Analysis of xx-mith-te3-00112857-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: .23.56...45........89.7.......7.16.4...3......1...537.....1456.5..63.1.7...5.7.43 initial

Autosolve

position: .23.56...45........89.7.......7.16.4...3......1...537.....1456.5..63.1.7...5.7.43 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: 0:00:18.037914

The following important HDP chains were detected:

* DIS # C2: 7 # E9: 8,9 => CTR => E9: 2
* DIS # C2: 7 + E9: 2 # D2: 8,9 => CTR => D2: 1
* PRF # C2: 7 + E9: 2 + D2: 1 # H5: 8,9 => SOL
* STA # C2: 7 + E9: 2 + D2: 1 + H5: 8,9
* CNT   3 HDP CHAINS / 104 HYP OPENED

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

Details

Positions

.23.56...45........89.7.......7.16.4...3......1...537.....1456.5..63.1.7...5.7.43 initial
.23.56...45........89.7.......7.16.4...3......1...537.....1456.5..63.1.7...5.7.43 autosolve
123456789457189236689273415238791654745362891916845372372914568594638127861527943 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
A1: 1,7
A3: 1,6
F3: 2,3
G3: 2,4
B4: 3,9
E5: 4,6
E6: 4,6
B8: 4,9
B9: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H5,I5: 1.. / H5 = 1  => 10 pairs (_) / I5 = 1  => 11 pairs (_)
A9,C9: 1.. / A9 = 1  => 14 pairs (_) / C9 = 1  => 10 pairs (_)
C2,C9: 1.. / C2 = 1  => 14 pairs (_) / C9 = 1  => 10 pairs (_)
F2,F3: 3.. / F2 = 3  => 14 pairs (_) / F3 = 3  =>  8 pairs (_)
H2,H3: 3.. / H2 = 3  =>  8 pairs (_) / H3 = 3  => 14 pairs (_)
A4,B4: 3.. / A4 = 3  =>  8 pairs (_) / B4 = 3  =>  9 pairs (_)
A7,B7: 3.. / A7 = 3  =>  9 pairs (_) / B7 = 3  =>  8 pairs (_)
F2,H2: 3.. / F2 = 3  => 14 pairs (_) / H2 = 3  =>  8 pairs (_)
F3,H3: 3.. / F3 = 3  =>  8 pairs (_) / H3 = 3  => 14 pairs (_)
A4,A7: 3.. / A4 = 3  =>  8 pairs (_) / A7 = 3  =>  9 pairs (_)
B4,B7: 3.. / B4 = 3  =>  9 pairs (_) / B7 = 3  =>  8 pairs (_)
D1,D3: 4.. / D1 = 4  => 10 pairs (_) / D3 = 4  => 10 pairs (_)
G1,G3: 4.. / G1 = 4  => 10 pairs (_) / G3 = 4  => 10 pairs (_)
E5,E6: 4.. / E5 = 4  =>  7 pairs (_) / E6 = 4  =>  6 pairs (_)
B8,C8: 4.. / B8 = 4  =>  9 pairs (_) / C8 = 4  =>  7 pairs (_)
D1,G1: 4.. / D1 = 4  => 10 pairs (_) / G1 = 4  => 10 pairs (_)
D3,G3: 4.. / D3 = 4  => 10 pairs (_) / G3 = 4  => 10 pairs (_)
C6,E6: 4.. / C6 = 4  =>  7 pairs (_) / E6 = 4  =>  6 pairs (_)
B5,B8: 4.. / B5 = 4  =>  7 pairs (_) / B8 = 4  =>  9 pairs (_)
H3,I3: 5.. / H3 = 5  =>  9 pairs (_) / I3 = 5  => 10 pairs (_)
C4,C5: 5.. / C4 = 5  => 11 pairs (_) / C5 = 5  => 14 pairs (_)
C4,H4: 5.. / C4 = 5  => 11 pairs (_) / H4 = 5  => 14 pairs (_)
I3,I5: 5.. / I3 = 5  => 10 pairs (_) / I5 = 5  =>  9 pairs (_)
C2,A3: 6.. / C2 = 6  =>  8 pairs (_) / A3 = 6  => 10 pairs (_)
I2,I3: 6.. / I2 = 6  => 10 pairs (_) / I3 = 6  =>  8 pairs (_)
E5,E6: 6.. / E5 = 6  =>  6 pairs (_) / E6 = 6  =>  7 pairs (_)
C2,I2: 6.. / C2 = 6  =>  8 pairs (_) / I2 = 6  => 10 pairs (_)
A3,I3: 6.. / A3 = 6  => 10 pairs (_) / I3 = 6  =>  8 pairs (_)
B5,B9: 6.. / B5 = 6  => 12 pairs (_) / B9 = 6  =>  8 pairs (_)
A1,C2: 7.. / A1 = 7  =>  9 pairs (_) / C2 = 7  => 18 pairs (_)
G1,G2: 7.. / G1 = 7  => 18 pairs (_) / G2 = 7  =>  9 pairs (_)
A1,G1: 7.. / A1 = 7  =>  9 pairs (_) / G1 = 7  => 18 pairs (_)
C2,G2: 7.. / C2 = 7  => 18 pairs (_) / G2 = 7  =>  9 pairs (_)
B5,B7: 7.. / B5 = 7  =>  9 pairs (_) / B7 = 7  =>  9 pairs (_)
* DURATION: 0:00:08.628852  START: 17:29:52.918676  END: 17:30:01.547528 2025-04-06
* CP COUNT: (34)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:17.767375  START: 17:30:09.326483  END: 17:30:27.093858 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00112857-base-pr-002.dot
* REASONING
* DIS # C2: 7 # E9: 8,9 => CTR => E9: 2
* DIS # C2: 7 + E9: 2 # D2: 8,9 => CTR => D2: 1
* PRF # C2: 7 + E9: 2 + D2: 1 # H5: 8,9 => SOL
* STA # C2: 7 + E9: 2 + D2: 1 + H5: 8,9
* CNT   3 HDP CHAINS / 104 HYP OPENED

