Analysis of xx-mith-te3-00022745-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: .2...6...4......63..9.3...........76.16.745...756..1.4...7.1.4.7...45..1...36..57 initial

Autosolve

position: .2...6...4......63..9.3...........76.16.745...756..1.4...7.1.4.7...45..1...36..57 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 5,8 => CTR => A1: 1,3
* CNT   1 HDP CHAINS /  13 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # A1: 5,8 => CTR => A1: 1,3
* STA A1: 1,3
* CNT   1 HDP CHAINS /  30 HYP OPENED

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

Pair Reduction Position

position: .2...6...4......63..9.3...........76.16.745...756..1.4...7.1.4.7...45..1...36..57 pair_reduction
Pair Reduction

See section Pair Reduction for the HDP chains leading to this result.

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:31.265632

The following important HDP chains were detected:

* DIS # B3: 6 # C1: 3 => CTR => C1: 1,7
* DIS # C1: 3 # B3: 6 => CTR => B3: 5,8
* PRF # C1: 3 + B3: 5,8 # I1: 8,9 => SOL
* STA # C1: 3 + B3: 5,8 + I1: 8,9
* CNT   3 HDP CHAINS / 167 HYP OPENED

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

Details

Positions

.2...6...4......63..9.3...........76.16.745...756..1.4...7.1.4.7...45..1...36..57 initial
.2...6...4......63..9.3...........76.16.745...756..1.4...7.1.4.7...45..1...36..57 autosolve
.2...6...4......63..9.3...........76.16.745...756..1.4...7.1.4.7...45..1...36..57 pair_reduction
123456789457189263689237415294518376316974528875623194538791642762845931941362857 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (3)
B2: 5,8
D4: 1,5
E4: 1,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H1,H3: 1.. / H1 = 1  =>  4 pairs (_) / H3 = 1  =>  9 pairs (_)
D4,E4: 1.. / D4 = 1  =>  1 pairs (_) / E4 = 1  =>  1 pairs (_)
A9,C9: 1.. / A9 = 1  => 12 pairs (_) / C9 = 1  => 11 pairs (_)
A1,C1: 3.. / A1 = 3  => 12 pairs (_) / C1 = 3  => 11 pairs (_)
F4,F6: 3.. / F4 = 3  => 27 pairs (_) / F6 = 3  =>  3 pairs (_)
A5,H5: 3.. / A5 = 3  => 13 pairs (_) / H5 = 3  =>  5 pairs (_)
D1,D3: 4.. / D1 = 4  =>  3 pairs (_) / D3 = 4  => 11 pairs (_)
G1,G3: 4.. / G1 = 4  => 11 pairs (_) / G3 = 4  =>  3 pairs (_)
B4,C4: 4.. / B4 = 4  => 14 pairs (_) / C4 = 4  =>  3 pairs (_)
B9,C9: 4.. / B9 = 4  =>  3 pairs (_) / C9 = 4  => 14 pairs (_)
D1,G1: 4.. / D1 = 4  =>  3 pairs (_) / G1 = 4  => 11 pairs (_)
D3,G3: 4.. / D3 = 4  => 11 pairs (_) / G3 = 4  =>  3 pairs (_)
B4,B9: 4.. / B4 = 4  => 14 pairs (_) / B9 = 4  =>  3 pairs (_)
C4,C9: 4.. / C4 = 4  =>  3 pairs (_) / C9 = 4  => 14 pairs (_)
I1,I3: 5.. / I1 = 5  =>  9 pairs (_) / I3 = 5  =>  5 pairs (_)
D4,E4: 5.. / D4 = 5  =>  1 pairs (_) / E4 = 5  =>  1 pairs (_)
A7,B7: 5.. / A7 = 5  =>  7 pairs (_) / B7 = 5  =>  6 pairs (_)
A3,B3: 6.. / A3 = 6  =>  7 pairs (_) / B3 = 6  =>  6 pairs (_)
G7,G8: 6.. / G7 = 6  =>  9 pairs (_) / G8 = 6  =>  8 pairs (_)
B8,G8: 6.. / B8 = 6  =>  9 pairs (_) / G8 = 6  =>  8 pairs (_)
A3,A7: 6.. / A3 = 6  =>  7 pairs (_) / A7 = 6  =>  6 pairs (_)
C1,C2: 7.. / C1 = 7  => 10 pairs (_) / C2 = 7  =>  3 pairs (_)
F2,F3: 7.. / F2 = 7  => 12 pairs (_) / F3 = 7  =>  3 pairs (_)
C1,G1: 7.. / C1 = 7  => 10 pairs (_) / G1 = 7  =>  3 pairs (_)
F3,G3: 7.. / F3 = 7  =>  3 pairs (_) / G3 = 7  => 12 pairs (_)
* DURATION: 0:00:06.017768  START: 09:24:39.352831  END: 09:24:45.370599 2025-04-04
* CP COUNT: (25)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:30.935711  START: 09:24:52.347842  END: 09:25:23.283553 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00022745-base-pr-002.dot
* REASONING
* DIS # B3: 6 # C1: 3 => CTR => C1: 1,7
* DIS # C1: 3 # B3: 6 => CTR => B3: 5,8
* PRF # C1: 3 + B3: 5,8 # I1: 8,9 => SOL
* STA # C1: 3 + B3: 5,8 + I1: 8,9
* CNT   3 HDP CHAINS / 167 HYP OPENED

