Analysis of xx-mith-te3-00088125-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 12.....89.5..8...6.......5.2..9.8.......45.6....2.7.1..81...62.56.8...919.26..5.8 initial

Autosolve

position: 12.....89.5..8...6.......5.2..9.8.......45.62...2.7.1..81...62.56.8...919.26..5.8 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: 0:00:11.199491

The following important HDP chains were detected:

* DIS # F2: 1,2 # E4: 1 => CTR => E4: 3,6
* DIS # F2: 3,4,9 # D1: 5 => CTR => D1: 4,7
* DIS # F2: 3,4,9 + D1: 4,7 # B3: 4,7 => CTR => B3: 3,9
* PRF # F2: 3,4,9 + D1: 4,7 + B3: 3,9 # B6: 3,4 => SOL
* STA # F2: 3,4,9 + D1: 4,7 + B3: 3,9 + B6: 3,4
* CNT   4 HDP CHAINS /  52 HYP OPENED

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

Details

Positions

12.....89.5..8...6.......5.2..9.8.......45.6....2.7.1..81...62.56.8...919.26..5.8 initial
12.....89.5..8...6.......5.2..9.8.......45.62...2.7.1..81...62.56.8...919.26..5.8 autosolve
123456789457189236698723154236918475719345862845267913381594627564872391972631548 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (6)
G2: 1,2
G3: 1,2
D5: 1,3
E6: 3,6
G5: 8,9
G6: 8,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G2,G3: 1.. / G2 = 1  =>  5 pairs (_) / G3 = 1  =>  4 pairs (_)
B4,B5: 1.. / B4 = 1  => 14 pairs (_) / B5 = 1  =>  9 pairs (_)
E4,D5: 1.. / E4 = 1  =>  9 pairs (_) / D5 = 1  => 14 pairs (_)
E9,F9: 1.. / E9 = 1  => 15 pairs (_) / F9 = 1  =>  7 pairs (_)
B4,E4: 1.. / B4 = 1  => 14 pairs (_) / E4 = 1  =>  9 pairs (_)
B5,D5: 1.. / B5 = 1  =>  9 pairs (_) / D5 = 1  => 14 pairs (_)
G2,G3: 2.. / G2 = 2  =>  4 pairs (_) / G3 = 2  =>  5 pairs (_)
E8,F8: 2.. / E8 = 2  =>  7 pairs (_) / F8 = 2  =>  7 pairs (_)
F2,G2: 2.. / F2 = 2  =>  5 pairs (_) / G2 = 2  =>  4 pairs (_)
E3,E8: 2.. / E3 = 2  =>  7 pairs (_) / E8 = 2  =>  7 pairs (_)
D1,E1: 5.. / D1 = 5  =>  8 pairs (_) / E1 = 5  =>  7 pairs (_)
C4,C6: 5.. / C4 = 5  => 12 pairs (_) / C6 = 5  =>  7 pairs (_)
I4,I6: 5.. / I4 = 5  =>  7 pairs (_) / I6 = 5  => 12 pairs (_)
D7,E7: 5.. / D7 = 5  =>  7 pairs (_) / E7 = 5  =>  8 pairs (_)
C4,I4: 5.. / C4 = 5  => 12 pairs (_) / I4 = 5  =>  7 pairs (_)
C6,I6: 5.. / C6 = 5  =>  7 pairs (_) / I6 = 5  => 12 pairs (_)
D1,D7: 5.. / D1 = 5  =>  8 pairs (_) / D7 = 5  =>  7 pairs (_)
E1,E7: 5.. / E1 = 5  =>  7 pairs (_) / E7 = 5  =>  8 pairs (_)
F1,F3: 6.. / F1 = 6  =>  8 pairs (_) / F3 = 6  =>  0 pairs (X)
E4,E6: 6.. / E4 = 6  => 14 pairs (_) / E6 = 6  =>  7 pairs (_)
C1,F1: 6.. / C1 = 6  =>  0 pairs (X) / F1 = 6  =>  8 pairs (_)
C4,E4: 6.. / C4 = 6  =>  7 pairs (_) / E4 = 6  => 14 pairs (_)
A3,A6: 6.. / A3 = 6  =>  8 pairs (_) / A6 = 6  => 13 pairs (_)
A3,C3: 8.. / A3 = 8  => 13 pairs (_) / C3 = 8  =>  6 pairs (_)
G5,G6: 8.. / G5 = 8  => 10 pairs (_) / G6 = 8  =>  4 pairs (_)
G5,G6: 9.. / G5 = 9  =>  4 pairs (_) / G6 = 9  => 10 pairs (_)
E7,F7: 9.. / E7 = 9  =>  8 pairs (_) / F7 = 9  =>  7 pairs (_)
C2,F2: 9.. / C2 = 9  =>  6 pairs (_) / F2 = 9  =>  0 pairs (*)
E3,E7: 9.. / E3 = 9  =>  7 pairs (_) / E7 = 9  =>  8 pairs (_)
* DURATION: 0:00:08.375149  START: 23:02:13.888398  END: 23:02:22.263547 2025-04-04
* CP COUNT: (29)
* SOLUTION FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:11.032336  START: 23:02:28.176119  END: 23:02:39.208455 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00088125-base-pr-002.dot
* REASONING
* DIS # F2: 1,2 # E4: 1 => CTR => E4: 3,6
* DIS # F2: 3,4,9 # D1: 5 => CTR => D1: 4,7
* DIS # F2: 3,4,9 + D1: 4,7 # B3: 4,7 => CTR => B3: 3,9
* PRF # F2: 3,4,9 + D1: 4,7 + B3: 3,9 # B6: 3,4 => SOL
* STA # F2: 3,4,9 + D1: 4,7 + B3: 3,9 + B6: 3,4
* CNT   4 HDP CHAINS /  52 HYP OPENED

