Analysis of xx-ph-02318902-2019_03_16-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.7..6....5.6........4..7.83.6....7.....2.6.......8..67.3...8...1............9.3 initial

Autosolve

position: 98.7..6..7.5.6........4..7.83.6....7..7..2.6......78..67.3...8.3.1...7.6..8.769.3 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: 0:01:34.087312

The following important HDP chains were detected:

* DIS # G3: 1,2 # B2: 4 => CTR => B2: 1,2
* DIS # I3: 1,2 # H1: 2,4 => CTR => H1: 1,3
* DIS # I3: 1,2 + H1: 1,3 # I1: 1 => CTR => I1: 2,4
* PRF # I3: 1,2 + H1: 1,3 + I1: 2,4 # G2: 3 => SOL
* STA # I3: 1,2 + H1: 1,3 + I1: 2,4 + G2: 3
* CNT   4 HDP CHAINS / 131 HYP OPENED

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

Details

Positions

98.7..6....5.6........4..7.83.6....7.....2.6.......8..67.3...8...1............9.3 initial
98.7..6..7.5.6........4..7.83.6....7..7..2.6......78..67.3...8.3.1...7.6..8.769.3 autosolve
982753614745261398163948572839614257517832469426597831674329185391485726258176943 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
A3: 1,2

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D9,H9: 1.. / D9 = 1  =>  1 pairs (_) / H9 = 1  =>  1 pairs (_)
C1,C3: 3.. / C1 = 3  =>  5 pairs (_) / C3 = 3  =>  2 pairs (_)
E5,E6: 3.. / E5 = 3  =>  1 pairs (_) / E6 = 3  =>  1 pairs (_)
G5,H6: 3.. / G5 = 3  =>  1 pairs (_) / H6 = 3  =>  1 pairs (_)
E5,G5: 3.. / E5 = 3  =>  1 pairs (_) / G5 = 3  =>  1 pairs (_)
E6,H6: 3.. / E6 = 3  =>  1 pairs (_) / H6 = 3  =>  1 pairs (_)
C1,B2: 4.. / C1 = 4  =>  4 pairs (_) / B2 = 4  =>  3 pairs (_)
B3,C3: 6.. / B3 = 6  =>  2 pairs (_) / C3 = 6  =>  5 pairs (_)
B6,C6: 6.. / B6 = 6  =>  5 pairs (_) / C6 = 6  =>  2 pairs (_)
B3,B6: 6.. / B3 = 6  =>  2 pairs (_) / B6 = 6  =>  5 pairs (_)
C3,C6: 6.. / C3 = 6  =>  5 pairs (_) / C6 = 6  =>  2 pairs (_)
I2,I3: 8.. / I2 = 8  =>  1 pairs (_) / I3 = 8  =>  1 pairs (_)
D5,E5: 8.. / D5 = 8  =>  1 pairs (_) / E5 = 8  =>  1 pairs (_)
E5,E8: 8.. / E5 = 8  =>  1 pairs (_) / E8 = 8  =>  1 pairs (_)
C7,B8: 9.. / C7 = 9  =>  2 pairs (_) / B8 = 9  =>  2 pairs (_)
* DURATION: 0:00:11.715180  START: 18:37:19.677634  END: 18:37:31.392814 2021-01-13
* CP COUNT: (15)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:01:33.548842  START: 18:37:38.432340  END: 18:39:11.981182 2021-01-13
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-02318902-2019_03_16-base-pr-002.dot
* REASONING
* DIS # G3: 1,2 # B2: 4 => CTR => B2: 1,2
* DIS # I3: 1,2 # H1: 2,4 => CTR => H1: 1,3
* DIS # I3: 1,2 + H1: 1,3 # I1: 1 => CTR => I1: 2,4
* PRF # I3: 1,2 + H1: 1,3 + I1: 2,4 # G2: 3 => SOL
* STA # I3: 1,2 + H1: 1,3 + I1: 2,4 + G2: 3
* CNT   4 HDP CHAINS / 131 HYP OPENED

