Analysis of xx-ph-00973765-13_03-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.7..6....7.5..4.........76.......8.3.4.......2..5.7.3...21....2...79....15...2. initial

Autosolve

position: 98.7..6....7.5..4.........76.......8.3.4.......2..5.7.3...21....2...79....15...2. 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: 0:01:12.045177

The following important HDP chains were detected:

* DIS # G2: 1,2 # G3: 1,2 => CTR => G3: 3,5,8
* DIS # I2: 1,2 # G3: 1,2 => CTR => G3: 3,5,8
* DIS # I2: 1,2 + G3: 3,5,8 # G4: 3,5 => CTR => G4: 1,2,4
* DIS # I2: 1,2 + G3: 3,5,8 + G4: 1,2,4 # H8: 3,5 => CTR => H8: 1,6,8
* DIS # I2: 1,2 + G3: 3,5,8 + G4: 1,2,4 + H8: 1,6,8 # H1: 1 => CTR => H1: 3,5
* DIS # I2: 1,2 + G3: 3,5,8 + G4: 1,2,4 + H8: 1,6,8 + H1: 3,5 # G3: 8 => CTR => G3: 3,5
* DIS # I2: 1,2 + G3: 3,5,8 + G4: 1,2,4 + H8: 1,6,8 + H1: 3,5 + G3: 3,5 # C5: 5,9 => CTR => C5: 8
* PRF # I2: 1,2 + G3: 3,5,8 + G4: 1,2,4 + H8: 1,6,8 + H1: 3,5 + G3: 3,5 + C5: 8 => SOL
* STA I2: 1,2
* CNT   8 HDP CHAINS / 112 HYP OPENED

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

Details

Positions

98.7..6....7.5..4.........76.......8.3.4.......2..5.7.3...21....2...79....15...2. initial
98.7..6....7.5..4.........76.......8.3.4.......2..5.7.3...21....2...79....15...2. autosolve
985714632267953841413286597674139258538472169192865473359621784826347915741598326 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (2)
A2: 1,2
B2: 1,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H8,I8: 1.. / H8 = 1  =>  3 pairs (_) / I8 = 1  =>  2 pairs (_)
A2,A3: 2.. / A2 = 2  =>  1 pairs (_) / A3 = 2  =>  2 pairs (_)
F1,I1: 2.. / F1 = 2  =>  3 pairs (_) / I1 = 2  =>  3 pairs (_)
C1,C3: 3.. / C1 = 3  =>  5 pairs (_) / C3 = 3  =>  3 pairs (_)
B4,A5: 7.. / B4 = 7  =>  2 pairs (_) / A5 = 7  =>  3 pairs (_)
E4,E5: 7.. / E4 = 7  =>  3 pairs (_) / E5 = 7  =>  2 pairs (_)
G7,G9: 7.. / G7 = 7  =>  2 pairs (_) / G9 = 7  =>  3 pairs (_)
B4,E4: 7.. / B4 = 7  =>  2 pairs (_) / E4 = 7  =>  3 pairs (_)
A5,E5: 7.. / A5 = 7  =>  3 pairs (_) / E5 = 7  =>  2 pairs (_)
B7,G7: 7.. / B7 = 7  =>  3 pairs (_) / G7 = 7  =>  2 pairs (_)
A5,A9: 7.. / A5 = 7  =>  3 pairs (_) / A9 = 7  =>  2 pairs (_)
I2,H3: 9.. / I2 = 9  =>  2 pairs (_) / H3 = 9  =>  2 pairs (_)
* DURATION: 0:00:07.212824  START: 02:16:00.647569  END: 02:16:07.860393 2021-01-04
* CP COUNT: (12)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:01:11.460916  START: 02:16:14.458808  END: 02:17:25.919724 2021-01-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00973765-13_03-base-pr-002.dot
* REASONING
* DIS # G2: 1,2 # G3: 1,2 => CTR => G3: 3,5,8
* DIS # I2: 1,2 # G3: 1,2 => CTR => G3: 3,5,8
* DIS # I2: 1,2 + G3: 3,5,8 # G4: 3,5 => CTR => G4: 1,2,4
* DIS # I2: 1,2 + G3: 3,5,8 + G4: 1,2,4 # H8: 3,5 => CTR => H8: 1,6,8
* DIS # I2: 1,2 + G3: 3,5,8 + G4: 1,2,4 + H8: 1,6,8 # H1: 1 => CTR => H1: 3,5
* DIS # I2: 1,2 + G3: 3,5,8 + G4: 1,2,4 + H8: 1,6,8 + H1: 3,5 # G3: 8 => CTR => G3: 3,5
* DIS # I2: 1,2 + G3: 3,5,8 + G4: 1,2,4 + H8: 1,6,8 + H1: 3,5 + G3: 3,5 # C5: 5,9 => CTR => C5: 8
* PRF # I2: 1,2 + G3: 3,5,8 + G4: 1,2,4 + H8: 1,6,8 + H1: 3,5 + G3: 3,5 + C5: 8 => SOL
* STA I2: 1,2
* CNT   8 HDP CHAINS / 112 HYP OPENED