Header Info

rating: 22046; r2: 473866; index: 88125

Solution

position: 123456789457189236698723154236918475719345862845267913381594627564872391972631548 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 # F2: 1,2 => UNS
* INC # F2: 3,4,9 => UNS
* INC # E3: 1,2 => UNS
* INC # F3: 1,2 => UNS
* INC # E4: 1,3 => UNS
* INC # E4: 6 => UNS
* INC # B5: 1,3 => UNS
* INC # B5: 7,9 => UNS
* INC # D2: 1,3 => UNS
* INC # D3: 1,3 => UNS
* INC # E4: 3,6 => UNS
* INC # E4: 1 => UNS
* INC # A6: 3,6 => UNS
* INC # C6: 3,6 => UNS
* INC # C5: 8,9 => UNS
* INC # C5: 3,7 => UNS
* INC # C6: 8,9 => UNS
* INC # C6: 3,4,5,6 => UNS
* CNT  18 HDP CHAINS /  18 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F2: 1,2 => UNS
* INC # F2: 3,4,9 => UNS
* INC # E3: 1,2 => UNS
* INC # F3: 1,2 => UNS
* INC # E4: 1,3 => UNS
* INC # E4: 6 => UNS
* INC # B5: 1,3 => UNS
* INC # B5: 7,9 => UNS
* INC # D2: 1,3 => UNS
* INC # D3: 1,3 => UNS
* INC # E4: 3,6 => UNS
* INC # E4: 1 => UNS
* INC # A6: 3,6 => UNS
* INC # C6: 3,6 => UNS
* INC # C5: 8,9 => UNS
* INC # C5: 3,7 => UNS
* INC # C6: 8,9 => UNS
* INC # C6: 3,4,5,6 => UNS
* CNT  18 HDP CHAINS /  18 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # F2: 1,2 => UNS
* INC # F2: 3,4,9 => UNS
* INC # E3: 1,2 => UNS
* INC # F3: 1,2 => UNS
* INC # E4: 1,3 => UNS
* INC # E4: 6 => UNS
* INC # B5: 1,3 => UNS
* INC # B5: 7,9 => UNS
* INC # D2: 1,3 => UNS
* INC # D3: 1,3 => UNS
* INC # E4: 3,6 => UNS
* INC # E4: 1 => UNS
* INC # A6: 3,6 => UNS
* INC # C6: 3,6 => UNS
* INC # C5: 8,9 => UNS
* INC # C5: 3,7 => UNS
* INC # C6: 8,9 => UNS
* INC # C6: 3,4,5,6 => UNS
* INC # F2: 1,2 # E3: 1,2 => UNS
* INC # F2: 1,2 # F3: 1,2 => UNS
* INC # F2: 1,2 # E3: 1,2 => UNS
* INC # F2: 1,2 # F3: 1,2 => UNS
* INC # F2: 1,2 # E4: 1,3 => UNS
* INC # F2: 1,2 # E4: 6 => UNS
* INC # F2: 1,2 # B5: 1,3 => UNS
* INC # F2: 1,2 # B5: 7,9 => UNS
* INC # F2: 1,2 # D3: 1,3 => UNS
* INC # F2: 1,2 # D3: 4,7 => UNS
* INC # F2: 1,2 # E4: 3,6 => UNS
* DIS # F2: 1,2 # E4: 1 => CTR => E4: 3,6
* INC # F2: 1,2 + E4: 3,6 # A6: 6,8 => UNS
* INC # F2: 1,2 + E4: 3,6 # A6: 4 => UNS
* INC # F2: 1,2 + E4: 3,6 # C6: 6,8 => UNS
* INC # F2: 1,2 + E4: 3,6 # C6: 4,5 => UNS
* INC # F2: 1,2 + E4: 3,6 # D1: 5,7 => UNS
* INC # F2: 1,2 + E4: 3,6 # D1: 3,4 => UNS
* INC # F2: 1,2 + E4: 3,6 # E7: 5,7 => UNS
* INC # F2: 1,2 + E4: 3,6 # E7: 9 => UNS
* INC # F2: 1,2 + E4: 3,6 # E3: 1,2 => UNS
* INC # F2: 1,2 + E4: 3,6 # F3: 1,2 => UNS
* INC # F2: 1,2 + E4: 3,6 # E3: 1,2 => UNS
* INC # F2: 1,2 + E4: 3,6 # F3: 1,2 => UNS
* INC # F2: 1,2 + E4: 3,6 # E7: 5,7 => UNS
* INC # F2: 1,2 + E4: 3,6 # E7: 9 => UNS
* INC # F2: 1,2 + E4: 3,6 # D1: 5,7 => UNS
* INC # F2: 1,2 + E4: 3,6 # D1: 3,4 => UNS
* INC # F2: 1,2 + E4: 3,6 => UNS
* INC # F2: 3,4,9 # D1: 4,7 => UNS
* DIS # F2: 3,4,9 # D1: 5 => CTR => D1: 4,7
* DIS # F2: 3,4,9 + D1: 4,7 # B3: 4,7 => CTR => B3: 3,9
* PRF # F2: 3,4,9 + D1: 4,7 + B3: 3,9 # B6: 3,4 => SOL
* STA # F2: 3,4,9 + D1: 4,7 + B3: 3,9 + B6: 3,4
* CNT  51 HDP CHAINS /  52 HYP OPENED