Analysis of xx-mith-te3-00153397-base.sdk

Contents

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

Original Sudoku

level: hard

position: 12..56....57......6.9..7...27....19....7..8.4...5....35...7..1.79..12.6....9.5... initial

Autosolve

position: 12..56....57......6.9..7...27....19....7..8.4...5....35...7..1.79..12.6....9.5... 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: 0:00:14.286393

The following important HDP chains were detected:

* DIS # I2: 6,8 # E6: 4,8,9 => CTR => E6: 2,6
* PRF # E5: 3,9 # H2: 3,4 => SOL
* STA # E5: 3,9 + H2: 3,4
* CNT   2 HDP CHAINS /  74 HYP OPENED

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

Details

Positions

`12..56....57......6.9..7...27....19....7..8.4...5....35...7..1.79..12.6....9.5...`	initial
`12..56....57......6.9..7...27....19....7..8.4...5....35...7..1.79..12.6....9.5...`	autosolve
`123456789457189236689237451278643195365791824941528673536874912794312568812965347`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
D2: 1,2
D3: 1,2
A5: 3,9
I4: 5,6
H5: 2,5
H6: 2,7
I8: 5,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D2,D3: 1.. / D2 = 1  =>  5 pairs (_) / D3 = 1  =>  9 pairs (_)
I2,I3: 1.. / I2 = 1  =>  9 pairs (_) / I3 = 1  =>  5 pairs (_)
F5,F6: 1.. / F5 = 1  =>  8 pairs (_) / F6 = 1  => 10 pairs (_)
B9,C9: 1.. / B9 = 1  =>  8 pairs (_) / C9 = 1  => 11 pairs (_)
D2,I2: 1.. / D2 = 1  =>  5 pairs (_) / I2 = 1  =>  9 pairs (_)
D3,I3: 1.. / D3 = 1  =>  9 pairs (_) / I3 = 1  =>  5 pairs (_)
D2,D3: 2.. / D2 = 2  =>  9 pairs (_) / D3 = 2  =>  5 pairs (_)
E5,E6: 2.. / E5 = 2  => 11 pairs (_) / E6 = 2  =>  9 pairs (_)
C7,C9: 2.. / C7 = 2  =>  8 pairs (_) / C9 = 2  => 11 pairs (_)
E5,H5: 2.. / E5 = 2  => 11 pairs (_) / H5 = 2  =>  9 pairs (_)
C4,C5: 5.. / C4 = 5  => 11 pairs (_) / C5 = 5  =>  9 pairs (_)
I4,H5: 5.. / I4 = 5  =>  9 pairs (_) / H5 = 5  => 11 pairs (_)
G8,I8: 5.. / G8 = 5  => 13 pairs (_) / I8 = 5  => 11 pairs (_)
C4,I4: 5.. / C4 = 5  => 11 pairs (_) / I4 = 5  =>  9 pairs (_)
C5,H5: 5.. / C5 = 5  =>  9 pairs (_) / H5 = 5  => 11 pairs (_)
G3,G8: 5.. / G3 = 5  => 11 pairs (_) / G8 = 5  => 13 pairs (_)
H3,H5: 5.. / H3 = 5  =>  9 pairs (_) / H5 = 5  => 11 pairs (_)
G2,I2: 6.. / G2 = 6  => 11 pairs (_) / I2 = 6  =>  9 pairs (_)
I4,G6: 6.. / I4 = 6  => 11 pairs (_) / G6 = 6  =>  9 pairs (_)
D7,E9: 6.. / D7 = 6  => 10 pairs (_) / E9 = 6  => 11 pairs (_)
D4,D7: 6.. / D4 = 6  => 11 pairs (_) / D7 = 6  => 10 pairs (_)
G2,G6: 6.. / G2 = 6  => 11 pairs (_) / G6 = 6  =>  9 pairs (_)
I2,I4: 6.. / I2 = 6  =>  9 pairs (_) / I4 = 6  => 11 pairs (_)
G6,H6: 7.. / G6 = 7  => 11 pairs (_) / H6 = 7  =>  9 pairs (_)
I1,I9: 7.. / I1 = 7  =>  8 pairs (_) / I9 = 7  =>  8 pairs (_)
E2,F2: 9.. / E2 = 9  =>  9 pairs (_) / F2 = 9  => 15 pairs (_)
G1,I1: 9.. / G1 = 9  =>  8 pairs (_) / I1 = 9  =>  8 pairs (_)
A5,A6: 9.. / A5 = 9  =>  8 pairs (_) / A6 = 9  => 10 pairs (_)
G7,I7: 9.. / G7 = 9  =>  8 pairs (_) / I7 = 9  =>  8 pairs (_)
G1,G7: 9.. / G1 = 9  =>  8 pairs (_) / G7 = 9  =>  8 pairs (_)
I1,I7: 9.. / I1 = 9  =>  8 pairs (_) / I7 = 9  =>  8 pairs (_)
* DURATION: 0:00:08.266701  START: 15:13:55.272787  END: 15:14:03.539488 2025-04-05
* CP COUNT: (31)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:14.057308  START: 15:14:08.559242  END: 15:14:22.616550 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00153397-base-pr-002.dot
* REASONING
* DIS # I2: 6,8 # E6: 4,8,9 => CTR => E6: 2,6
* PRF # E5: 3,9 # H2: 3,4 => SOL
* STA # E5: 3,9 + H2: 3,4
* CNT   2 HDP CHAINS /  74 HYP OPENED

