Analysis of xx-mith-te3-00133883-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: ...456.8945..8.......3.2.54.......1.5....7.989..8..5.7.14......7.5.1....89..4..7. initial

Autosolve

position: ...456.8945..8.......3.2.54.......1.5....7.989..8..5.7.14.....57.5.1..4.89..4..71 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: 0:00:26.986708

The following important HDP chains were detected:

* DIS # D2: 1 # B5: 6 => CTR => B5: 2,3
* DIS # D2: 1 + B5: 2,3 # A1: 2,3 => CTR => A1: 1
* PRF # D2: 1 + B5: 2,3 + A1: 1 # E5: 2,6 => SOL
* STA # D2: 1 + B5: 2,3 + A1: 1 + E5: 2,6
* CNT   3 HDP CHAINS / 119 HYP OPENED

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

Details

Positions

...456.8945..8.......3.2.54.......1.5....7.989..8..5.7.14......7.5.1....89..4..7. initial
...456.8945..8.......3.2.54.......1.5....7.989..8..5.7.14.....57.5.1..4.89..4..71 autosolve
123456789457189236689372154278594613531267498946831527314728965765913842892645371 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
A3: 1,6
F2: 1,9
E3: 7,9
B4: 7,8
C4: 7,8
F9: 3,5
G7: 8,9
G8: 8,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,A3: 1.. / A1 = 1  => 11 pairs (_) / A3 = 1  => 11 pairs (_)
D2,F2: 1.. / D2 = 1  =>  8 pairs (_) / F2 = 1  =>  9 pairs (_)
G1,G3: 1.. / G1 = 1  => 11 pairs (_) / G3 = 1  => 11 pairs (_)
C5,C6: 1.. / C5 = 1  =>  8 pairs (_) / C6 = 1  =>  9 pairs (_)
D5,F6: 1.. / D5 = 1  =>  9 pairs (_) / F6 = 1  =>  8 pairs (_)
A1,G1: 1.. / A1 = 1  => 11 pairs (_) / G1 = 1  => 11 pairs (_)
A3,G3: 1.. / A3 = 1  => 11 pairs (_) / G3 = 1  => 11 pairs (_)
C5,D5: 1.. / C5 = 1  =>  8 pairs (_) / D5 = 1  =>  9 pairs (_)
C6,F6: 1.. / C6 = 1  =>  9 pairs (_) / F6 = 1  =>  8 pairs (_)
D2,D5: 1.. / D2 = 1  =>  8 pairs (_) / D5 = 1  =>  9 pairs (_)
F2,F6: 1.. / F2 = 1  =>  9 pairs (_) / F6 = 1  =>  8 pairs (_)
B5,B6: 4.. / B5 = 4  =>  8 pairs (_) / B6 = 4  => 10 pairs (_)
F4,F6: 4.. / F4 = 4  => 10 pairs (_) / F6 = 4  =>  8 pairs (_)
G4,G5: 4.. / G4 = 4  =>  8 pairs (_) / G5 = 4  => 10 pairs (_)
