Analysis of xx-mith-te3-00099663-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: ...45..89....8923..98...5.42.....493346.9.....7.......5...2...8...5.8.2....93..45 initial

Autosolve

position: ...45..89....8923..98...5.42.....493346.9.....7.......5...2...8...5.8.2....93..45 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: 0:00:32.578371

The following important HDP chains were detected:

* DIS # F6: 1,4,5 # B4: 1,5 => CTR => B4: 8
* PRF # F6: 1,4,5 + B4: 8 # F7: 1,7 => SOL
* STA # F6: 1,4,5 + B4: 8 + F7: 1,7
* CNT   2 HDP CHAINS / 128 HYP OPENED

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

Details

Positions

...45..89....8923..98...5.42.....493346.9.....7.......5...2...8...5.8.2....93..45 initial
...45..89....8923..98...5.42.....493346.9.....7.......5...2...8...5.8.2....93..45 autosolve
123456789457189236698273514281765493346892157975314862534621978769548321812937645 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
B1: 2,3
C1: 2,3
D3: 2,3
F3: 2,3
C4: 1,5
E6: 1,4
G7: 3,9
G8: 3,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B1,C1: 2.. / B1 = 2  =>  6 pairs (_) / C1 = 2  => 14 pairs (_)
D3,F3: 2.. / D3 = 2  =>  7 pairs (_) / F3 = 2  =>  6 pairs (_)
I5,I6: 2.. / I5 = 2  => 12 pairs (_) / I6 = 2  =>  9 pairs (_)
B9,C9: 2.. / B9 = 2  => 14 pairs (_) / C9 = 2  =>  6 pairs (_)
B1,B9: 2.. / B1 = 2  =>  6 pairs (_) / B9 = 2  => 14 pairs (_)
C1,C9: 2.. / C1 = 2  => 14 pairs (_) / C9 = 2  =>  6 pairs (_)
B1,C1: 3.. / B1 = 3  => 14 pairs (_) / C1 = 3  =>  6 pairs (_)
D3,F3: 3.. / D3 = 3  =>  6 pairs (_) / F3 = 3  =>  7 pairs (_)
D6,F6: 3.. / D6 = 3  =>  7 pairs (_) / F6 = 3  =>  6 pairs (_)
G7,G8: 3.. / G7 = 3  => 11 pairs (_) / G8 = 3  =>  7 pairs (_)
D3,D6: 3.. / D3 = 3  =>  6 pairs (_) / D6 = 3  =>  7 pairs (_)
F3,F6: 3.. / F3 = 3  =>  7 pairs (_) / F6 = 3  =>  6 pairs (_)
A2,C2: 4.. / A2 = 4  =>  8 pairs (_) / C2 = 4  => 10 pairs (_)
E6,F6: 4.. / E6 = 4  =>  7 pairs (_) / F6 = 4  => 15 pairs (_)
F7,E8: 4.. / F7 = 4  =>  7 pairs (_) / E8 = 4  => 15 pairs (_)
C7,F7: 4.. / C7 = 4  => 15 pairs (_) / F7 = 4  =>  7 pairs (_)
A2,A8: 4.. / A2 = 4  =>  8 pairs (_) / A8 = 4  => 10 pairs (_)
E6,E8: 4.. / E6 = 4  =>  7 pairs (_) / E8 = 4  => 15 pairs (_)
F6,F7: 4.. / F6 = 4  => 15 pairs (_) / F7 = 4  =>  7 pairs (_)
B2,C2: 5.. / B2 = 5  =>  9 pairs (_) / C2 = 5  => 20 pairs (_)
H5,H6: 5.. / H5 = 5  => 10 pairs (_) / H6 = 5  => 10 pairs (_)
F5,H5: 5.. / F5 = 5  => 10 pairs (_) / H5 = 5  => 10 pairs (_)
B2,B4: 5.. / B2 = 5  =>  9 pairs (_) / B4 = 5  => 20 pairs (_)
B4,A6: 8.. / B4 = 8  => 11 pairs (_) / A6 = 8  => 13 pairs (_)
G5,G6: 8.. / G5 = 8  => 10 pairs (_) / G6 = 8  => 12 pairs (_)
A9,B9: 8.. / A9 = 8  => 11 pairs (_) / B9 = 8  => 13 pairs (_)
B4,D4: 8.. / B4 = 8  => 11 pairs (_) / D4 = 8  => 13 pairs (_)
D5,G5: 8.. / D5 = 8  => 12 pairs (_) / G5 = 8  => 10 pairs (_)
A6,A9: 8.. / A6 = 8  => 13 pairs (_) / A9 = 8  => 11 pairs (_)
B4,B9: 8.. / B4 = 8  => 11 pairs (_) / B9 = 8  => 13 pairs (_)
A6,C6: 9.. / A6 = 9  => 13 pairs (_) / C6 = 9  =>  8 pairs (_)
G7,G8: 9.. / G7 = 9  =>  7 pairs (_) / G8 = 9  => 11 pairs (_)
C7,G7: 9.. / C7 = 9  => 11 pairs (_) / G7 = 9  =>  7 pairs (_)
A6,A8: 9.. / A6 = 9  => 13 pairs (_) / A8 = 9  =>  8 pairs (_)
* DURATION: 0:00:11.054475  START: 00:51:25.124414  END: 00:51:36.178889 2025-04-05
* CP COUNT: (34)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:32.292691  START: 00:51:42.445993  END: 00:52:14.738684 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00099663-base-pr-002.dot
* REASONING
* DIS # F6: 1,4,5 # B4: 1,5 => CTR => B4: 8
* PRF # F6: 1,4,5 + B4: 8 # F7: 1,7 => SOL
* STA # F6: 1,4,5 + B4: 8 + F7: 1,7
* CNT   2 HDP CHAINS / 128 HYP OPENED