Header Info

973765;13_03;GP;24;11.30;11.30;10.10

Solution

position: 985714632267953841413286597674139258538472169192865473359621784826347915741598326 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 # A3: 1,2 => UNS
* INC # A3: 4,5 => UNS
* INC # D2: 1,2 => UNS
* INC # G2: 1,2 => UNS
* INC # I2: 1,2 => UNS
* INC # B3: 1,6 => UNS
* INC # B3: 4,5 => UNS
* INC # D2: 1,6 => UNS
* INC # D2: 2,3,8,9 => UNS
* CNT   9 HDP CHAINS /   9 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A3: 1,2 => UNS
* INC # A3: 4,5 => UNS
* INC # D2: 1,2 => UNS
* INC # G2: 1,2 => UNS
* INC # I2: 1,2 => UNS
* INC # B3: 1,6 => UNS
* INC # B3: 4,5 => UNS
* INC # D2: 1,6 => UNS
* INC # D2: 2,3,8,9 => UNS
* CNT   9 HDP CHAINS /   9 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A3: 1,2 => UNS
* INC # A3: 4,5 => UNS
* INC # D2: 1,2 => UNS
* INC # G2: 1,2 => UNS
* INC # I2: 1,2 => UNS
* INC # B3: 1,6 => UNS
* INC # B3: 4,5 => UNS
* INC # D2: 1,6 => UNS
* INC # D2: 2,3,8,9 => UNS
* INC # A3: 1,2 # D2: 1,2 => UNS
* INC # A3: 1,2 # G2: 1,2 => UNS
* INC # A3: 1,2 # I2: 1,2 => UNS
* INC # A3: 1,2 # D3: 1,2 => UNS
* INC # A3: 1,2 # G3: 1,2 => UNS
* INC # A3: 1,2 # C1: 4,5 => UNS
* INC # A3: 1,2 # C3: 4,5 => UNS
* INC # A3: 1,2 # B4: 4,5 => UNS
* INC # A3: 1,2 # B7: 4,5 => UNS
* INC # A3: 1,2 # A8: 4,8 => UNS
* INC # A3: 1,2 # A9: 4,8 => UNS
* INC # A3: 1,2 => UNS
* INC # A3: 4,5 # B3: 1,6 => UNS
* INC # A3: 4,5 # B3: 4,5 => UNS
* INC # A3: 4,5 # D2: 1,6 => UNS
* INC # A3: 4,5 # D2: 3,8,9 => UNS
* INC # A3: 4,5 # C1: 4,5 => UNS
* INC # A3: 4,5 # B3: 4,5 => UNS
* INC # A3: 4,5 # C3: 4,5 => UNS
* INC # A3: 4,5 # A8: 4,5 => UNS
* INC # A3: 4,5 # A8: 8 => UNS
* INC # A3: 4,5 # B4: 4,9 => UNS
* INC # A3: 4,5 # C4: 4,9 => UNS
* INC # A3: 4,5 # I6: 4,9 => UNS
* INC # A3: 4,5 # I6: 1,3,6 => UNS
* INC # A3: 4,5 # B7: 4,9 => UNS
* INC # A3: 4,5 # B9: 4,9 => UNS
* INC # A3: 4,5 => UNS
* INC # D2: 1,2 # A3: 1,2 => UNS
* INC # D2: 1,2 # A3: 4,5 => UNS
* INC # D2: 1,2 # D3: 1,2 => UNS
* INC # D2: 1,2 # D3: 3,6,8,9 => UNS
* INC # D2: 1,2 # D4: 1,2 => UNS
* INC # D2: 1,2 # D4: 3,9 => UNS
* INC # D2: 1,2 # G3: 3,8 => UNS
* INC # D2: 1,2 # H3: 3,8 => UNS
* INC # D2: 1,2 # F2: 3,8 => UNS
* INC # D2: 1,2 # F2: 9 => UNS
* INC # D2: 1,2 # G9: 3,8 => UNS
* INC # D2: 1,2 # G9: 4,7 => UNS
* INC # D2: 1,2 # H3: 3,9 => UNS
* INC # D2: 1,2 # H3: 1,5,8 => UNS
* INC # D2: 1,2 # F2: 3,9 => UNS
* INC # D2: 1,2 # F2: 8 => UNS
* INC # D2: 1,2 # I6: 3,9 => UNS
* INC # D2: 1,2 # I6: 1,4,6 => UNS
* INC # D2: 1,2 => UNS
* INC # G2: 1,2 # A3: 1,2 => UNS
* INC # G2: 1,2 # A3: 4,5 => UNS
* INC # G2: 1,2 # I1: 1,2 => UNS
* DIS # G2: 1,2 # G3: 1,2 => CTR => G3: 3,5,8