F4,G4: 4.. / F4 = 4  => 10 pairs (_) / G4 = 4  =>  8 pairs (_)
B5,G5: 4.. / B5 = 4  =>  8 pairs (_) / G5 = 4  => 10 pairs (_)
B6,F6: 4.. / B6 = 4  => 10 pairs (_) / F6 = 4  =>  8 pairs (_)
D4,F4: 5.. / D4 = 5  =>  8 pairs (_) / F4 = 5  => 12 pairs (_)
D9,F9: 5.. / D9 = 5  => 12 pairs (_) / F9 = 5  =>  8 pairs (_)
D4,D9: 5.. / D4 = 5  =>  8 pairs (_) / D9 = 5  => 12 pairs (_)
F4,F9: 5.. / F4 = 5  => 12 pairs (_) / F9 = 5  =>  8 pairs (_)
D2,E3: 7.. / D2 = 7  => 10 pairs (_) / E3 = 7  =>  8 pairs (_)
B4,C4: 7.. / B4 = 7  =>  7 pairs (_) / C4 = 7  => 10 pairs (_)
D7,E7: 7.. / D7 = 7  =>  8 pairs (_) / E7 = 7  => 10 pairs (_)
D2,D7: 7.. / D2 = 7  => 10 pairs (_) / D7 = 7  =>  8 pairs (_)
E3,E7: 7.. / E3 = 7  =>  8 pairs (_) / E7 = 7  => 10 pairs (_)
B3,C3: 8.. / B3 = 8  =>  7 pairs (_) / C3 = 8  => 10 pairs (_)
B4,C4: 8.. / B4 = 8  => 10 pairs (_) / C4 = 8  =>  7 pairs (_)
F7,F8: 8.. / F7 = 8  =>  7 pairs (_) / F8 = 8  =>  8 pairs (_)
G7,G8: 8.. / G7 = 8  =>  8 pairs (_) / G8 = 8  =>  7 pairs (_)
F7,G7: 8.. / F7 = 8  =>  7 pairs (_) / G7 = 8  =>  8 pairs (_)
F8,G8: 8.. / F8 = 8  =>  8 pairs (_) / G8 = 8  =>  7 pairs (_)
B3,B4: 8.. / B3 = 8  =>  7 pairs (_) / B4 = 8  => 10 pairs (_)
C3,C4: 8.. / C3 = 8  => 10 pairs (_) / C4 = 8  =>  7 pairs (_)
C2,C3: 9.. / C2 = 9  => 10 pairs (_) / C3 = 9  =>  8 pairs (_)
G7,G8: 9.. / G7 = 9  =>  7 pairs (_) / G8 = 9  =>  8 pairs (_)
C3,E3: 9.. / C3 = 9  =>  8 pairs (_) / E3 = 9  => 10 pairs (_)
* DURATION: 0:00:12.132337  START: 10:53:47.599912  END: 10:53:59.732249 2025-04-05
* CP COUNT: (37)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:26.731783  START: 10:54:07.116735  END: 10:54:33.848518 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00133883-base-pr-002.dot
* REASONING
* DIS # D2: 1 # B5: 6 => CTR => B5: 2,3
* DIS # D2: 1 + B5: 2,3 # A1: 2,3 => CTR => A1: 1
* PRF # D2: 1 + B5: 2,3 + A1: 1 # E5: 2,6 => SOL
* STA # D2: 1 + B5: 2,3 + A1: 1 + E5: 2,6
* CNT   3 HDP CHAINS / 119 HYP OPENED

