Analysis of xx-mith-te3-00107406-base.sdk

Contents

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

Original Sudoku

level: hard

position: 1....6.8.4..18...6....37.14.763.........7164..14..8.73.4...3....95......8.1...4.7 initial

Autosolve

position: 1..4.6.8.4..18...6....37.14.763.........7164..14..8.73.42..3....95......8.1...4.7 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: 0:00:05.017619

The following important HDP chains were detected:

* PRF # C5: 8,9 # G2: 2,5 => SOL
* STA # C5: 8,9 + G2: 2,5
* CNT   1 HDP CHAINS /  21 HYP OPENED

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

Details

Positions

`1....6.8.4..18...6....37.14.763.........7164..14..8.73.4...3....95......8.1...4.7`	initial
`1..4.6.8.4..18...6....37.14.763.........7164..14..8.73.42..3....95......8.1...4.7`	autosolve
`123456789457189236968237514276394158389571642514628973642713895795842361831965427`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
C3: 8,9
G4: 1,8
I4: 1,8
A7: 6,7
B9: 3,6
D7: 7,8
D8: 7,8
F8: 2,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G4,I4: 1.. / G4 = 1  =>  7 pairs (_) / I4 = 1  =>  7 pairs (_)
E7,E8: 1.. / E7 = 1  =>  8 pairs (_) / E8 = 1  =>  8 pairs (_)
A8,B9: 3.. / A8 = 3  => 10 pairs (_) / B9 = 3  => 20 pairs (_)
B9,H9: 3.. / B9 = 3  => 20 pairs (_) / H9 = 3  => 10 pairs (_)
A5,A8: 3.. / A5 = 3  => 20 pairs (_) / A8 = 3  => 10 pairs (_)
E4,F4: 4.. / E4 = 4  =>  7 pairs (_) / F4 = 4  => 25 pairs (_)
E8,F8: 4.. / E8 = 4  => 25 pairs (_) / F8 = 4  =>  7 pairs (_)
E4,E8: 4.. / E4 = 4  =>  7 pairs (_) / E8 = 4  => 25 pairs (_)
F4,F8: 4.. / F4 = 4  => 25 pairs (_) / F8 = 4  =>  7 pairs (_)
A3,B3: 6.. / A3 = 6  => 10 pairs (_) / B3 = 6  => 20 pairs (_)
D6,E6: 6.. / D6 = 6  =>  8 pairs (_) / E6 = 6  => 22 pairs (_)
B3,B9: 6.. / B3 = 6  => 20 pairs (_) / B9 = 6  => 10 pairs (_)
D6,D9: 6.. / D6 = 6  =>  8 pairs (_) / D9 = 6  => 22 pairs (_)
C1,C2: 7.. / C1 = 7  =>  9 pairs (_) / C2 = 7  => 10 pairs (_)
G1,G2: 7.. / G1 = 7  => 10 pairs (_) / G2 = 7  =>  9 pairs (_)
A7,A8: 7.. / A7 = 7  =>  6 pairs (_) / A8 = 7  => 18 pairs (_)
D7,D8: 7.. / D7 = 7  => 18 pairs (_) / D8 = 7  =>  6 pairs (_)
C1,G1: 7.. / C1 = 7  =>  9 pairs (_) / G1 = 7  => 10 pairs (_)
C2,G2: 7.. / C2 = 7  => 10 pairs (_) / G2 = 7  =>  9 pairs (_)
A7,D7: 7.. / A7 = 7  =>  6 pairs (_) / D7 = 7  => 18 pairs (_)
A8,D8: 7.. / A8 = 7  => 18 pairs (_) / D8 = 7  =>  6 pairs (_)
B3,C3: 8.. / B3 = 8  => 13 pairs (_) / C3 = 8  =>  9 pairs (_)
B5,C5: 8.. / B5 = 8  =>  9 pairs (_) / C5 = 8  => 13 pairs (_)
G4,I4: 8.. / G4 = 8  =>  7 pairs (_) / I4 = 8  =>  7 pairs (_)
D7,D8: 8.. / D7 = 8  =>  6 pairs (_) / D8 = 8  => 18 pairs (_)
B3,B5: 8.. / B3 = 8  => 13 pairs (_) / B5 = 8  =>  9 pairs (_)
C3,C5: 8.. / C3 = 8  =>  9 pairs (_) / C5 = 8  => 13 pairs (_)
* DURATION: 0:00:08.277218  START: 17:07:45.779939  END: 17:07:54.057157 2025-04-06
* CP COUNT: (27)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:04.896298  START: 17:07:59.515201  END: 17:08:04.411499 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00107406-base-pr-002.dot
* REASONING
* PRF # C5: 8,9 # G2: 2,5 => SOL
* STA # C5: 8,9 + G2: 2,5
* CNT   1 HDP CHAINS /  21 HYP OPENED

Header Info

rating: 26990; r2: 532082; index: 107406

Solution

position: 123456789457189236968237514276394158389571642514628973642713895795842361831965427 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 # C5: 8,9 => UNS
* INC # C5: 3 => UNS
* INC # G7: 1,8 => UNS
* INC # G8: 1,8 => UNS
* INC # I7: 1,8 => UNS
* INC # I8: 1,8 => UNS
* INC # A8: 6,7 => UNS
* INC # A8: 3 => UNS
* INC # A8: 3,6 => UNS
* INC # A8: 7 => UNS
* INC # H9: 3,6 => UNS
* INC # H9: 2,5,9 => UNS
* INC # E8: 2,4 => UNS
* INC # E8: 1,6 => UNS
* INC # F4: 2,4 => UNS
* INC # F4: 5,9 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C5: 8,9 => UNS
* INC # C5: 3 => UNS
* INC # G7: 1,8 => UNS
* INC # G8: 1,8 => UNS
* INC # I7: 1,8 => UNS
* INC # I8: 1,8 => UNS
* INC # A8: 6,7 => UNS
* INC # A8: 3 => UNS
* INC # A8: 3,6 => UNS
* INC # A8: 7 => UNS
* INC # H9: 3,6 => UNS
* INC # H9: 2,5,9 => UNS
* INC # E8: 2,4 => UNS
* INC # E8: 1,6 => UNS
* INC # F4: 2,4 => UNS
* INC # F4: 5,9 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # C5: 8,9 => UNS
* INC # C5: 3 => UNS
* INC # G7: 1,8 => UNS
* INC # G8: 1,8 => UNS
* INC # I7: 1,8 => UNS
* INC # I8: 1,8 => UNS
* INC # A8: 6,7 => UNS
* INC # A8: 3 => UNS
* INC # A8: 3,6 => UNS
* INC # A8: 7 => UNS
* INC # H9: 3,6 => UNS
* INC # H9: 2,5,9 => UNS
* INC # E8: 2,4 => UNS
* INC # E8: 1,6 => UNS
* INC # F4: 2,4 => UNS
* INC # F4: 5,9 => UNS
* INC # C5: 8,9 # E1: 2,5 => UNS
* INC # C5: 8,9 # I1: 2,5 => UNS
* INC # C5: 8,9 # F2: 2,5 => UNS
* PRF # C5: 8,9 # G2: 2,5 => SOL
* STA # C5: 8,9 + G2: 2,5
* CNT  20 HDP CHAINS /  21 HYP OPENED