Header Info

2318902;2019_03_16;PAQ;22;11.30;1.20;1.20

Solution

position: 982753614745261398163948572839614257517832469426597831674329185391485726258176943 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 # B2: 1,2 => UNS
* INC # B3: 1,2 => UNS
* INC # D3: 1,2 => UNS
* INC # G3: 1,2 => UNS
* INC # I3: 1,2 => UNS
* INC # A6: 1,2 => UNS
* INC # A6: 4,5 => UNS
* CNT   7 HDP CHAINS /   7 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 1,2 => UNS
* INC # B3: 1,2 => UNS
* INC # D3: 1,2 => UNS
* INC # G3: 1,2 => UNS
* INC # I3: 1,2 => UNS
* INC # A6: 1,2 => UNS
* INC # A6: 4,5 => UNS
* CNT   7 HDP CHAINS /   7 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 1,2 => UNS
* INC # B3: 1,2 => UNS
* INC # D3: 1,2 => UNS
* INC # G3: 1,2 => UNS
* INC # I3: 1,2 => UNS
* INC # A6: 1,2 => UNS
* INC # A6: 4,5 => UNS
* INC # B2: 1,2 # D2: 1,2 => UNS
* INC # B2: 1,2 # G2: 1,2 => UNS
* INC # B2: 1,2 # H2: 1,2 => UNS
* INC # B2: 1,2 # I2: 1,2 => UNS
* INC # B2: 1,2 # B6: 1,2 => UNS
* INC # B2: 1,2 # B6: 4,5,9 => UNS
* INC # B2: 1,2 # D3: 1,2 => UNS
* INC # B2: 1,2 # G3: 1,2 => UNS
* INC # B2: 1,2 # I3: 1,2 => UNS
* INC # B2: 1,2 # A6: 1,2 => UNS
* INC # B2: 1,2 # A6: 4,5 => UNS
* INC # B2: 1,2 # B6: 2,9 => UNS
* INC # B2: 1,2 # B6: 1,4,5 => UNS
* INC # B2: 1,2 # H4: 2,9 => UNS
* INC # B2: 1,2 # H4: 1,4,5 => UNS
* INC # B2: 1,2 # B8: 2,9 => UNS
* INC # B2: 1,2 # B8: 4,5 => UNS
* INC # B2: 1,2 # E7: 2,9 => UNS
* INC # B2: 1,2 # E7: 1,5 => UNS
* INC # B2: 1,2 => UNS
* INC # B3: 1,2 # A6: 1,2 => UNS
* INC # B3: 1,2 # A6: 4,5 => UNS
* INC # B3: 1,2 # E1: 1,5 => UNS
* INC # B3: 1,2 # E1: 2 => UNS
* INC # B3: 1,2 # H1: 1,5 => UNS
* INC # B3: 1,2 # I1: 1,5 => UNS
* INC # B3: 1,2 # F4: 1,5 => UNS
* INC # B3: 1,2 # F7: 1,5 => UNS
* INC # B3: 1,2 # F3: 3,5 => UNS
* INC # B3: 1,2 # F3: 8,9 => UNS
* INC # B3: 1,2 # G5: 3,5 => UNS
* INC # B3: 1,2 # G5: 1,4 => UNS
* INC # B3: 1,2 # B8: 2,5 => UNS
* INC # B3: 1,2 # A9: 2,5 => UNS
* INC # B3: 1,2 # D9: 2,5 => UNS
* INC # B3: 1,2 # H9: 2,5 => UNS
* INC # B3: 1,2 => UNS
* INC # D3: 1,2 # B2: 2,4 => UNS
* INC # D3: 1,2 # B2: 1 => UNS
* INC # D3: 1,2 # H1: 2,4 => UNS
* INC # D3: 1,2 # I1: 2,4 => UNS
* INC # D3: 1,2 # C4: 2,4 => UNS
* INC # D3: 1,2 # C7: 2,4 => UNS
* INC # D3: 1,2 # B2: 1,2 => UNS
* INC # D3: 1,2 # B2: 4 => UNS
* INC # D3: 1,2 # A6: 1,2 => UNS
* INC # D3: 1,2 # A6: 4,5 => UNS
* INC # D3: 1,2 # E1: 1,2 => UNS
* INC # D3: 1,2 # D2: 1,2 => UNS
* INC # D3: 1,2 # D9: 1,2 => UNS
* INC # D3: 1,2 # D9: 4,5 => UNS
* INC # D3: 1,2 # D2: 8,9 => UNS
* INC # D3: 1,2 # F2: 8,9 => UNS
* INC # D3: 1,2 # F8: 8,9 => UNS
* INC # D3: 1,2 # F8: 4,5 => UNS
* INC # D3: 1,2 # I2: 8,9 => UNS
* INC # D3: 1,2 # I2: 1,2,4 => UNS
* INC # D3: 1,2 => UNS
* INC # G3: 1,2 # B2: 2,4 => UNS
* INC # G3: 1,2 # B2: 1 => UNS
* INC # G3: 1,2 # H1: 2,4 => UNS
* INC # G3: 1,2 # I1: 2,4 => UNS