Header Info

rating: 35437; r2: 651050; index: 133883

Solution

position: 123456789457189236689372154278594613531267498946831527314728965765913842892645371 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 # G3: 1,6 => UNS
* INC # G3: 7 => UNS
* INC # D2: 1,9 => UNS
* INC # D2: 7 => UNS
* INC # D2: 7,9 => UNS
* INC # D2: 1 => UNS
* INC # C3: 7,9 => UNS
* INC # C3: 6,8 => UNS
* INC # E7: 7,9 => UNS
* INC # E7: 2,3,6 => UNS
* INC # B3: 7,8 => UNS
* INC # B3: 6 => UNS
* INC # C3: 7,8 => UNS
* INC # C3: 6,9 => UNS
* INC # F4: 3,5 => UNS
* INC # F4: 4,9 => UNS
* INC # F7: 8,9 => UNS
* INC # F7: 3 => UNS
* INC # F8: 8,9 => UNS
* INC # F8: 3 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G3: 1,6 => UNS
* INC # G3: 7 => UNS
* INC # D2: 1,9 => UNS
* INC # D2: 7 => UNS
* INC # D2: 7,9 => UNS
* INC # D2: 1 => UNS
* INC # C3: 7,9 => UNS
* INC # C3: 6,8 => UNS
* INC # E7: 7,9 => UNS
* INC # E7: 2,3,6 => UNS
* INC # B3: 7,8 => UNS
* INC # B3: 6 => UNS
* INC # C3: 7,8 => UNS
* INC # C3: 6,9 => UNS
* INC # F4: 3,5 => UNS
* INC # F4: 4,9 => UNS
* INC # F7: 8,9 => UNS
* INC # F7: 3 => UNS
* INC # F8: 8,9 => UNS
* INC # F8: 3 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # G3: 1,6 => UNS
* INC # G3: 7 => UNS
* INC # D2: 1,9 => UNS
* INC # D2: 7 => UNS
* INC # D2: 7,9 => UNS
* INC # D2: 1 => UNS
* INC # C3: 7,9 => UNS
* INC # C3: 6,8 => UNS
* INC # E7: 7,9 => UNS
* INC # E7: 2,3,6 => UNS
* INC # B3: 7,8 => UNS
* INC # B3: 6 => UNS
* INC # C3: 7,8 => UNS
* INC # C3: 6,9 => UNS
* INC # F4: 3,5 => UNS
* INC # F4: 4,9 => UNS
* INC # F7: 8,9 => UNS
* INC # F7: 3 => UNS
* INC # F8: 8,9 => UNS
* INC # F8: 3 => UNS
* INC # G3: 1,6 # A1: 2,3 => UNS
* INC # G3: 1,6 # C1: 2,3 => UNS
* INC # G3: 1,6 # C2: 2,3 => UNS
* INC # G3: 1,6 # G1: 2,3 => UNS
* INC # G3: 1,6 # G1: 1,7 => UNS
* INC # G3: 1,6 # B5: 2,3 => UNS
* INC # G3: 1,6 # B6: 2,3 => UNS
* INC # G3: 1,6 # B8: 2,3 => UNS
* INC # G3: 1,6 # C3: 7,8 => UNS
* INC # G3: 1,6 # C3: 9 => UNS
* INC # G3: 1,6 # D2: 1,9 => UNS
* INC # G3: 1,6 # D2: 7 => UNS
* INC # G3: 1,6 # D2: 7,9 => UNS
* INC # G3: 1,6 # D2: 1 => UNS
* INC # G3: 1,6 # C3: 7,9 => UNS
* INC # G3: 1,6 # C3: 8 => UNS
* INC # G3: 1,6 # E7: 7,9 => UNS
* INC # G3: 1,6 # E7: 2,3,6 => UNS
* INC # G3: 1,6 # C3: 7,8 => UNS
* INC # G3: 1,6 # C3: 9 => UNS
* INC # G3: 1,6 # F4: 3,5 => UNS
* INC # G3: 1,6 # F4: 4,9 => UNS
* INC # G3: 1,6 # F7: 8,9 => UNS
* INC # G3: 1,6 # F7: 3 => UNS
* INC # G3: 1,6 # F8: 8,9 => UNS