Header Info

rating: 25109; r2: 801645; index: 99663

Solution

position: 123456789457189236698273514281765493346892157975314862534621978769548321812937645 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 # D6: 2,3 => UNS
* INC # D6: 1,8 => UNS
* INC # F6: 2,3 => UNS
* INC # F6: 1,4,5 => UNS
* INC # B4: 1,5 => UNS
* INC # C6: 1,5 => UNS
* INC # F4: 1,5 => UNS
* INC # F4: 6,7 => UNS
* INC # C2: 1,5 => UNS
* INC # C2: 4,7 => UNS
* INC # F6: 1,4 => UNS
* INC # F6: 2,3,5 => UNS
* INC # E8: 1,4 => UNS
* INC # E8: 6,7 => UNS
* INC # C7: 3,9 => UNS
* INC # C7: 1,4,7 => UNS
* INC # C8: 3,9 => UNS
* INC # C8: 1,4,7 => UNS
* CNT  18 HDP CHAINS /  18 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D6: 2,3 => UNS
* INC # D6: 1,8 => UNS
* INC # F6: 2,3 => UNS
* INC # F6: 1,4,5 => UNS
* INC # B4: 1,5 => UNS
* INC # C6: 1,5 => UNS
* INC # F4: 1,5 => UNS
* INC # F4: 6,7 => UNS
* INC # C2: 1,5 => UNS
* INC # C2: 4,7 => UNS
* INC # F6: 1,4 => UNS
* INC # F6: 2,3,5 => UNS
* INC # E8: 1,4 => UNS
* INC # E8: 6,7 => UNS
* INC # C7: 3,9 => UNS
* INC # C7: 1,4,7 => UNS
* INC # C8: 3,9 => UNS
* INC # C8: 1,4,7 => UNS
* CNT  18 HDP CHAINS /  18 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # D6: 2,3 => UNS
* INC # D6: 1,8 => UNS
* INC # F6: 2,3 => UNS
* INC # F6: 1,4,5 => UNS
* INC # B4: 1,5 => UNS
* INC # C6: 1,5 => UNS
* INC # F4: 1,5 => UNS
* INC # F4: 6,7 => UNS
* INC # C2: 1,5 => UNS
* INC # C2: 4,7 => UNS
* INC # F6: 1,4 => UNS
* INC # F6: 2,3,5 => UNS
* INC # E8: 1,4 => UNS
* INC # E8: 6,7 => UNS
* INC # C7: 3,9 => UNS
* INC # C7: 1,4,7 => UNS
* INC # C8: 3,9 => UNS
* INC # C8: 1,4,7 => UNS
* INC # D6: 2,3 # F6: 2,3 => UNS
* INC # D6: 2,3 # F6: 1,4,5 => UNS
* INC # D6: 2,3 # B4: 1,5 => UNS
* INC # D6: 2,3 # C6: 1,5 => UNS
* INC # D6: 2,3 # F4: 1,5 => UNS
* INC # D6: 2,3 # F4: 6,7 => UNS
* INC # D6: 2,3 # C2: 1,5 => UNS
* INC # D6: 2,3 # C2: 4,7 => UNS
