Analysis of xx-mith-te3-00102481-base.sdk

Contents

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

Original Sudoku

level: hard

position: ..34..78.4.7....3668....5.4...6....3.7.89.....4...2...5...7.4.87.8.4536...4...... initial

Autosolve

position: ..34..78.4.7....3668....5.4...6....3.7.89.....4...2...5...7.4.87.8.4536...4...... 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: 0:00:13.752456

The following important HDP chains were detected:

* PRF # C4: 1,5 # B1: 2,9 => SOL
* STA # C4: 1,5 + B1: 2,9
* CNT   1 HDP CHAINS /  65 HYP OPENED

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

Details

Positions

`..34..78.4.7....3668....5.4...6....3.7.89.....4...2...5...7.4.87.8.4536...4......`	initial
`..34..78.4.7....3668....5.4...6....3.7.89.....4...2...5...7.4.87.8.4536...4......`	autosolve
`123456789457189236689723514295617843371894625846532971562371498718945362934268157`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
E4: 1,5
F4: 4,7
H4: 4,7
B7: 3,6
B9: 3,6
H9: 5,7
I9: 5,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A5,A6: 3.. / A5 = 3  =>  8 pairs (_) / A6 = 3  => 10 pairs (_)
B7,B9: 3.. / B7 = 3  =>  6 pairs (_) / B9 = 3  =>  7 pairs (_)
A5,F5: 3.. / A5 = 3  =>  8 pairs (_) / F5 = 3  => 10 pairs (_)
F4,F5: 4.. / F4 = 4  =>  5 pairs (_) / F5 = 4  =>  5 pairs (_)
H4,H5: 4.. / H4 = 4  =>  5 pairs (_) / H5 = 4  =>  5 pairs (_)
F4,H4: 4.. / F4 = 4  =>  5 pairs (_) / H4 = 4  =>  5 pairs (_)
F5,H5: 4.. / F5 = 4  =>  5 pairs (_) / H5 = 4  =>  5 pairs (_)
B1,B2: 5.. / B1 = 5  =>  7 pairs (_) / B2 = 5  => 16 pairs (_)
H9,I9: 5.. / H9 = 5  =>  5 pairs (_) / I9 = 5  =>  4 pairs (_)
B1,E1: 5.. / B1 = 5  =>  7 pairs (_) / E1 = 5  => 16 pairs (_)
C4,E4: 5.. / C4 = 5  => 10 pairs (_) / E4 = 5  =>  9 pairs (_)
D2,D6: 5.. / D2 = 5  =>  7 pairs (_) / D6 = 5  => 11 pairs (_)
E1,F1: 6.. / E1 = 6  =>  8 pairs (_) / F1 = 6  =>  6 pairs (_)
C5,C6: 6.. / C5 = 6  => 10 pairs (_) / C6 = 6  =>  7 pairs (_)
G5,G6: 6.. / G5 = 6  =>  7 pairs (_) / G6 = 6  => 10 pairs (_)
B7,B9: 6.. / B7 = 6  =>  7 pairs (_) / B9 = 6  =>  6 pairs (_)
C5,G5: 6.. / C5 = 6  => 10 pairs (_) / G5 = 6  =>  7 pairs (_)
C6,G6: 6.. / C6 = 6  =>  7 pairs (_) / G6 = 6  => 10 pairs (_)
B7,F7: 6.. / B7 = 6  =>  7 pairs (_) / F7 = 6  =>  6 pairs (_)
E1,E9: 6.. / E1 = 6  =>  8 pairs (_) / E9 = 6  =>  6 pairs (_)
D3,F3: 7.. / D3 = 7  =>  5 pairs (_) / F3 = 7  =>  5 pairs (_)
F4,D6: 7.. / F4 = 7  =>  5 pairs (_) / D6 = 7  =>  5 pairs (_)
H9,I9: 7.. / H9 = 7  =>  4 pairs (_) / I9 = 7  =>  5 pairs (_)
F4,H4: 7.. / F4 = 7  =>  5 pairs (_) / H4 = 7  =>  5 pairs (_)
D3,D6: 7.. / D3 = 7  =>  5 pairs (_) / D6 = 7  =>  5 pairs (_)
F3,F4: 7.. / F3 = 7  =>  5 pairs (_) / F4 = 7  =>  5 pairs (_)
I6,I9: 7.. / I6 = 7  =>  4 pairs (_) / I9 = 7  =>  5 pairs (_)
E2,F2: 8.. / E2 = 8  =>  8 pairs (_) / F2 = 8  =>  8 pairs (_)
A4,A6: 8.. / A4 = 8  =>  7 pairs (_) / A6 = 8  =>  8 pairs (_)
G4,G6: 8.. / G4 = 8  =>  8 pairs (_) / G6 = 8  =>  7 pairs (_)
E9,F9: 8.. / E9 = 8  =>  8 pairs (_) / F9 = 8  =>  8 pairs (_)
A4,G4: 8.. / A4 = 8  =>  7 pairs (_) / G4 = 8  =>  8 pairs (_)
A6,G6: 8.. / A6 = 8  =>  8 pairs (_) / G6 = 8  =>  7 pairs (_)
E2,E9: 8.. / E2 = 8  =>  8 pairs (_) / E9 = 8  =>  8 pairs (_)
F2,F9: 8.. / F2 = 8  =>  8 pairs (_) / F9 = 8  =>  8 pairs (_)
* DURATION: 0:00:10.613483  START: 16:42:48.174090  END: 16:42:58.787573 2025-04-06
* CP COUNT: (35)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:13.491798  START: 16:43:03.648776  END: 16:43:17.140574 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00102481-base-pr-002.dot
* REASONING
* PRF # C4: 1,5 # B1: 2,9 => SOL
* STA # C4: 1,5 + B1: 2,9
* CNT   1 HDP CHAINS /  65 HYP OPENED

