Analysis of xx-mith-te3-00122071-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: .2..56...45.....36698.3.....75.4...3.1..7.54....3.51.75..71.3.47...6.......5..67. initial

Autosolve

position: .2..56...45.....36698.3.....75.4...3.1..7.54....3.51.75..71.3.47...6.......5..67. 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: 0:00:10.459400

The following important HDP chains were detected:

* DIS # C1: 1,3 # E9: 8,9 => CTR => E9: 2
* DIS # C1: 1,3 + E9: 2 # H4: 8,9 => CTR => H4: 2,6
* PRF # C1: 1,3 + E9: 2 + H4: 2,6 # D4: 8,9 => SOL
* STA # C1: 1,3 + E9: 2 + H4: 2,6 + D4: 8,9
* CNT   3 HDP CHAINS /  28 HYP OPENED

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

Details

Positions

.2..56...45.....36698.3.....75.4...3.1..7.54....3.51.75..71.3.47...6.......5..67. initial
.2..56...45.....36698.3.....75.4...3.1..7.54....3.51.75..71.3.47...6.......5..67. autosolve
123456789457189236698237415275841963319672548846395127562718394731964852984523671 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (3)
A1: 1,3
C2: 1,7
B7: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D4,F4: 1.. / D4 = 1  => 12 pairs (_) / F4 = 1  =>  3 pairs (_)
A1,A9: 1.. / A1 = 1  => 14 pairs (_) / A9 = 1  =>  7 pairs (_)
A1,C1: 3.. / A1 = 3  =>  7 pairs (_) / C1 = 3  => 14 pairs (_)
A5,C5: 3.. / A5 = 3  => 14 pairs (_) / C5 = 3  =>  7 pairs (_)
B8,B9: 3.. / B8 = 3  =>  4 pairs (_) / B9 = 3  =>  4 pairs (_)
F8,F9: 3.. / F8 = 3  =>  4 pairs (_) / F9 = 3  =>  4 pairs (_)
B8,F8: 3.. / B8 = 3  =>  4 pairs (_) / F8 = 3  =>  4 pairs (_)
B9,F9: 3.. / B9 = 3  =>  4 pairs (_) / F9 = 3  =>  4 pairs (_)
A1,A5: 3.. / A1 = 3  =>  7 pairs (_) / A5 = 3  => 14 pairs (_)
C1,C5: 3.. / C1 = 3  => 14 pairs (_) / C5 = 3  =>  7 pairs (_)
G1,G3: 4.. / G1 = 4  =>  6 pairs (_) / G3 = 4  =>  7 pairs (_)
B6,C6: 4.. / B6 = 4  =>  5 pairs (_) / C6 = 4  =>  7 pairs (_)
D1,G1: 4.. / D1 = 4  =>  7 pairs (_) / G1 = 4  =>  6 pairs (_)
H3,I3: 5.. / H3 = 5  =>  4 pairs (_) / I3 = 5  =>  5 pairs (_)
H8,I8: 5.. / H8 = 5  =>  5 pairs (_) / I8 = 5  =>  4 pairs (_)
H3,H8: 5.. / H3 = 5  =>  4 pairs (_) / H8 = 5  =>  5 pairs (_)
I3,I8: 5.. / I3 = 5  =>  5 pairs (_) / I8 = 5  =>  4 pairs (_)
D4,D5: 6.. / D4 = 6  => 18 pairs (_) / D5 = 6  =>  5 pairs (_)
H4,H6: 6.. / H4 = 6  =>  5 pairs (_) / H6 = 6  => 18 pairs (_)
B7,C7: 6.. / B7 = 6  =>  4 pairs (_) / C7 = 6  =>  7 pairs (_)
D4,H4: 6.. / D4 = 6  => 18 pairs (_) / H4 = 6  =>  5 pairs (_)
C5,D5: 6.. / C5 = 6  => 18 pairs (_) / D5 = 6  =>  5 pairs (_)
B6,B7: 6.. / B6 = 6  =>  7 pairs (_) / B7 = 6  =>  4 pairs (_)
C1,C2: 7.. / C1 = 7  =>  5 pairs (_) / C2 = 7  => 16 pairs (_)
F2,F3: 7.. / F2 = 7  =>  5 pairs (_) / F3 = 7  =>  6 pairs (_)
C1,G1: 7.. / C1 = 7  =>  5 pairs (_) / G1 = 7  => 16 pairs (_)
F3,G3: 7.. / F3 = 7  =>  6 pairs (_) / G3 = 7  =>  5 pairs (_)
* DURATION: 0:00:07.051415  START: 19:10:32.856583  END: 19:10:39.907998 2025-04-06
* CP COUNT: (27)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:10.327444  START: 19:10:42.463019  END: 19:10:52.790463 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00122071-base-pr-002.dot
* REASONING
* DIS # C1: 1,3 # E9: 8,9 => CTR => E9: 2
* DIS # C1: 1,3 + E9: 2 # H4: 8,9 => CTR => H4: 2,6
* PRF # C1: 1,3 + E9: 2 + H4: 2,6 # D4: 8,9 => SOL
* STA # C1: 1,3 + E9: 2 + H4: 2,6 + D4: 8,9
* CNT   3 HDP CHAINS /  28 HYP OPENED