* INC # G3: 1,2 # C4: 2,4 => UNS
* INC # G3: 1,2 # C7: 2,4 => UNS
* INC # G3: 1,2 # B2: 1,2 => UNS
* DIS # G3: 1,2 # B2: 4 => CTR => B2: 1,2
* INC # G3: 1,2 + B2: 1,2 # A6: 1,2 => UNS
* INC # G3: 1,2 + B2: 1,2 # A6: 4,5 => UNS
* INC # G3: 1,2 + B2: 1,2 # H1: 1,2 => UNS
* INC # G3: 1,2 + B2: 1,2 # I1: 1,2 => UNS
* INC # G3: 1,2 + B2: 1,2 # G2: 1,2 => UNS
* INC # G3: 1,2 + B2: 1,2 # H2: 1,2 => UNS
* INC # G3: 1,2 + B2: 1,2 # I2: 1,2 => UNS
* INC # G3: 1,2 + B2: 1,2 # G4: 1,2 => UNS
* INC # G3: 1,2 + B2: 1,2 # G7: 1,2 => UNS
* INC # G3: 1,2 + B2: 1,2 # D2: 1,2 => UNS
* INC # G3: 1,2 + B2: 1,2 # G2: 1,2 => UNS
* INC # G3: 1,2 + B2: 1,2 # H2: 1,2 => UNS
* INC # G3: 1,2 + B2: 1,2 # I2: 1,2 => UNS
* INC # G3: 1,2 + B2: 1,2 # B6: 1,2 => UNS
* INC # G3: 1,2 + B2: 1,2 # B6: 4,5,9 => UNS
* INC # G3: 1,2 + B2: 1,2 # A6: 1,2 => UNS
* INC # G3: 1,2 + B2: 1,2 # A6: 4,5 => UNS
* INC # G3: 1,2 + B2: 1,2 # H1: 1,2 => UNS
* INC # G3: 1,2 + B2: 1,2 # I1: 1,2 => UNS
* INC # G3: 1,2 + B2: 1,2 # G2: 1,2 => UNS
* INC # G3: 1,2 + B2: 1,2 # H2: 1,2 => UNS
* INC # G3: 1,2 + B2: 1,2 # I2: 1,2 => UNS
* INC # G3: 1,2 + B2: 1,2 # G4: 1,2 => UNS
* INC # G3: 1,2 + B2: 1,2 # G7: 1,2 => UNS
* INC # G3: 1,2 + B2: 1,2 # B6: 2,9 => UNS
* INC # G3: 1,2 + B2: 1,2 # B6: 1,4,5 => UNS
* INC # G3: 1,2 + B2: 1,2 # H4: 2,9 => UNS
* INC # G3: 1,2 + B2: 1,2 # H4: 1,4,5 => UNS
* INC # G3: 1,2 + B2: 1,2 # B8: 2,9 => UNS
* INC # G3: 1,2 + B2: 1,2 # B8: 4,5 => UNS
* INC # G3: 1,2 + B2: 1,2 # E7: 2,9 => UNS
* INC # G3: 1,2 + B2: 1,2 # E7: 1,5 => UNS
* INC # G3: 1,2 + B2: 1,2 => UNS
* INC # I3: 1,2 # B2: 2,4 => UNS
* INC # I3: 1,2 # B2: 1 => UNS
* DIS # I3: 1,2 # H1: 2,4 => CTR => H1: 1,3
* INC # I3: 1,2 + H1: 1,3 # I1: 2,4 => UNS
* INC # I3: 1,2 + H1: 1,3 # I1: 2,4 => UNS
* DIS # I3: 1,2 + H1: 1,3 # I1: 1 => CTR => I1: 2,4
* INC # I3: 1,2 + H1: 1,3 + I1: 2,4 # C4: 2,4 => UNS
* INC # I3: 1,2 + H1: 1,3 + I1: 2,4 # C7: 2,4 => UNS
* INC # I3: 1,2 + H1: 1,3 + I1: 2,4 # C4: 2,4 => UNS
* INC # I3: 1,2 + H1: 1,3 + I1: 2,4 # C7: 2,4 => UNS
* INC # I3: 1,2 + H1: 1,3 + I1: 2,4 # A6: 1,2 => UNS
* INC # I3: 1,2 + H1: 1,3 + I1: 2,4 # A6: 4,5 => UNS
* INC # I3: 1,2 + H1: 1,3 + I1: 2,4 # F1: 1,3 => UNS
* INC # I3: 1,2 + H1: 1,3 + I1: 2,4 # F1: 5 => UNS
* INC # I3: 1,2 + H1: 1,3 + I1: 2,4 # G2: 1,3 => UNS
* INC # I3: 1,2 + H1: 1,3 + I1: 2,4 # G2: 4 => UNS
* INC # I3: 1,2 + H1: 1,3 + I1: 2,4 # D5: 8,9 => UNS
* INC # I3: 1,2 + H1: 1,3 + I1: 2,4 # D8: 8,9 => UNS
* INC # I3: 1,2 + H1: 1,3 + I1: 2,4 # F8: 8,9 => UNS
* INC # I3: 1,2 + H1: 1,3 + I1: 2,4 # F8: 4,5 => UNS
* INC # I3: 1,2 + H1: 1,3 + I1: 2,4 # C4: 2,4 => UNS
* INC # I3: 1,2 + H1: 1,3 + I1: 2,4 # C7: 2,4 => UNS
* INC # I3: 1,2 + H1: 1,3 + I1: 2,4 # G2: 1,4 => UNS
* PRF # I3: 1,2 + H1: 1,3 + I1: 2,4 # G2: 3 => SOL
* STA # I3: 1,2 + H1: 1,3 + I1: 2,4 + G2: 3
* CNT 130 HDP CHAINS / 131 HYP OPENED