Header Info

rating: 28782; r2: 570470; index: 112857

Solution

position: 123456789457189236689273415238791654745362891916845372372914568594638127861527943 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 # C2: 1,7 => UNS
* INC # C2: 6 => UNS
* INC # C2: 1,6 => UNS
* INC # C2: 7 => UNS
* INC # I3: 1,6 => UNS
* INC # I3: 2,5 => UNS
* INC # A9: 1,6 => UNS
* INC # A9: 2,8,9 => UNS
* INC # F2: 2,3 => UNS
* INC # F2: 8,9 => UNS
* INC # H3: 2,3 => UNS
* INC # H3: 1,5 => UNS
* INC # D3: 2,4 => UNS
* INC # D3: 1 => UNS
* INC # A4: 3,9 => UNS
* INC # A4: 2,8 => UNS
* INC # B7: 3,9 => UNS
* INC # B7: 7 => UNS
* INC # B5: 4,6 => UNS
* INC # C5: 4,6 => UNS
* INC # C6: 4,6 => UNS
* INC # C6: 2,8 => UNS
* INC # B5: 4,9 => UNS
* INC # B5: 6,7 => UNS
* INC # A9: 6,9 => UNS
* INC # A9: 1,2,8 => UNS
* INC # B5: 6,9 => UNS
* INC # B5: 4,7 => UNS
* CNT  28 HDP CHAINS /  28 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C2: 1,7 => UNS
* INC # C2: 6 => UNS
* INC # C2: 1,6 => UNS
* INC # C2: 7 => UNS
* INC # I3: 1,6 => UNS
* INC # I3: 2,5 => UNS
* INC # A9: 1,6 => UNS
* INC # A9: 2,8,9 => UNS
* INC # F2: 2,3 => UNS
* INC # F2: 8,9 => UNS
* INC # H3: 2,3 => UNS
* INC # H3: 1,5 => UNS
* INC # D3: 2,4 => UNS
* INC # D3: 1 => UNS
* INC # A4: 3,9 => UNS
* INC # A4: 2,8 => UNS
* INC # B7: 3,9 => UNS
* INC # B7: 7 => UNS
* INC # B5: 4,6 => UNS
* INC # C5: 4,6 => UNS
* INC # C6: 4,6 => UNS
* INC # C6: 2,8 => UNS
* INC # B5: 4,9 => UNS
* INC # B5: 6,7 => UNS
* INC # A9: 6,9 => UNS
* INC # A9: 1,2,8 => UNS
* INC # B5: 6,9 => UNS
* INC # B5: 4,7 => UNS
* CNT  28 HDP CHAINS /  28 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # C2: 1,7 => UNS
* INC # C2: 6 => UNS
* INC # C2: 1,6 => UNS
* INC # C2: 7 => UNS
* INC # I3: 1,6 => UNS
* INC # I3: 2,5 => UNS
* INC # A9: 1,6 => UNS
* INC # A9: 2,8,9 => UNS
* INC # F2: 2,3 => UNS
* INC # F2: 8,9 => UNS
* INC # H3: 2,3 => UNS
* INC # H3: 1,5 => UNS
* INC # D3: 2,4 => UNS
* INC # D3: 1 => UNS
* INC # A4: 3,9 => UNS
* INC # A4: 2,8 => UNS
* INC # B7: 3,9 => UNS
* INC # B7: 7 => UNS
* INC # B5: 4,6 => UNS
* INC # C5: 4,6 => UNS
* INC # C6: 4,6 => UNS
* INC # C6: 2,8 => UNS
* INC # B5: 4,9 => UNS
* INC # B5: 6,7 => UNS
* INC # A9: 6,9 => UNS
* INC # A9: 1,2,8 => UNS
* INC # B5: 6,9 => UNS
* INC # B5: 4,7 => UNS
* INC # C2: 1,7 # F2: 2,3 => UNS
* INC # C2: 1,7 # F2: 8,9 => UNS
* INC # C2: 1,7 # H3: 2,3 => UNS
* INC # C2: 1,7 # H3: 1,5 => UNS