Header Info

rating: 25753; r2: 533395; index: 102481

Solution

position: 123456789457189236689723514295617843371894625846532971562371498718945362934268157 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 # D6: 1,5 => UNS
* INC # E6: 1,5 => UNS
* INC # C4: 1,5 => UNS
* INC # C4: 2,9 => UNS
* INC # E1: 1,5 => UNS
* INC # E2: 1,5 => UNS
* INC # F7: 3,6 => UNS
* INC # F7: 1,9 => UNS
* INC # E9: 3,6 => UNS
* INC # F9: 3,6 => UNS
* INC # H6: 5,7 => UNS
* INC # H6: 1,9 => UNS
* INC # I6: 5,7 => UNS
* INC # I6: 1,9 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D6: 1,5 => UNS
* INC # E6: 1,5 => UNS
* INC # C4: 1,5 => UNS
* INC # C4: 2,9 => UNS
* INC # E1: 1,5 => UNS
* INC # E2: 1,5 => UNS
* INC # F7: 3,6 => UNS
* INC # F7: 1,9 => UNS
* INC # E9: 3,6 => UNS
* INC # F9: 3,6 => UNS
* INC # H6: 5,7 => UNS
* INC # H6: 1,9 => UNS
* INC # I6: 5,7 => UNS
* INC # I6: 1,9 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # D6: 1,5 => UNS
* INC # E6: 1,5 => UNS
* INC # C4: 1,5 => UNS
* INC # C4: 2,9 => UNS
* INC # E1: 1,5 => UNS
* INC # E2: 1,5 => UNS
* INC # F7: 3,6 => UNS
* INC # F7: 1,9 => UNS
* INC # E9: 3,6 => UNS
* INC # F9: 3,6 => UNS
* INC # H6: 5,7 => UNS
* INC # H6: 1,9 => UNS
* INC # I6: 5,7 => UNS
* INC # I6: 1,9 => UNS
* INC # D6: 1,5 # E1: 1,2 => UNS
* INC # D6: 1,5 # D2: 1,2 => UNS
* INC # D6: 1,5 # E2: 1,2 => UNS
* INC # D6: 1,5 # C3: 1,2 => UNS
* INC # D6: 1,5 # H3: 1,2 => UNS
* INC # D6: 1,5 # E9: 1,2 => UNS
* INC # D6: 1,5 # E9: 6,8 => UNS
* INC # D6: 1,5 # C4: 1,5 => UNS
* INC # D6: 1,5 # C4: 2,9 => UNS
* INC # D6: 1,5 # E1: 1,5 => UNS
* INC # D6: 1,5 # E2: 1,5 => UNS
* INC # D6: 1,5 # C6: 1,5 => UNS
* INC # D6: 1,5 # H6: 1,5 => UNS
* INC # D6: 1,5 # I6: 1,5 => UNS
* INC # D6: 1,5 # D2: 1,5 => UNS
* INC # D6: 1,5 # D2: 2,9 => UNS
* INC # D6: 1,5 # H6: 5,7 => UNS
* INC # D6: 1,5 # H6: 1,9 => UNS
* INC # D6: 1,5 # I6: 5,7 => UNS
* INC # D6: 1,5 # I6: 1,9 => UNS
* INC # D6: 1,5 => UNS
* INC # E6: 1,5 # E9: 2,6 => UNS
* INC # E6: 1,5 # E9: 3,8 => UNS
* INC # E6: 1,5 # E9: 2,8 => UNS
* INC # E6: 1,5 # E9: 3,6 => UNS
* INC # E6: 1,5 # D3: 2,3 => UNS
* INC # E6: 1,5 # D3: 1,7,9 => UNS
* INC # E6: 1,5 # E9: 2,3 => UNS
* INC # E6: 1,5 # E9: 6,8 => UNS
* INC # E6: 1,5 # C4: 1,5 => UNS
* INC # E6: 1,5 # C4: 2,9 => UNS
* INC # E6: 1,5 # D3: 3,7 => UNS
* INC # E6: 1,5 # D3: 1,2,9 => UNS
* INC # E6: 1,5 # C6: 1,5 => UNS
* INC # E6: 1,5 # H6: 1,5 => UNS
* INC # E6: 1,5 # I6: 1,5 => UNS
* INC # E6: 1,5 # F7: 3,6 => UNS
* INC # E6: 1,5 # F7: 1,9 => UNS
* INC # E6: 1,5 # E9: 3,6 => UNS
* INC # E6: 1,5 # F9: 3,6 => UNS
* INC # E6: 1,5 # H6: 5,7 => UNS
* INC # E6: 1,5 # H6: 1,9 => UNS
* INC # E6: 1,5 # I6: 5,7 => UNS
* INC # E6: 1,5 # I6: 1,9 => UNS
* INC # E6: 1,5 => UNS
* INC # C4: 1,5 # A4: 2,9 => UNS
* INC # C4: 1,5 # A4: 8 => UNS
* INC # C4: 1,5 # G4: 2,9 => UNS
* INC # C4: 1,5 # G4: 8 => UNS
* PRF # C4: 1,5 # B1: 2,9 => SOL
* STA # C4: 1,5 + B1: 2,9
* CNT  64 HDP CHAINS /  65 HYP OPENED