Analysis of xx-mith-te3-00129638-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 1.3.567.9.57..9...69....5.......4..17.63.5........2.5.36.5..19....6....3.7.9..6.5 initial

Autosolve

position: 1.3.567.9.57..9..669....5.......4.617.63.5.......62.5736.5..19....6...73.7.9..6.5 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: 0:00:14.823955

The following important HDP chains were detected:

* DIS # E2: 8 # C3: 2,4 => CTR => C3: 8
* DIS # E2: 8 + C3: 8 # A9: 2,4 => CTR => A9: 8
* PRF # E2: 8 + C3: 8 + A9: 8 # G8: 2,4 => SOL
* STA # E2: 8 + C3: 8 + A9: 8 + G8: 2,4
* CNT   3 HDP CHAINS /  66 HYP OPENED

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

Details

Positions

1.3.567.9.57..9...69....5.......4..17.63.5........2.5.36.5..19....6....3.7.9..6.5 initial
1.3.567.9.57..9..669....5.......4.617.63.5.......62.5736.5..19....6...73.7.9..6.5 autosolve
123456789457189236698273514235794861786315942941862357362547198519628473874931625 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
H2: 1,3
H3: 1,3
D4: 7,8
D6: 1,8
A8: 5,9
C8: 5,9
F7: 7,8
F8: 1,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H2,H3: 1.. / H2 = 1  =>  6 pairs (_) / H3 = 1  =>  7 pairs (_)
E5,D6: 1.. / E5 = 1  => 10 pairs (_) / D6 = 1  => 10 pairs (_)
B8,C9: 1.. / B8 = 1  =>  0 pairs (*) / C9 = 1  =>  0 pairs (X)
B5,E5: 1.. / B5 = 1  => 10 pairs (_) / E5 = 1  => 10 pairs (_)
C6,C9: 1.. / C6 = 1  =>  0 pairs (*) / C9 = 1  =>  0 pairs (X)
H2,H3: 3.. / H2 = 3  =>  7 pairs (_) / H3 = 3  =>  6 pairs (_)
B4,B6: 3.. / B4 = 3  =>  8 pairs (_) / B6 = 3  =>  9 pairs (_)
G4,G6: 3.. / G4 = 3  =>  9 pairs (_) / G6 = 3  =>  8 pairs (_)
E9,F9: 3.. / E9 = 3  => 10 pairs (_) / F9 = 3  =>  8 pairs (_)
E2,H2: 3.. / E2 = 3  =>  6 pairs (_) / H2 = 3  =>  7 pairs (_)
B4,G4: 3.. / B4 = 3  =>  8 pairs (_) / G4 = 3  =>  9 pairs (_)
B6,G6: 3.. / B6 = 3  =>  9 pairs (_) / G6 = 3  =>  8 pairs (_)
F3,F9: 3.. / F3 = 3  => 10 pairs (_) / F9 = 3  =>  8 pairs (_)
A4,C4: 5.. / A4 = 5  =>  7 pairs (_) / C4 = 5  =>  6 pairs (_)
A8,C8: 5.. / A8 = 5  =>  6 pairs (_) / C8 = 5  =>  7 pairs (_)
A4,A8: 5.. / A4 = 5  =>  7 pairs (_) / A8 = 5  =>  6 pairs (_)
C4,C8: 5.. / C4 = 5  =>  6 pairs (_) / C8 = 5  =>  7 pairs (_)
D4,E4: 7.. / D4 = 7  =>  8 pairs (_) / E4 = 7  => 14 pairs (_)
E7,F7: 7.. / E7 = 7  => 10 pairs (_) / F7 = 7  =>  7 pairs (_)
D3,D4: 7.. / D3 = 7  => 14 pairs (_) / D4 = 7  =>  8 pairs (_)
F3,F7: 7.. / F3 = 7  => 10 pairs (_) / F7 = 7  =>  7 pairs (_)
E4,E5: 9.. / E4 = 9  =>  8 pairs (_) / E5 = 9  => 13 pairs (_)
A8,C8: 9.. / A8 = 9  =>  7 pairs (_) / C8 = 9  =>  6 pairs (_)
E5,G5: 9.. / E5 = 9  => 13 pairs (_) / G5 = 9  =>  8 pairs (_)
* DURATION: 0:00:08.240835  START: 09:51:50.919834  END: 09:51:59.160669 2025-04-05
* CP COUNT: (24)
* SOLUTION FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:14.578478  START: 09:52:10.216156  END: 09:52:24.794634 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00129638-base-pr-002.dot
* REASONING
* DIS # E2: 8 # C3: 2,4 => CTR => C3: 8
* DIS # E2: 8 + C3: 8 # A9: 2,4 => CTR => A9: 8
* PRF # E2: 8 + C3: 8 + A9: 8 # G8: 2,4 => SOL
* STA # E2: 8 + C3: 8 + A9: 8 + G8: 2,4
* CNT   3 HDP CHAINS /  66 HYP OPENED