Header Info

rating: 4625; r2: 83003; index: 22745

Solution

position: 123456789457189263689237415294518376316974528875623194538791642762845931941362857 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:

* DIS # A1: 5,8 => CTR => A1: 1,3
* INC # A1: 1,3 => UNS
* INC # A3: 5,8 => UNS
* INC # B3: 5,8 => UNS
* INC # D2: 5,8 => UNS
* INC # E2: 5,8 => UNS
* INC # B7: 5,8 => UNS
* INC # B7: 3,6,9 => UNS
* INC # D1: 1,5 => UNS
* INC # D2: 1,5 => UNS
* INC # D3: 1,5 => UNS
* INC # E1: 1,5 => UNS
* INC # E2: 1,5 => UNS
* CNT  13 HDP CHAINS /  13 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A1: 5,8 => CTR => A1: 1,3
* INC A1: 1,3 # B3: 5,8 => UNS
* INC A1: 1,3 # B3: 5,8 => UNS
* INC A1: 1,3 # B3: 6 => UNS
* INC A1: 1,3 # D2: 5,8 => UNS
* INC A1: 1,3 # E2: 5,8 => UNS
* INC A1: 1,3 # D1: 1,5 => UNS
* INC A1: 1,3 # D2: 1,5 => UNS
* INC A1: 1,3 # D3: 1,5 => UNS
* INC A1: 1,3 # E1: 1,5 => UNS
* INC A1: 1,3 # E2: 1,5 => UNS
* INC A1: 1,3 # C1: 1,3 => UNS
* INC A1: 1,3 # C1: 7 => UNS
* INC A1: 1,3 # B3: 5,8 => UNS
* INC A1: 1,3 # B3: 6 => UNS
* INC A1: 1,3 # D2: 5,8 => UNS
* INC A1: 1,3 # E2: 5,8 => UNS
* INC A1: 1,3 # C1: 1,7 => UNS
* INC A1: 1,3 # C1: 3 => UNS
* INC A1: 1,3 # B3: 5,6 => UNS
* INC A1: 1,3 # B3: 8 => UNS
* INC A1: 1,3 # D1: 1,5 => UNS
* INC A1: 1,3 # D2: 1,5 => UNS
* INC A1: 1,3 # D3: 1,5 => UNS
* INC A1: 1,3 # E1: 1,5 => UNS
* INC A1: 1,3 # E2: 1,5 => UNS
* INC A1: 1,3 # B7: 5,6 => UNS
* INC A1: 1,3 # B7: 3,9 => UNS
* INC A1: 1,3 # B4: 4,9 => UNS
* INC A1: 1,3 # B4: 3 => UNS
* STA A1: 1,3
* CNT  30 HDP CHAINS /  30 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # C1: 1,3 => UNS
* INC # C1: 7 => UNS
* INC # B3: 5,8 => UNS
* INC # B3: 6 => UNS
* INC # D2: 5,8 => UNS
* INC # E2: 5,8 => UNS
* INC # C1: 1,7 => UNS
* INC # C1: 3 => UNS
* INC # B3: 5,6 => UNS
* INC # B3: 8 => UNS
* INC # D1: 1,5 => UNS
* INC # D2: 1,5 => UNS
* INC # D3: 1,5 => UNS
* INC # E1: 1,5 => UNS
* INC # E2: 1,5 => UNS
* INC # B7: 5,6 => UNS
* INC # B7: 3,9 => UNS
* INC # B4: 4,9 => UNS
* INC # B4: 3 => UNS
* INC # C1: 1,3 # B3: 5,8 => UNS
* INC # C1: 1,3 # B3: 6 => UNS
* INC # C1: 1,3 # D2: 5,8 => UNS
* INC # C1: 1,3 # E2: 5,8 => UNS
* INC # C1: 1,3 # B3: 5,6 => UNS
* INC # C1: 1,3 # B3: 8 => UNS
* INC # C1: 1,3 # I1: 8,9 => UNS
* INC # C1: 1,3 # G2: 8,9 => UNS
* INC # C1: 1,3 # E1: 8,9 => UNS
* INC # C1: 1,3 # E1: 5 => UNS