Header Info

rating: 31759; r2: 598109; index: 122071

Solution

position: 123456789457189236698237415275841963319672548846395127562718394731964852984523671 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 # C1: 1,3 => UNS
* INC # C1: 7 => UNS
* INC # C1: 1,7 => UNS
* INC # C1: 3 => UNS
* INC # F2: 1,7 => UNS
* INC # F2: 2,8,9 => UNS
* INC # B6: 6,8 => UNS
* INC # B6: 4 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C1: 1,3 => UNS
* INC # C1: 7 => UNS
* INC # C1: 1,7 => UNS
* INC # C1: 3 => UNS
* INC # F2: 1,7 => UNS
* INC # F2: 2,8,9 => UNS
* INC # B6: 6,8 => UNS
* INC # B6: 4 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # C1: 1,3 => UNS
* INC # C1: 7 => UNS
* INC # C1: 1,7 => UNS
* INC # C1: 3 => UNS
* INC # F2: 1,7 => UNS
* INC # F2: 2,8,9 => UNS
* INC # B6: 6,8 => UNS
* INC # B6: 4 => UNS
* INC # C1: 1,3 # D2: 8,9 => UNS
* INC # C1: 1,3 # F2: 8,9 => UNS
* INC # C1: 1,3 # E6: 8,9 => UNS
* DIS # C1: 1,3 # E9: 8,9 => CTR => E9: 2
* INC # C1: 1,3 + E9: 2 # D2: 8,9 => UNS
* INC # C1: 1,3 + E9: 2 # F2: 8,9 => UNS
* DIS # C1: 1,3 + E9: 2 # H4: 8,9 => CTR => H4: 2,6
* INC # C1: 1,3 + E9: 2 + H4: 2,6 # H6: 8,9 => UNS
* INC # C1: 1,3 + E9: 2 + H4: 2,6 # H7: 8,9 => UNS
* INC # C1: 1,3 + E9: 2 + H4: 2,6 # H6: 8,9 => UNS
* INC # C1: 1,3 + E9: 2 + H4: 2,6 # H7: 8,9 => UNS
* INC # C1: 1,3 + E9: 2 + H4: 2,6 # I5: 8,9 => UNS
* INC # C1: 1,3 + E9: 2 + H4: 2,6 # I9: 8,9 => UNS
* INC # C1: 1,3 + E9: 2 + H4: 2,6 # I8: 1,5 => UNS
* INC # C1: 1,3 + E9: 2 + H4: 2,6 # I8: 2 => UNS
* INC # C1: 1,3 + E9: 2 + H4: 2,6 # I5: 8,9 => UNS
* INC # C1: 1,3 + E9: 2 + H4: 2,6 # H6: 8,9 => UNS
* INC # C1: 1,3 + E9: 2 + H4: 2,6 # A4: 8,9 => UNS
* PRF # C1: 1,3 + E9: 2 + H4: 2,6 # D4: 8,9 => SOL
* STA # C1: 1,3 + E9: 2 + H4: 2,6 + D4: 8,9
* CNT  27 HDP CHAINS /  28 HYP OPENED