* INC # C2: 1,7 # D3: 2,4 => UNS
* INC # C2: 1,7 # D3: 1 => UNS
* INC # C2: 1,7 # A4: 3,9 => UNS
* INC # C2: 1,7 # A4: 2,8 => UNS
* INC # C2: 1,7 # B7: 3,9 => UNS
* INC # C2: 1,7 # B7: 7 => UNS
* INC # C2: 1,7 # B5: 4,6 => UNS
* INC # C2: 1,7 # C5: 4,6 => UNS
* INC # C2: 1,7 # B5: 4,6 => UNS
* INC # C2: 1,7 # C5: 4,6 => UNS
* INC # C2: 1,7 # B5: 4,9 => UNS
* INC # C2: 1,7 # B5: 6,7 => UNS
* INC # C2: 1,7 # B5: 6,9 => UNS
* INC # C2: 1,7 # B5: 4,7 => UNS
* INC # C2: 1,7 => UNS
* INC # C2: 6 # G1: 8,9 => UNS
* INC # C2: 6 # I1: 8,9 => UNS
* INC # C2: 6 # I2: 8,9 => UNS
* INC # C2: 6 # D1: 8,9 => UNS
* INC # C2: 6 # D1: 1,4 => UNS
* INC # C2: 6 # H4: 8,9 => UNS
* INC # C2: 6 # H8: 8,9 => UNS
* INC # C2: 6 # A4: 3,9 => UNS
* INC # C2: 6 # A4: 2,8 => UNS
* INC # C2: 6 # B7: 3,9 => UNS
* INC # C2: 6 # B7: 7 => UNS
* INC # C2: 6 # B5: 4,6 => UNS
* INC # C2: 6 # B5: 7,9 => UNS
* INC # C2: 6 # B5: 4,9 => UNS
* INC # C2: 6 # B5: 6,7 => UNS
* INC # C2: 6 # A9: 6,9 => UNS
* INC # C2: 6 # A9: 2,8 => UNS
* INC # C2: 6 # B5: 6,9 => UNS
* INC # C2: 6 # B5: 4,7 => UNS
* INC # C2: 6 => UNS
* INC # C2: 1,6 # I2: 1,6 => UNS
* INC # C2: 1,6 # I2: 2,8,9 => UNS
* INC # C2: 1,6 # C9: 1,6 => UNS
* INC # C2: 1,6 # C9: 2,8 => UNS
* INC # C2: 1,6 # I3: 1,6 => UNS
* INC # C2: 1,6 # I3: 2,5 => UNS
* INC # C2: 1,6 # A9: 1,6 => UNS
* INC # C2: 1,6 # A9: 2,8,9 => UNS
* INC # C2: 1,6 # F2: 2,3 => UNS
* INC # C2: 1,6 # F2: 8,9 => UNS
* INC # C2: 1,6 # H3: 2,3 => UNS
* INC # C2: 1,6 # H3: 1,5 => UNS
* INC # C2: 1,6 # D3: 2,4 => UNS
* INC # C2: 1,6 # D3: 1 => UNS
* INC # C2: 1,6 # A4: 3,9 => UNS
* INC # C2: 1,6 # A4: 2,8 => UNS
* INC # C2: 1,6 # B7: 3,9 => UNS
* INC # C2: 1,6 # B7: 7 => UNS
* INC # C2: 1,6 # B5: 4,6 => UNS
* INC # C2: 1,6 # C5: 4,6 => UNS
* INC # C2: 1,6 # C6: 4,6 => UNS
* INC # C2: 1,6 # C6: 2,8 => UNS
* INC # C2: 1,6 # B5: 4,9 => UNS
* INC # C2: 1,6 # B5: 6,7 => UNS
* INC # C2: 1,6 # A9: 6,9 => UNS
* INC # C2: 1,6 # A9: 1,2,8 => UNS
* INC # C2: 1,6 # B5: 6,9 => UNS
* INC # C2: 1,6 # B5: 4,7 => UNS
* INC # C2: 1,6 => UNS
* INC # C2: 7 # D2: 8,9 => UNS
* INC # C2: 7 # F2: 8,9 => UNS
* INC # C2: 7 # E4: 8,9 => UNS
* DIS # C2: 7 # E9: 8,9 => CTR => E9: 2
* DIS # C2: 7 + E9: 2 # D2: 8,9 => CTR => D2: 1
* INC # C2: 7 + E9: 2 + D2: 1 # H4: 8,9 => UNS
* PRF # C2: 7 + E9: 2 + D2: 1 # H5: 8,9 => SOL
* STA # C2: 7 + E9: 2 + D2: 1 + H5: 8,9
* CNT 103 HDP CHAINS / 104 HYP OPENED