Analysis of xx-mith-te3-00015918-base.sdk

Contents

Original Sudoku
Autosolve
Pair Reduction Variants
Details
Solution
Appendix: Full HDP Chains

Original Sudoku

level: hard

position: 12.45.......7.9132...1......3.....7..67...29...1..73.6.1....62..9267..136..21.... initial

Autosolve

position: 12.45.......7.9132...1......3.....7..67...29...1..73.6.1....62..9267..136..21.... autosolve

Pair Reduction Variants

Pair Reduction Analysis

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

Pair Reduction

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

Deep Pair Reduction

Time used: 0:00:16.329366

The following important HDP chains were detected:

* DIS # F1: 6,8 # A8: 8 => CTR => A8: 4,5
* PRF # F1: 6,8 + A8: 4,5 # G4: 4,5 => SOL
* STA # F1: 6,8 + A8: 4,5 + G4: 4,5
* CNT   2 HDP CHAINS /  72 HYP OPENED

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

Details

Positions

`12.45.......7.9132...1......3.....7..67...29...1..73.6.1....62..9267..136..21....`	initial
`12.45.......7.9132...1......3.....7..67...29...1..73.6.1....62..9267..136..21....`	autosolve
`123456789456789132789132564235961478867345291941827356314598627592674813678213945`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
A3: 3,7
B3: 7,8
E2: 6,8
H1: 6,8
A4: 2,9
A6: 2,9
A7: 3,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F4,F5: 1.. / F4 = 1  => 12 pairs (_) / F5 = 1  =>  7 pairs (_)
I4,I5: 1.. / I4 = 1  =>  7 pairs (_) / I5 = 1  => 12 pairs (_)
F4,I4: 1.. / F4 = 1  => 12 pairs (_) / I4 = 1  =>  7 pairs (_)
F5,I5: 1.. / F5 = 1  =>  7 pairs (_) / I5 = 1  => 12 pairs (_)
E3,F3: 2.. / E3 = 2  => 13 pairs (_) / F3 = 2  =>  7 pairs (_)
A4,A6: 2.. / A4 = 2  =>  6 pairs (_) / A6 = 2  =>  8 pairs (_)
A6,E6: 2.. / A6 = 2  =>  8 pairs (_) / E6 = 2  =>  6 pairs (_)
F3,F4: 2.. / F3 = 2  =>  7 pairs (_) / F4 = 2  => 13 pairs (_)
C1,F1: 3.. / C1 = 3  => 13 pairs (_) / F1 = 3  => 11 pairs (_)
C9,F9: 3.. / C9 = 3  => 11 pairs (_) / F9 = 3  => 13 pairs (_)
A3,A7: 3.. / A3 = 3  => 11 pairs (_) / A7 = 3  => 13 pairs (_)
D5,D7: 3.. / D5 = 3  =>  8 pairs (_) / D7 = 3  => 10 pairs (_)
H1,H3: 6.. / H1 = 6  =>  9 pairs (_) / H3 = 6  => 15 pairs (_)
E4,F4: 6.. / E4 = 6  => 11 pairs (_) / F4 = 6  =>  8 pairs (_)
C2,E2: 6.. / C2 = 6  => 10 pairs (_) / E2 = 6  => 10 pairs (_)
A3,B3: 7.. / A3 = 7  => 13 pairs (_) / B3 = 7  => 11 pairs (_)
G1,I1: 7.. / G1 = 7  =>  8 pairs (_) / I1 = 7  => 10 pairs (_)
A7,B9: 7.. / A7 = 7  => 11 pairs (_) / B9 = 7  => 13 pairs (_)
A7,I7: 7.. / A7 = 7  => 11 pairs (_) / I7 = 7  => 13 pairs (_)
A3,A7: 7.. / A3 = 7  => 13 pairs (_) / A7 = 7  => 11 pairs (_)
B3,B9: 7.. / B3 = 7  => 11 pairs (_) / B9 = 7  => 13 pairs (_)
G1,G9: 7.. / G1 = 7  =>  8 pairs (_) / G9 = 7  => 10 pairs (_)
C1,C3: 9.. / C1 = 9  => 14 pairs (_) / C3 = 9  => 10 pairs (_)
A4,A6: 9.. / A4 = 9  =>  8 pairs (_) / A6 = 9  =>  6 pairs (_)
D7,E7: 9.. / D7 = 9  => 14 pairs (_) / E7 = 9  =>  7 pairs (_)
G9,I9: 9.. / G9 = 9  =>  8 pairs (_) / I9 = 9  =>  8 pairs (_)
* DURATION: 0:00:09.365629  START: 05:41:01.062575  END: 05:41:10.428204 2025-04-06
* CP COUNT: (26)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:16.123809  START: 05:41:17.129887  END: 05:41:33.253696 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00015918-base-pr-002.dot
* REASONING
* DIS # F1: 6,8 # A8: 8 => CTR => A8: 4,5
* PRF # F1: 6,8 + A8: 4,5 # G4: 4,5 => SOL
* STA # F1: 6,8 + A8: 4,5 + G4: 4,5
* CNT   2 HDP CHAINS /  72 HYP OPENED

Header Info

rating: 3503; r2: 53945; index: 15918

Solution

position: 123456789456789132789132564235961478867345291941827356314598627592674813678213945 solved