* INC # D6: 2,3 # D4: 1,8 => UNS
* INC # D6: 2,3 # D4: 6,7 => UNS
* INC # D6: 2,3 # G5: 1,8 => UNS
* INC # D6: 2,3 # G5: 7 => UNS
* INC # D6: 2,3 # F6: 2,3 => UNS
* INC # D6: 2,3 # F6: 1,4,5 => UNS
* INC # D6: 2,3 # F6: 1,4 => UNS
* INC # D6: 2,3 # F6: 2,3,5 => UNS
* INC # D6: 2,3 # E8: 1,4 => UNS
* INC # D6: 2,3 # E8: 6,7 => UNS
* INC # D6: 2,3 # C7: 3,9 => UNS
* INC # D6: 2,3 # C7: 1,4,7 => UNS
* INC # D6: 2,3 # C8: 3,9 => UNS
* INC # D6: 2,3 # C8: 1,4,7 => UNS
* INC # D6: 2,3 => UNS
* INC # D6: 1,8 # B4: 1,5 => UNS
* INC # D6: 1,8 # C6: 1,5 => UNS
* INC # D6: 1,8 # F4: 1,5 => UNS
* INC # D6: 1,8 # F4: 6,7 => UNS
* INC # D6: 1,8 # C2: 1,5 => UNS
* INC # D6: 1,8 # C2: 4,7 => UNS
* INC # D6: 1,8 # F4: 1,5 => UNS
* INC # D6: 1,8 # F4: 6,7 => UNS
* INC # D6: 1,8 # H5: 1,5 => UNS
* INC # D6: 1,8 # H5: 7 => UNS
* INC # D6: 1,8 # D4: 1,8 => UNS
* INC # D6: 1,8 # D4: 6,7 => UNS
* INC # D6: 1,8 # A6: 1,8 => UNS
* INC # D6: 1,8 # A6: 9 => UNS
* INC # D6: 1,8 # H5: 1,7 => UNS
* INC # D6: 1,8 # H5: 5 => UNS
* INC # D6: 1,8 # I2: 1,7 => UNS
* INC # D6: 1,8 # I8: 1,7 => UNS
* INC # D6: 1,8 # H6: 1,6 => UNS
* INC # D6: 1,8 # H6: 5 => UNS
* INC # D6: 1,8 # G1: 1,6 => UNS
* INC # D6: 1,8 # G9: 1,6 => UNS
* INC # D6: 1,8 # C7: 3,9 => UNS
* INC # D6: 1,8 # C7: 1,7 => UNS
* INC # D6: 1,8 # C8: 3,9 => UNS
* INC # D6: 1,8 # C8: 1,4,7 => UNS
* INC # D6: 1,8 => UNS
* INC # F6: 2,3 # D6: 2,3 => UNS
* INC # F6: 2,3 # D6: 1,8 => UNS
* INC # F6: 2,3 # B4: 1,5 => UNS
* INC # F6: 2,3 # C6: 1,5 => UNS
* INC # F6: 2,3 # F4: 1,5 => UNS
* INC # F6: 2,3 # F4: 6,7 => UNS
* INC # F6: 2,3 # C2: 1,5 => UNS
* INC # F6: 2,3 # C2: 4,7 => UNS
* INC # F6: 2,3 # F4: 1,5 => UNS
* INC # F6: 2,3 # F4: 6,7 => UNS
* INC # F6: 2,3 # H5: 1,5 => UNS
* INC # F6: 2,3 # H5: 7 => UNS
* INC # F6: 2,3 # D6: 2,3 => UNS
* INC # F6: 2,3 # D6: 1,8 => UNS
* INC # F6: 2,3 # C7: 3,9 => UNS
* INC # F6: 2,3 # C7: 1,7 => UNS