Header Info

rating: 42227; r2: 762856; index: 153397

Solution

position: 123456789457189236689237451278643195365791824941528673536874912794312568812965347 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 # I2: 1,2 => UNS
* INC # I2: 6,8 => UNS
* INC # I3: 1,2 => UNS
* INC # I3: 5,8 => UNS
* INC # E5: 3,9 => UNS
* INC # F5: 3,9 => UNS
* INC # C4: 5,6 => UNS
* INC # C4: 3,4,8 => UNS
* INC # H3: 2,5 => UNS
* INC # H3: 3,4,8 => UNS
* INC # G6: 2,7 => UNS
* INC # G6: 6 => UNS
* INC # H9: 2,7 => UNS
* INC # H9: 3,4,8 => UNS
* INC # I3: 5,8 => UNS
* INC # I3: 1,2 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # I2: 1,2 => UNS
* INC # I2: 6,8 => UNS
* INC # I3: 1,2 => UNS
* INC # I3: 5,8 => UNS
* INC # E5: 3,9 => UNS
* INC # F5: 3,9 => UNS
* INC # C4: 5,6 => UNS
* INC # C4: 3,4,8 => UNS
* INC # H3: 2,5 => UNS
* INC # H3: 3,4,8 => UNS
* INC # G6: 2,7 => UNS
* INC # G6: 6 => UNS
* INC # H9: 2,7 => UNS
* INC # H9: 3,4,8 => UNS
* INC # I3: 5,8 => UNS
* INC # I3: 1,2 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # I2: 1,2 => UNS
* INC # I2: 6,8 => UNS
* INC # I3: 1,2 => UNS
* INC # I3: 5,8 => UNS
* INC # E5: 3,9 => UNS
* INC # F5: 3,9 => UNS
* INC # C4: 5,6 => UNS
* INC # C4: 3,4,8 => UNS
* INC # H3: 2,5 => UNS
* INC # H3: 3,4,8 => UNS
* INC # G6: 2,7 => UNS
* INC # G6: 6 => UNS
* INC # H9: 2,7 => UNS
* INC # H9: 3,4,8 => UNS
* INC # I3: 5,8 => UNS
* INC # I3: 1,2 => UNS
* INC # I2: 1,2 # I3: 1,2 => UNS
* INC # I2: 1,2 # I3: 5,8 => UNS
* INC # I2: 1,2 # I3: 1,2 => UNS
* INC # I2: 1,2 # I3: 5,8 => UNS
* INC # I2: 1,2 # G9: 2,7 => UNS
* INC # I2: 1,2 # G9: 3,4 => UNS
* INC # I2: 1,2 # H9: 2,7 => UNS
* INC # I2: 1,2 # H9: 3,4,8 => UNS
* INC # I2: 1,2 # B5: 1,6 => UNS