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 # B9: 7,8 => UNS
* INC # B9: 4,5 => UNS
* INC # F1: 6,8 => UNS
* INC # E3: 6,8 => UNS
* INC # F3: 6,8 => UNS
* INC # C2: 6,8 => UNS
* INC # C2: 4,5 => UNS
* INC # E4: 6,8 => UNS
* INC # E4: 2,4,9 => UNS
* INC # H3: 6,8 => UNS
* INC # H3: 4,5 => UNS
* INC # C1: 6,8 => UNS
* INC # F1: 6,8 => UNS
* INC # E4: 2,9 => UNS
* INC # E4: 4,6,8 => UNS
* INC # E6: 2,9 => UNS
* INC # E6: 4,8 => UNS
* CNT  17 HDP CHAINS /  17 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B9: 7,8 => UNS
* INC # B9: 4,5 => UNS
* INC # F1: 6,8 => UNS
* INC # E3: 6,8 => UNS
* INC # F3: 6,8 => UNS
* INC # C2: 6,8 => UNS
* INC # C2: 4,5 => UNS
* INC # E4: 6,8 => UNS
* INC # E4: 2,4,9 => UNS
* INC # H3: 6,8 => UNS
* INC # H3: 4,5 => UNS
* INC # C1: 6,8 => UNS
* INC # F1: 6,8 => UNS
* INC # E4: 2,9 => UNS
* INC # E4: 4,6,8 => UNS
* INC # E6: 2,9 => UNS
* INC # E6: 4,8 => UNS
* CNT  17 HDP CHAINS /  17 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # B9: 7,8 => UNS
* INC # B9: 4,5 => UNS
* INC # F1: 6,8 => UNS
* INC # E3: 6,8 => UNS
* INC # F3: 6,8 => UNS
* INC # C2: 6,8 => UNS
* INC # C2: 4,5 => UNS
* INC # E4: 6,8 => UNS
* INC # E4: 2,4,9 => UNS
* INC # H3: 6,8 => UNS
* INC # H3: 4,5 => UNS
* INC # C1: 6,8 => UNS
* INC # F1: 6,8 => UNS
* INC # E4: 2,9 => UNS
* INC # E4: 4,6,8 => UNS
* INC # E6: 2,9 => UNS
* INC # E6: 4,8 => UNS
* INC # B9: 7,8 # A2: 4,5 => UNS
* INC # B9: 7,8 # C2: 4,5 => UNS
* INC # B9: 7,8 # F1: 6,8 => UNS
* INC # B9: 7,8 # E3: 6,8 => UNS
* INC # B9: 7,8 # F3: 6,8 => UNS
* INC # B9: 7,8 # C2: 6,8 => UNS
* INC # B9: 7,8 # C2: 4,5 => UNS
* INC # B9: 7,8 # E4: 6,8 => UNS
* INC # B9: 7,8 # E4: 2,4,9 => UNS
* INC # B9: 7,8 # H3: 6,8 => UNS
* INC # B9: 7,8 # H3: 4,5 => UNS
* INC # B9: 7,8 # C1: 6,8 => UNS
* INC # B9: 7,8 # F1: 6,8 => UNS
* INC # B9: 7,8 # E4: 2,9 => UNS
* INC # B9: 7,8 # E4: 4,6,8 => UNS
* INC # B9: 7,8 # E6: 2,9 => UNS
* INC # B9: 7,8 # E6: 4,8 => UNS
* INC # B9: 7,8 # C4: 4,5 => UNS
* INC # B9: 7,8 # A5: 4,5 => UNS
* INC # B9: 7,8 # H6: 4,5 => UNS
* INC # B9: 7,8 # H6: 8 => UNS
* INC # B9: 7,8 # G9: 7,8 => UNS
* INC # B9: 7,8 # I9: 7,8 => UNS
* INC # B9: 7,8 => UNS
* INC # B9: 4,5 # E3: 6,8 => UNS
* INC # B9: 4,5 # E3: 2 => UNS
* INC # B9: 4,5 # C2: 6,8 => UNS
* INC # B9: 4,5 # C2: 4,5 => UNS
* INC # B9: 4,5 # E3: 2,6 => UNS
* INC # B9: 4,5 # E3: 8 => UNS
* INC # B9: 4,5 # H3: 6,8 => UNS
* INC # B9: 4,5 # H3: 4,5 => UNS
* INC # B9: 4,5 # C1: 6,8 => UNS
* INC # B9: 4,5 # C1: 9 => UNS
* INC # B9: 4,5 # E4: 2,9 => UNS
* INC # B9: 4,5 # E4: 4,6 => UNS
* INC # B9: 4,5 # E6: 2,9 => UNS
* INC # B9: 4,5 # E6: 4 => UNS
* INC # B9: 4,5 # E4: 2,6 => UNS
* INC # B9: 4,5 # E4: 4,9 => UNS
* INC # B9: 4,5 # C7: 4,5 => UNS
* INC # B9: 4,5 # A8: 4,5 => UNS
* INC # B9: 4,5 # F9: 4,5 => UNS
* INC # B9: 4,5 # H9: 4,5 => UNS
* INC # B9: 4,5 # B2: 4,5 => UNS
* INC # B9: 4,5 # B6: 4,5 => UNS
* INC # B9: 4,5 # G1: 7,9 => UNS
* INC # B9: 4,5 # G1: 8 => UNS
* INC # B9: 4,5 # I1: 7,9 => UNS
* INC # B9: 4,5 # I1: 8 => UNS
* INC # B9: 4,5 => UNS
* INC # F1: 6,8 # A8: 4,5 => UNS
* DIS # F1: 6,8 # A8: 8 => CTR => A8: 4,5
* PRF # F1: 6,8 + A8: 4,5 # G4: 4,5 => SOL
* STA # F1: 6,8 + A8: 4,5 + G4: 4,5
* CNT  71 HDP CHAINS /  72 HYP OPENED