # G3: 4 # E8: 3,6 => CTR => E8: 2,4
* INC # G3: 4 + E8: 2,4 # E9: 3,6 => UNS
* INC # G3: 4 + E8: 2,4 # E9: 3,6 => UNS
* DIS # G3: 4 + E8: 2,4 # E9: 2,4 => CTR => E9: 3,6
* INC # G3: 4 + E8: 2,4 + E9: 3,6 # G8: 3,6 => UNS
* DIS # G3: 4 + E8: 2,4 + E9: 3,6 # G8: 2 => CTR => G8: 3,6
* INC # G3: 4 + E8: 2,4 + E9: 3,6 + G8: 3,6 # D6: 3,6 => UNS
* DIS # G3: 4 + E8: 2,4 + E9: 3,6 + G8: 3,6 # D6: 5 => CTR => D6: 3,6
* PRF # G3: 4 + E8: 2,4 + E9: 3,6 + G8: 3,6 + D6: 3,6 # C9: 2,3 => SOL
* STA # G3: 4 + E8: 2,4 + E9: 3,6 + G8: 3,6 + D6: 3,6 + C9: 2,3
* CNT  90 HDP CHAINS /  91 HYP OPENED