* INC # G2: 1,2 + G3: 3,5,8 # I1: 1,2 => UNS
* INC # G2: 1,2 + G3: 3,5,8 # I1: 3,5 => UNS
* INC # G2: 1,2 + G3: 3,5,8 # G4: 1,2 => UNS
* INC # G2: 1,2 + G3: 3,5,8 # G5: 1,2 => UNS
* INC # G2: 1,2 + G3: 3,5,8 # H3: 3,9 => UNS
* INC # G2: 1,2 + G3: 3,5,8 # H3: 1,5,8 => UNS
* INC # G2: 1,2 + G3: 3,5,8 # D2: 3,9 => UNS
* INC # G2: 1,2 + G3: 3,5,8 # F2: 3,9 => UNS
* INC # G2: 1,2 + G3: 3,5,8 # I6: 3,9 => UNS
* INC # G2: 1,2 + G3: 3,5,8 # I6: 1,4,6 => UNS
* INC # G2: 1,2 + G3: 3,5,8 # A3: 1,2 => UNS
* INC # G2: 1,2 + G3: 3,5,8 # A3: 4,5 => UNS
* INC # G2: 1,2 + G3: 3,5,8 # I1: 1,2 => UNS
* INC # G2: 1,2 + G3: 3,5,8 # I1: 3,5 => UNS
* INC # G2: 1,2 + G3: 3,5,8 # G4: 1,2 => UNS
* INC # G2: 1,2 + G3: 3,5,8 # G5: 1,2 => UNS
* INC # G2: 1,2 + G3: 3,5,8 # H3: 3,9 => UNS
* INC # G2: 1,2 + G3: 3,5,8 # H3: 1,5,8 => UNS
* INC # G2: 1,2 + G3: 3,5,8 # D2: 3,9 => UNS
* INC # G2: 1,2 + G3: 3,5,8 # F2: 3,9 => UNS
* INC # G2: 1,2 + G3: 3,5,8 # I6: 3,9 => UNS
* INC # G2: 1,2 + G3: 3,5,8 # I6: 1,4,6 => UNS
* INC # G2: 1,2 + G3: 3,5,8 => UNS
* INC # I2: 1,2 # A3: 1,2 => UNS
* INC # I2: 1,2 # A3: 4,5 => UNS
* INC # I2: 1,2 # G3: 3,8 => UNS
* INC # I2: 1,2 # G3: 1,2,5 => UNS
* INC # I2: 1,2 # D2: 3,8 => UNS
* INC # I2: 1,2 # F2: 3,8 => UNS
* INC # I2: 1,2 # I1: 1,2 => UNS
* DIS # I2: 1,2 # G3: 1,2 => CTR => G3: 3,5,8
* INC # I2: 1,2 + G3: 3,5,8 # I1: 1,2 => UNS
* INC # I2: 1,2 + G3: 3,5,8 # I1: 3,5 => UNS
* INC # I2: 1,2 + G3: 3,5,8 # A3: 1,2 => UNS
* INC # I2: 1,2 + G3: 3,5,8 # A3: 4,5 => UNS
* INC # I2: 1,2 + G3: 3,5,8 # G3: 3,8 => UNS
* INC # I2: 1,2 + G3: 3,5,8 # G3: 5 => UNS
* INC # I2: 1,2 + G3: 3,5,8 # D2: 3,8 => UNS
* INC # I2: 1,2 + G3: 3,5,8 # F2: 3,8 => UNS
* INC # I2: 1,2 + G3: 3,5,8 # I1: 1,2 => UNS
* INC # I2: 1,2 + G3: 3,5,8 # I1: 3,5 => UNS
* DIS # I2: 1,2 + G3: 3,5,8 # G4: 3,5 => CTR => G4: 1,2,4
* INC # I2: 1,2 + G3: 3,5,8 + G4: 1,2,4 # H1: 3,5 => UNS
* DIS # I2: 1,2 + G3: 3,5,8 + G4: 1,2,4 # H8: 3,5 => CTR => H8: 1,6,8
* INC # I2: 1,2 + G3: 3,5,8 + G4: 1,2,4 + H8: 1,6,8 # H1: 3,5 => UNS
* DIS # I2: 1,2 + G3: 3,5,8 + G4: 1,2,4 + H8: 1,6,8 # H1: 1 => CTR => H1: 3,5
* INC # I2: 1,2 + G3: 3,5,8 + G4: 1,2,4 + H8: 1,6,8 + H1: 3,5 # A3: 1,2 => UNS
* INC # I2: 1,2 + G3: 3,5,8 + G4: 1,2,4 + H8: 1,6,8 + H1: 3,5 # A3: 4,5 => UNS
* INC # I2: 1,2 + G3: 3,5,8 + G4: 1,2,4 + H8: 1,6,8 + H1: 3,5 # G3: 3,5 => UNS
* DIS # I2: 1,2 + G3: 3,5,8 + G4: 1,2,4 + H8: 1,6,8 + H1: 3,5 # G3: 8 => CTR => G3: 3,5
* DIS # I2: 1,2 + G3: 3,5,8 + G4: 1,2,4 + H8: 1,6,8 + H1: 3,5 + G3: 3,5 # C5: 5,9 => CTR => C5: 8
* PRF # I2: 1,2 + G3: 3,5,8 + G4: 1,2,4 + H8: 1,6,8 + H1: 3,5 + G3: 3,5 + C5: 8 => SOL
* STA I2: 1,2
* CNT 112 HDP CHAINS / 112 HYP OPENED