* INC # C1: 1,3 # H5: 8,9 => UNS
* INC # C1: 1,3 # H6: 8,9 => UNS
* INC # C1: 1,3 # H8: 8,9 => UNS
* INC # C1: 1,3 # D2: 1,5 => UNS
* INC # C1: 1,3 # D2: 2,8,9 => UNS
* INC # C1: 1,3 # E2: 1,5 => UNS
* INC # C1: 1,3 # E2: 2,8,9 => UNS
* INC # C1: 1,3 # B7: 5,6 => UNS
* INC # C1: 1,3 # B7: 3,9 => UNS
* INC # C1: 1,3 # B4: 4,9 => UNS
* INC # C1: 1,3 # B4: 3 => UNS
* INC # C1: 1,3 => UNS
* INC # C1: 7 # B3: 5,8 => UNS
* INC # C1: 7 # B3: 6 => UNS
* INC # C1: 7 # D2: 5,8 => UNS
* INC # C1: 7 # E2: 5,8 => UNS
* INC # C1: 7 # B3: 5,6 => UNS
* INC # C1: 7 # B3: 8 => UNS
* INC # C1: 7 # D1: 1,5 => UNS
* INC # C1: 7 # D3: 1,5 => UNS
* INC # C1: 7 # E1: 1,5 => UNS
* INC # C1: 7 # E1: 8,9 => UNS
* INC # C1: 7 # B7: 5,6 => UNS
* INC # C1: 7 # B7: 3,9 => UNS
* INC # C1: 7 # B7: 3,6 => UNS
* INC # C1: 7 # B7: 5,9 => UNS
* INC # C1: 7 # B8: 3,6 => UNS
* INC # C1: 7 # B8: 9 => UNS
* INC # C1: 7 => UNS
* INC # B3: 5,8 # C1: 1,3 => UNS
* INC # B3: 5,8 # C1: 7 => UNS
* INC # B3: 5,8 # D2: 5,8 => UNS
* INC # B3: 5,8 # E2: 5,8 => UNS
* INC # B3: 5,8 # C1: 1,7 => UNS
* INC # B3: 5,8 # C1: 3 => UNS
* INC # B3: 5,8 # D3: 5,8 => UNS
* INC # B3: 5,8 # I3: 5,8 => UNS
* INC # B3: 5,8 # D1: 1,5 => UNS
* INC # B3: 5,8 # D2: 1,5 => UNS
* INC # B3: 5,8 # D3: 1,5 => UNS
* INC # B3: 5,8 # E1: 1,5 => UNS
* INC # B3: 5,8 # E2: 1,5 => UNS
* INC # B3: 5,8 # B4: 4,9 => UNS
* INC # B3: 5,8 # B4: 3 => UNS
* INC # B3: 5,8 => UNS
* INC # B3: 6 # C1: 1,3 => UNS
* INC # B3: 6 # C1: 7 => UNS
* INC # B3: 6 # C1: 1,7 => UNS
* DIS # B3: 6 # C1: 3 => CTR => C1: 1,7
* INC # B3: 6 + C1: 1,7 # G3: 2,8 => UNS
* INC # B3: 6 + C1: 1,7 # H3: 2,8 => UNS
* INC # B3: 6 + C1: 1,7 # D3: 2,8 => UNS
* INC # B3: 6 + C1: 1,7 # F3: 2,8 => UNS
* INC # B3: 6 + C1: 1,7 # I5: 2,8 => UNS
* INC # B3: 6 + C1: 1,7 # I7: 2,8 => UNS
* INC # B3: 6 + C1: 1,7 # D2: 1,5 => UNS
* INC # B3: 6 + C1: 1,7 # D2: 2,9 => UNS
* INC # B3: 6 + C1: 1,7 # E2: 1,5 => UNS
* INC # B3: 6 + C1: 1,7 # E2: 2,9 => UNS
* INC # B3: 6 + C1: 1,7 # G3: 2,8 => UNS
* INC # B3: 6 + C1: 1,7 # H3: 2,8 => UNS
* INC # B3: 6 + C1: 1,7 # D3: 2,8 => UNS
* INC # B3: 6 + C1: 1,7 # F3: 2,8 => UNS
* INC # B3: 6 + C1: 1,7 # I5: 2,8 => UNS
* INC # B3: 6 + C1: 1,7 # I7: 2,8 => UNS
* INC # B3: 6 + C1: 1,7 # D2: 1,5 => UNS
* INC # B3: 6 + C1: 1,7 # D2: 2,9 => UNS
* INC # B3: 6 + C1: 1,7 # E2: 1,5 => UNS