* INC # F6: 2,3 # C8: 3,9 => UNS
* INC # F6: 2,3 # C8: 1,4,7 => UNS
* INC # F6: 2,3 => UNS
* DIS # F6: 1,4,5 # B4: 1,5 => CTR => B4: 8
* INC # F6: 1,4,5 + B4: 8 # C6: 1,5 => UNS
* INC # F6: 1,4,5 + B4: 8 # C6: 1,5 => UNS
* INC # F6: 1,4,5 + B4: 8 # C6: 9 => UNS
* INC # F6: 1,4,5 + B4: 8 # F4: 1,5 => UNS
* INC # F6: 1,4,5 + B4: 8 # F4: 6,7 => UNS
* INC # F6: 1,4,5 + B4: 8 # F6: 1,4 => UNS
* INC # F6: 1,4,5 + B4: 8 # F6: 5 => UNS
* INC # F6: 1,4,5 + B4: 8 # E8: 1,4 => UNS
* INC # F6: 1,4,5 + B4: 8 # E8: 6,7 => UNS
* INC # F6: 1,4,5 + B4: 8 # I2: 1,7 => UNS
* INC # F6: 1,4,5 + B4: 8 # I8: 1,7 => UNS
* INC # F6: 1,4,5 + B4: 8 # C7: 3,9 => UNS
* INC # F6: 1,4,5 + B4: 8 # C7: 4,7 => UNS
* INC # F6: 1,4,5 + B4: 8 # C8: 3,9 => UNS
* INC # F6: 1,4,5 + B4: 8 # C8: 4,7 => UNS
* INC # F6: 1,4,5 + B4: 8 # G1: 1,7 => UNS
* INC # F6: 1,4,5 + B4: 8 # I2: 1,7 => UNS
* INC # F6: 1,4,5 + B4: 8 # A3: 1,7 => UNS
* INC # F6: 1,4,5 + B4: 8 # E3: 1,7 => UNS
* INC # F6: 1,4,5 + B4: 8 # C6: 1,5 => UNS
* INC # F6: 1,4,5 + B4: 8 # C6: 9 => UNS
* INC # F6: 1,4,5 + B4: 8 # F4: 1,5 => UNS
* INC # F6: 1,4,5 + B4: 8 # F4: 6,7 => UNS
* INC # F6: 1,4,5 + B4: 8 # C6: 1,9 => UNS
* INC # F6: 1,4,5 + B4: 8 # C6: 5 => UNS
* INC # F6: 1,4,5 + B4: 8 # F6: 1,4 => UNS
* INC # F6: 1,4,5 + B4: 8 # F6: 5 => UNS
* INC # F6: 1,4,5 + B4: 8 # E8: 1,4 => UNS
* INC # F6: 1,4,5 + B4: 8 # E8: 6,7 => UNS
* INC # F6: 1,4,5 + B4: 8 # G1: 1,7 => UNS
* INC # F6: 1,4,5 + B4: 8 # G9: 1,7 => UNS
* INC # F6: 1,4,5 + B4: 8 # I2: 1,7 => UNS
* INC # F6: 1,4,5 + B4: 8 # I8: 1,7 => UNS
* INC # F6: 1,4,5 + B4: 8 # C7: 3,9 => UNS
* INC # F6: 1,4,5 + B4: 8 # C7: 4,7 => UNS
* INC # F6: 1,4,5 + B4: 8 # I8: 1,7 => UNS
* INC # F6: 1,4,5 + B4: 8 # G9: 1,7 => UNS
* INC # F6: 1,4,5 + B4: 8 # D7: 1,7 => UNS
* PRF # F6: 1,4,5 + B4: 8 # F7: 1,7 => SOL
* STA # F6: 1,4,5 + B4: 8 + F7: 1,7
* CNT 127 HDP CHAINS / 128 HYP OPENED