* INC # I2: 1,2 # B5: 3 => UNS
* INC # I2: 1,2 # C5: 1,6 => UNS
* INC # I2: 1,2 # C5: 3 => UNS
* INC # I2: 1,2 # I1: 8,9 => UNS
* INC # I2: 1,2 # I1: 7 => UNS
* INC # I2: 1,2 # I3: 5,8 => UNS
* INC # I2: 1,2 # I3: 1,2 => UNS
* INC # I2: 1,2 => UNS
* INC # I2: 6,8 # E5: 3,9 => UNS
* INC # I2: 6,8 # F5: 3,9 => UNS
* INC # I2: 6,8 # C4: 5,6 => UNS
* INC # I2: 6,8 # C4: 3,4,8 => UNS
* INC # I2: 6,8 # E6: 2,6 => UNS
* DIS # I2: 6,8 # E6: 4,8,9 => CTR => E6: 2,6
* INC # I2: 6,8 + E6: 2,6 # E5: 3,9 => UNS
* INC # I2: 6,8 + E6: 2,6 # F5: 3,9 => UNS
* INC # I2: 6,8 + E6: 2,6 # E5: 2,6 => UNS
* INC # I2: 6,8 + E6: 2,6 # E5: 3,9 => UNS
* INC # I2: 6,8 + E6: 2,6 # C4: 5,6 => UNS
* INC # I2: 6,8 + E6: 2,6 # C4: 3,4,8 => UNS
* INC # I2: 6,8 + E6: 2,6 => UNS
* INC # I3: 1,2 # I2: 1,2 => UNS
* INC # I3: 1,2 # I2: 6,8 => UNS
* INC # I3: 1,2 # I2: 1,2 => UNS
* INC # I3: 1,2 # I2: 6,8 => UNS
* INC # I3: 1,2 # E5: 3,9 => UNS
* INC # I3: 1,2 # F5: 3,9 => UNS
* INC # I3: 1,2 # C4: 5,6 => UNS
* INC # I3: 1,2 # C4: 3,4,8 => UNS
* INC # I3: 1,2 # G6: 2,7 => UNS
* INC # I3: 1,2 # G6: 6 => UNS
* INC # I3: 1,2 # H9: 2,7 => UNS
* INC # I3: 1,2 # H9: 3,4,8 => UNS
* INC # I3: 1,2 => UNS
* INC # I3: 5,8 # B5: 1,6 => UNS
* INC # I3: 5,8 # B5: 3 => UNS
* INC # I3: 5,8 # C5: 1,6 => UNS
* INC # I3: 5,8 # C5: 3 => UNS
* INC # I3: 5,8 # G8: 3,4 => UNS
* INC # I3: 5,8 # G9: 3,4 => UNS
* INC # I3: 5,8 # H9: 3,4 => UNS
* INC # I3: 5,8 # B7: 3,4 => UNS
* INC # I3: 5,8 # F7: 3,4 => UNS
* INC # I3: 5,8 # G3: 3,4 => UNS
* INC # I3: 5,8 # G3: 2,5 => UNS
* INC # I3: 5,8 => UNS
* INC # E5: 3,9 # H1: 3,4 => UNS
* PRF # E5: 3,9 # H2: 3,4 => SOL
* STA # E5: 3,9 + H2: 3,4
* CNT  73 HDP CHAINS /  74 HYP OPENED