* INC # B3: 6 + C1: 1,7 # E2: 2,9 => UNS
* INC # B3: 6 + C1: 1,7 # C8: 2,8 => UNS
* INC # B3: 6 + C1: 1,7 # C9: 2,8 => UNS
* INC # B3: 6 + C1: 1,7 # E7: 2,8 => UNS
* INC # B3: 6 + C1: 1,7 # I7: 2,8 => UNS
* INC # B3: 6 + C1: 1,7 => UNS
* INC # D2: 5,8 # C1: 1,3 => UNS
* INC # D2: 5,8 # C1: 7 => UNS
* INC # D2: 5,8 # B3: 5,8 => UNS
* INC # D2: 5,8 # B3: 6 => UNS
* INC # D2: 5,8 # C1: 1,7 => UNS
* INC # D2: 5,8 # C1: 3 => UNS
* INC # D2: 5,8 # B3: 5,6 => UNS
* INC # D2: 5,8 # B3: 8 => UNS
* INC # D2: 5,8 # D1: 5,8 => UNS
* INC # D2: 5,8 # E1: 5,8 => UNS
* INC # D2: 5,8 # D3: 5,8 => UNS
* INC # D2: 5,8 # D1: 1,5 => UNS
* INC # D2: 5,8 # D3: 1,5 => UNS
* INC # D2: 5,8 # E1: 1,5 => UNS
* INC # D2: 5,8 # E1: 8,9 => UNS
* INC # D2: 5,8 # B7: 5,6 => UNS
* INC # D2: 5,8 # B7: 3,9 => UNS
* INC # D2: 5,8 # B4: 4,9 => UNS
* INC # D2: 5,8 # B4: 3 => UNS
* INC # D2: 5,8 => UNS
* INC # E2: 5,8 # C1: 1,3 => UNS
* INC # E2: 5,8 # C1: 7 => UNS
* INC # E2: 5,8 # B3: 5,8 => UNS
* INC # E2: 5,8 # B3: 6 => UNS
* INC # E2: 5,8 # C1: 1,7 => UNS
* INC # E2: 5,8 # C1: 3 => UNS
* INC # E2: 5,8 # B3: 5,6 => UNS
* INC # E2: 5,8 # B3: 8 => UNS
* INC # E2: 5,8 # D1: 5,8 => UNS
* INC # E2: 5,8 # E1: 5,8 => UNS
* INC # E2: 5,8 # D3: 5,8 => UNS
* INC # E2: 5,8 # D1: 1,5 => UNS
* INC # E2: 5,8 # D3: 1,5 => UNS
* INC # E2: 5,8 # E1: 1,5 => UNS
* INC # E2: 5,8 # E1: 8,9 => UNS
* INC # E2: 5,8 # B7: 5,6 => UNS
* INC # E2: 5,8 # B7: 3,9 => UNS
* INC # E2: 5,8 # B4: 4,9 => UNS
* INC # E2: 5,8 # B4: 3 => UNS
* INC # E2: 5,8 => UNS
* INC # C1: 1,7 # B3: 5,8 => UNS
* INC # C1: 1,7 # B3: 6 => UNS
* INC # C1: 1,7 # D2: 5,8 => UNS
* INC # C1: 1,7 # E2: 5,8 => UNS
* INC # C1: 1,7 # B3: 5,6 => UNS
* INC # C1: 1,7 # B3: 8 => UNS
* INC # C1: 1,7 # D1: 1,5 => UNS
* INC # C1: 1,7 # D2: 1,5 => UNS
* INC # C1: 1,7 # D3: 1,5 => UNS
* INC # C1: 1,7 # E1: 1,5 => UNS
* INC # C1: 1,7 # E2: 1,5 => UNS
* INC # C1: 1,7 # B7: 5,6 => UNS
* INC # C1: 1,7 # B7: 3,9 => UNS
* INC # C1: 1,7 # B7: 3,6 => UNS
* INC # C1: 1,7 # B7: 5,9 => UNS
* INC # C1: 1,7 # B8: 3,6 => UNS
* INC # C1: 1,7 # B8: 9 => UNS
* INC # C1: 1,7 => UNS
* INC # C1: 3 # B3: 5,8 => UNS
* DIS # C1: 3 # B3: 6 => CTR => B3: 5,8
* INC # C1: 3 + B3: 5,8 # D2: 5,8 => UNS
* INC # C1: 3 + B3: 5,8 # E2: 5,8 => UNS
* PRF # C1: 3 + B3: 5,8 # I1: 8,9 => SOL
* STA # C1: 3 + B3: 5,8 + I1: 8,9
* CNT 166 HDP CHAINS / 167 HYP OPENED