* INC # G3: 1,6 # F8: 3 => UNS
* INC # G3: 1,6 => UNS
* INC # G3: 7 # B1: 2,3 => UNS
* INC # G3: 7 # C1: 2,3 => UNS
* INC # G3: 7 # A4: 2,3 => UNS
* INC # G3: 7 # A7: 2,3 => UNS
* INC # G3: 7 # F7: 8,9 => UNS
* INC # G3: 7 # F7: 3 => UNS
* INC # G3: 7 # F8: 8,9 => UNS
* INC # G3: 7 # F8: 3 => UNS
* INC # G3: 7 => UNS
* INC # D2: 1,9 # A1: 2,3 => UNS
* INC # D2: 1,9 # C1: 2,3 => UNS
* INC # D2: 1,9 # C2: 2,3 => UNS
* INC # D2: 1,9 # G1: 2,3 => UNS
* INC # D2: 1,9 # G1: 1,7 => UNS
* INC # D2: 1,9 # B5: 2,3 => UNS
* INC # D2: 1,9 # B6: 2,3 => UNS
* INC # D2: 1,9 # B8: 2,3 => UNS
* INC # D2: 1,9 # F4: 3,5 => UNS
* INC # D2: 1,9 # F4: 4,9 => UNS
* INC # D2: 1,9 # F7: 8,9 => UNS
* INC # D2: 1,9 # F7: 3 => UNS
* INC # D2: 1,9 # F8: 8,9 => UNS
* INC # D2: 1,9 # F8: 3 => UNS
* INC # D2: 1,9 => UNS
* INC # D2: 7 # B3: 7,8 => UNS
* INC # D2: 7 # B3: 6 => UNS
* INC # D2: 7 # C3: 7,8 => UNS
* INC # D2: 7 # C3: 6 => UNS
* INC # D2: 7 # F7: 8,9 => UNS
* INC # D2: 7 # F7: 3 => UNS
* INC # D2: 7 # F8: 8,9 => UNS
* INC # D2: 7 # F8: 3 => UNS
* INC # D2: 7 => UNS
* INC # D2: 7,9 # G3: 1,6 => UNS
* INC # D2: 7,9 # G3: 7 => UNS
* INC # D2: 7,9 # C2: 7,9 => UNS
* INC # D2: 7,9 # C2: 2,3,6 => UNS
* INC # D2: 7,9 # D7: 7,9 => UNS
* INC # D2: 7,9 # D7: 2,6 => UNS
* INC # D2: 7,9 # C3: 7,9 => UNS
* INC # D2: 7,9 # C3: 6,8 => UNS
* INC # D2: 7,9 # E7: 7,9 => UNS
* INC # D2: 7,9 # E7: 2,3,6 => UNS
* INC # D2: 7,9 # B3: 7,8 => UNS
* INC # D2: 7,9 # B3: 6 => UNS
* INC # D2: 7,9 # C3: 7,8 => UNS
* INC # D2: 7,9 # C3: 6,9 => UNS
* INC # D2: 7,9 # F4: 3,4 => UNS
* INC # D2: 7,9 # F4: 5,9 => UNS
* INC # D2: 7,9 # B6: 3,4 => UNS
* INC # D2: 7,9 # B6: 2,6 => UNS
* INC # D2: 7,9 # F4: 3,5 => UNS
* INC # D2: 7,9 # F4: 4,9 => UNS
* INC # D2: 7,9 # F7: 8,9 => UNS
* INC # D2: 7,9 # F7: 3 => UNS
* INC # D2: 7,9 # F8: 8,9 => UNS
* INC # D2: 7,9 # F8: 3 => UNS
* INC # D2: 7,9 => UNS
* INC # D2: 1 # A1: 2,3 => UNS
* INC # D2: 1 # C1: 2,3 => UNS
* INC # D2: 1 # C2: 2,3 => UNS
* INC # D2: 1 # G1: 2,3 => UNS
* INC # D2: 1 # G1: 1,7 => UNS
* INC # D2: 1 # B5: 2,3 => UNS
* DIS # D2: 1 # B5: 6 => CTR => B5: 2,3
* DIS # D2: 1 + B5: 2,3 # A1: 2,3 => CTR => A1: 1
* INC # D2: 1 + B5: 2,3 + A1: 1 # C1: 2,3 => UNS
* INC # D2: 1 + B5: 2,3 + A1: 1 # C2: 2,3 => UNS
* INC # D2: 1 + B5: 2,3 + A1: 1 # G1: 2,3 => UNS
* INC # D2: 1 + B5: 2,3 + A1: 1 # G1: 7 => UNS
* PRF # D2: 1 + B5: 2,3 + A1: 1 # E5: 2,6 => SOL
* STA # D2: 1 + B5: 2,3 + A1: 1 + E5: 2,6
* CNT 118 HDP CHAINS / 119 HYP OPENED