Header Info

rating: 34161; r2: 644198; index: 129638

Solution

position: 123456789457189236698273514235794861786315942941862357362547198519628473874931625 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 # E2: 1,3 => UNS
* INC # E2: 8 => UNS
* INC # E3: 1,3 => UNS
* INC # F3: 1,3 => UNS
* INC # E4: 7,8 => UNS
* INC # E4: 9 => UNS
* INC # D3: 7,8 => UNS
* INC # D3: 1,2,4 => UNS
* INC # E5: 1,8 => UNS
* INC # E5: 9 => UNS
* INC # B6: 1,8 => UNS
* INC # C6: 1,8 => UNS
* INC # D2: 1,8 => UNS
* INC # D3: 1,8 => UNS
* INC # A4: 5,9 => UNS
* INC # A4: 2,8 => UNS
* INC # C4: 5,9 => UNS
* INC # C4: 2,8 => UNS
* INC # E7: 7,8 => UNS
* INC # E7: 2,4 => UNS
* INC # F3: 7,8 => UNS
* INC # F3: 1,3 => UNS
* INC # E8: 1,8 => UNS
* INC # E9: 1,8 => UNS
* INC # F9: 1,8 => UNS
* INC # B8: 1,8 => UNS
* INC # B8: 2,4 => UNS
* INC # F3: 1,8 => UNS
* INC # F3: 3,7 => UNS
* CNT  29 HDP CHAINS /  29 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E2: 1,3 => UNS
* INC # E2: 8 => UNS
* INC # E3: 1,3 => UNS
* INC # F3: 1,3 => UNS
* INC # E4: 7,8 => UNS
* INC # E4: 9 => UNS
* INC # D3: 7,8 => UNS
* INC # D3: 1,2,4 => UNS
* INC # E5: 1,8 => UNS
* INC # E5: 9 => UNS
* INC # B6: 1,8 => UNS
* INC # C6: 1,8 => UNS
* INC # D2: 1,8 => UNS
* INC # D3: 1,8 => UNS
* INC # A4: 5,9 => UNS
* INC # A4: 2,8 => UNS
* INC # C4: 5,9 => UNS
* INC # C4: 2,8 => UNS
* INC # E7: 7,8 => UNS
* INC # E7: 2,4 => UNS
* INC # F3: 7,8 => UNS
* INC # F3: 1,3 => UNS
* INC # E8: 1,8 => UNS
* INC # E9: 1,8 => UNS
* INC # F9: 1,8 => UNS
* INC # B8: 1,8 => UNS
* INC # B8: 2,4 => UNS
* INC # F3: 1,8 => UNS
* INC # F3: 3,7 => UNS
* CNT  29 HDP CHAINS /  29 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # E2: 1,3 => UNS
* INC # E2: 8 => UNS
* INC # E3: 1,3 => UNS
* INC # F3: 1,3 => UNS
* INC # E4: 7,8 => UNS
* INC # E4: 9 => UNS
* INC # D3: 7,8 => UNS
* INC # D3: 1,2,4 => UNS
* INC # E5: 1,8 => UNS
* INC # E5: 9 => UNS
* INC # B6: 1,8 => UNS
* INC # C6: 1,8 => UNS
* INC # D2: 1,8 => UNS
* INC # D3: 1,8 => UNS
* INC # A4: 5,9 => UNS
* INC # A4: 2,8 => UNS
* INC # C4: 5,9 => UNS
* INC # C4: 2,8 => UNS
* INC # E7: 7,8 => UNS
* INC # E7: 2,4 => UNS
* INC # F3: 7,8 => UNS
* INC # F3: 1,3 => UNS
* INC # E8: 1,8 => UNS
* INC # E9: 1,8 => UNS
* INC # F9: 1,8 => UNS
* INC # B8: 1,8 => UNS
* INC # B8: 2,4 => UNS
* INC # F3: 1,8 => UNS
* INC # F3: 3,7 => UNS
* INC # E2: 1,3 # E3: 1,3 => UNS
* INC # E2: 1,3 # F3: 1,3 => UNS
* INC # E2: 1,3 # E9: 1,3 => UNS
* INC # E2: 1,3 # E9: 2,4,8 => UNS
* INC # E2: 1,3 # E3: 1,3 => UNS
* INC # E2: 1,3 # F3: 1,3 => UNS
* INC # E2: 1,3 # E4: 7,8 => UNS
* INC # E2: 1,3 # E4: 9 => UNS
* INC # E2: 1,3 # D3: 7,8 => UNS
* INC # E2: 1,3 # D3: 1,2,4 => UNS
* INC # E2: 1,3 # E5: 1,8 => UNS
* INC # E2: 1,3 # E5: 9 => UNS
* INC # E2: 1,3 # B6: 1,8 => UNS
* INC # E2: 1,3 # C6: 1,8 => UNS
* INC # E2: 1,3 # D3: 1,8 => UNS
* INC # E2: 1,3 # D3: 2,4,7 => UNS
* INC # E2: 1,3 # A4: 5,9 => UNS
* INC # E2: 1,3 # A4: 2,8 => UNS
* INC # E2: 1,3 # C4: 5,9 => UNS
* INC # E2: 1,3 # C4: 2,8 => UNS
* INC # E2: 1,3 # E7: 7,8 => UNS
* INC # E2: 1,3 # E7: 2,4 => UNS
* INC # E2: 1,3 # F3: 7,8 => UNS
* INC # E2: 1,3 # F3: 1,3 => UNS
* INC # E2: 1,3 # E8: 1,8 => UNS
* INC # E2: 1,3 # E9: 1,8 => UNS
* INC # E2: 1,3 # F9: 1,8 => UNS
* INC # E2: 1,3 # B8: 1,8 => UNS
* INC # E2: 1,3 # B8: 2,4 => UNS
* INC # E2: 1,3 # F3: 1,8 => UNS
* INC # E2: 1,3 # F3: 3,7 => UNS
* INC # E2: 1,3 => UNS
* INC # E2: 8 # B1: 2,4 => UNS
* DIS # E2: 8 # C3: 2,4 => CTR => C3: 8
* DIS # E2: 8 + C3: 8 # A9: 2,4 => CTR => A9: 8
* PRF # E2: 8 + C3: 8 + A9: 8 # G8: 2,4 => SOL
* STA # E2: 8 + C3: 8 + A9: 8 + G8: 2,4
* CNT  65 HDP CHAINS /  66 HYP OPENED