Analysis of xx-ph-00000316-296-base.sdk

Contents

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

Original Sudoku

level: hard

position: 1...5...9.5.....3...9........1.6...7...8...2.6....43...1..9..737..3..8.......2.4. initial

Autosolve

position: 1...5...9.5.....3...9........1.6...7...8...2.6....43...1..9..737..3..8.......2.4. 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: 0:00:23.082829

The following important HDP chains were detected:

* DIS # H3: 6,8 # G4: 5,9 => CTR => G4: 4
* DIS # H3: 6,8 + G4: 4 # A4: 5,9 => CTR => A4: 2,3,8
* PRF # H3: 6,8 + G4: 4 + A4: 2,3,8 # D4: 5,9 => SOL
* STA # H3: 6,8 + G4: 4 + A4: 2,3,8 + D4: 5,9
* CNT   3 HDP CHAINS /  31 HYP OPENED

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

Details

Positions

`1...5...9.5.....3...9........1.6...7...8...2.6....43...1..9..737..3..8.......2.4.`	initial
`1...5...9.5.....3...9........1.6...7...8...2.6....43...1..9..737..3..8.......2.4.`	autosolve
`123456789456789132879231564281963457345817926697524318514698273762345891938172645`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (2)
H1: 6,8
E8: 1,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G7,I8: 2.. / G7 = 2  =>  2 pairs (_) / I8 = 2  =>  3 pairs (_)
E3,E5: 3.. / E3 = 3  =>  3 pairs (_) / E5 = 3  =>  3 pairs (_)
D7,E8: 4.. / D7 = 4  =>  5 pairs (_) / E8 = 4  =>  2 pairs (_)
G5,I5: 6.. / G5 = 6  =>  3 pairs (_) / I5 = 6  =>  3 pairs (_)
D9,E9: 7.. / D9 = 7  =>  3 pairs (_) / E9 = 7  =>  4 pairs (_)
F7,E9: 8.. / F7 = 8  =>  3 pairs (_) / E9 = 8  =>  3 pairs (_)
D2,F2: 9.. / D2 = 9  =>  3 pairs (_) / F2 = 9  =>  3 pairs (_)
H8,G9: 9.. / H8 = 9  =>  6 pairs (_) / G9 = 9  =>  3 pairs (_)
B8,H8: 9.. / B8 = 9  =>  3 pairs (_) / H8 = 9  =>  6 pairs (_)
* DURATION: 0:00:07.277061  START: 12:34:40.470554  END: 12:34:47.747615 2020-10-17
* CP COUNT: (9)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:22.870661  START: 12:34:54.197112  END: 12:35:17.067773 2020-10-17
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00000316-296-base-pr-002.dot
* REASONING
* DIS # H3: 6,8 # G4: 5,9 => CTR => G4: 4
* DIS # H3: 6,8 + G4: 4 # A4: 5,9 => CTR => A4: 2,3,8
* PRF # H3: 6,8 + G4: 4 + A4: 2,3,8 # D4: 5,9 => SOL
* STA # H3: 6,8 + G4: 4 + A4: 2,3,8 + D4: 5,9
* CNT   3 HDP CHAINS /  31 HYP OPENED

Header Info

316;296;elev;23;11.40;11.40;10.00

Solution

position: 123456789456789132879231564281963457345817926697524318514698273762345891938172645 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: 6,8 => UNS
* INC # H3: 6,8 => UNS
* INC # I3: 6,8 => UNS
* INC # B1: 6,8 => UNS
* INC # C1: 6,8 => UNS
* INC # F1: 6,8 => UNS
* INC # E2: 1,4 => UNS
* INC # E3: 1,4 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # I2: 6,8 => UNS
* INC # H3: 6,8 => UNS
* INC # I3: 6,8 => UNS
* INC # B1: 6,8 => UNS
* INC # C1: 6,8 => UNS
* INC # F1: 6,8 => UNS
* INC # E2: 1,4 => UNS
* INC # E3: 1,4 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # I2: 6,8 => UNS
* INC # H3: 6,8 => UNS
* INC # I3: 6,8 => UNS
* INC # B1: 6,8 => UNS
* INC # C1: 6,8 => UNS
* INC # F1: 6,8 => UNS
* INC # E2: 1,4 => UNS
* INC # E3: 1,4 => UNS
* INC # I2: 6,8 # B1: 6,8 => UNS
* INC # I2: 6,8 # C1: 6,8 => UNS
* INC # I2: 6,8 # F1: 6,8 => UNS
* INC # I2: 6,8 # C2: 6,8 => UNS
* INC # I2: 6,8 # F2: 6,8 => UNS
* INC # I2: 6,8 # G3: 1,5 => UNS
* INC # I2: 6,8 # I3: 1,5 => UNS
* INC # I2: 6,8 # H6: 1,5 => UNS
* INC # I2: 6,8 # H8: 1,5 => UNS
* INC # I2: 6,8 # E2: 1,4 => UNS
* INC # I2: 6,8 # E3: 1,4 => UNS
* INC # I2: 6,8 => UNS
* INC # H3: 6,8 # B1: 6,8 => UNS
* INC # H3: 6,8 # C1: 6,8 => UNS
* INC # H3: 6,8 # F1: 6,8 => UNS
* INC # H3: 6,8 # B3: 6,8 => UNS
* INC # H3: 6,8 # F3: 6,8 => UNS
* DIS # H3: 6,8 # G4: 5,9 => CTR => G4: 4
* INC # H3: 6,8 + G4: 4 # G5: 5,9 => UNS
* INC # H3: 6,8 + G4: 4 # H6: 5,9 => UNS
* DIS # H3: 6,8 + G4: 4 # A4: 5,9 => CTR => A4: 2,3,8
* PRF # H3: 6,8 + G4: 4 + A4: 2,3,8 # D4: 5,9 => SOL
* STA # H3: 6,8 + G4: 4 + A4: 2,3,8 + D4: 5,9
* CNT  30 HDP CHAINS /  31 HYP OPENED