Analysis of xx-ph-02236731-2018_12_25-base.sdk

Contents

Original Sudoku

level: very deep

Original Sudoku

position: 9876..5..6...8..9...47.....57.3....646..5.3....3....5...65..4.......2.61......... initial

Autosolve

position: 9876..5..6...8..9...47..6..57.3....646..5.3....3....5...65..4.......2.61........5 autosolve
Autosolve

Pair Reduction Variants

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Deep Constraint Pair Analysis

Time used: 0:00:00.000006

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

Very Deep Constraint Pair Analysis

Very Deep Constraint Pair Analysis

Time used: 0:00:45.127230

List of important HDP chains detected for H1,H4: 4..:

* DIS # H1: 4 # E1: 2 # F9: 8,9 => CTR => F9: 3,4,6,7
* PRF # H1: 4 # E1: 2 + F9: 3,4,6,7 # C8: 8,9 => SOL
* STA # H1: 4 # E1: 2 + F9: 3,4,6,7 + C8: 8,9
* CNT   2 HDP CHAINS /  49 HYP OPENED

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

Details

This sudoku is very deep. Here is some information that may be helpful on how to proceed.

Positions

9876..5..6...8..9...47.....57.3....646..5.3....3....5...65..4.......2.61......... initial
9876..5..6...8..9...47..6..57.3....646..5.3....3....5...65..4.......2.61........5 autosolve

Classification

level: very deep

Pairing Analysis

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H4,I6: 4.. / H4 = 4  =>  0 pairs (_) / I6 = 4  =>  3 pairs (_)
B8,B9: 4.. / B8 = 4  =>  2 pairs (_) / B9 = 4  =>  0 pairs (_)
H1,H4: 4.. / H1 = 4  =>  3 pairs (_) / H4 = 4  =>  0 pairs (_)
F2,F3: 5.. / F2 = 5  =>  1 pairs (_) / F3 = 5  =>  0 pairs (_)
B8,C8: 5.. / B8 = 5  =>  1 pairs (_) / C8 = 5  =>  1 pairs (_)
B3,F3: 5.. / B3 = 5  =>  1 pairs (_) / F3 = 5  =>  0 pairs (_)
C2,C8: 5.. / C2 = 5  =>  1 pairs (_) / C8 = 5  =>  1 pairs (_)
E6,F6: 6.. / E6 = 6  =>  0 pairs (_) / F6 = 6  =>  0 pairs (_)
E9,F9: 6.. / E9 = 6  =>  0 pairs (_) / F9 = 6  =>  0 pairs (_)
E6,E9: 6.. / E6 = 6  =>  0 pairs (_) / E9 = 6  =>  0 pairs (_)
F6,F9: 6.. / F6 = 6  =>  0 pairs (_) / F9 = 6  =>  0 pairs (_)
G2,I2: 7.. / G2 = 7  =>  1 pairs (_) / I2 = 7  =>  2 pairs (_)
H3,I3: 8.. / H3 = 8  =>  1 pairs (_) / I3 = 8  =>  0 pairs (_)
E3,F3: 9.. / E3 = 9  =>  0 pairs (_) / F3 = 9  =>  1 pairs (_)
* DURATION: 0:00:09.131590  START: 08:17:49.911803  END: 08:17:59.043393 2020-09-24
* CP COUNT: (14)
* INCONCLUSIVE

--------------------------------------------------
* DEEP CONSTRAINT PAIRS (PAIR REDUCTION)
H1,H4: 4.. / H1 = 4 ==>  3 pairs (_) / H4 = 4 ==>  0 pairs (_)
H4,I6: 4.. / H4 = 4 ==>  0 pairs (_) / I6 = 4 ==>  3 pairs (_)
G2,I2: 7.. / G2 = 7 ==>  1 pairs (_) / I2 = 7 ==>  2 pairs (_)
B8,B9: 4.. / B8 = 4 ==>  2 pairs (_) / B9 = 4 ==>  0 pairs (_)
C2,C8: 5.. / C2 = 5 ==>  1 pairs (_) / C8 = 5 ==>  1 pairs (_)
B8,C8: 5.. / B8 = 5 ==>  1 pairs (_) / C8 = 5 ==>  1 pairs (_)
E3,F3: 9.. / E3 = 9 ==>  0 pairs (_) / F3 = 9 ==>  1 pairs (_)
H3,I3: 8.. / H3 = 8 ==>  1 pairs (_) / I3 = 8 ==>  0 pairs (_)
B3,F3: 5.. / B3 = 5 ==>  1 pairs (_) / F3 = 5 ==>  0 pairs (_)
F2,F3: 5.. / F2 = 5 ==>  1 pairs (_) / F3 = 5 ==>  0 pairs (_)
F6,F9: 6.. / F6 = 6 ==>  0 pairs (_) / F9 = 6 ==>  0 pairs (_)
E6,E9: 6.. / E6 = 6 ==>  0 pairs (_) / E9 = 6 ==>  0 pairs (_)
E9,F9: 6.. / E9 = 6 ==>  0 pairs (_) / F9 = 6 ==>  0 pairs (_)
E6,F6: 6.. / E6 = 6 ==>  0 pairs (_) / F6 = 6 ==>  0 pairs (_)
* DURATION: 0:01:10.862976  START: 08:17:59.043989  END: 08:19:09.906965 2020-09-24
* DCP COUNT: (14)
* INCONCLUSIVE

--------------------------------------------------
* VERY DEEP CONSTRAINT PAIRS (PAIR REDUCTION, RECURSIVE)
H1,H4: 4.. / H1 = 4 ==>  0 pairs (*) / H4 = 4  =>  0 pairs (X)
* DURATION: 0:00:45.123505  START: 08:19:10.073117  END: 08:19:55.196622 2020-09-24
* REASONING H1,H4: 4..
* DIS # H1: 4 # E1: 2 # F9: 8,9 => CTR => F9: 3,4,6,7
* PRF # H1: 4 # E1: 2 + F9: 3,4,6,7 # C8: 8,9 => SOL
* STA # H1: 4 # E1: 2 + F9: 3,4,6,7 + C8: 8,9
* CNT   2 HDP CHAINS /  49 HYP OPENED
* VDCP COUNT: (1)
* SOLUTION FOUND

Header Info

2236731;2018_12_25;PAQ;26;11.60;1.20;1.20

Appendix: Full HDP Chains

A1. Deep Constraint Pair Analysis

Full list of HDP chains traversed for H1,H4: 4..:

* INC # H1: 4 # E1: 1,3 => UNS
* INC # H1: 4 # E1: 2 => UNS
* INC # H1: 4 # F7: 1,3 => UNS
* INC # H1: 4 # F9: 1,3 => UNS
* INC # H1: 4 # I2: 2,3 => UNS
* INC # H1: 4 # H3: 2,3 => UNS
* INC # H1: 4 # I3: 2,3 => UNS
* INC # H1: 4 # E1: 2,3 => UNS
* INC # H1: 4 # E1: 1 => UNS
* INC # H1: 4 # I7: 2,3 => UNS
* INC # H1: 4 # I7: 7,8,9 => UNS
* INC # H1: 4 => UNS
* INC # H4: 4 => UNS
* CNT  13 HDP CHAINS /  13 HYP OPENED

Full list of HDP chains traversed for H4,I6: 4..:

* INC # I6: 4 # E1: 1,3 => UNS
* INC # I6: 4 # E1: 2 => UNS
* INC # I6: 4 # F7: 1,3 => UNS
* INC # I6: 4 # F9: 1,3 => UNS
* INC # I6: 4 # I2: 2,3 => UNS
* INC # I6: 4 # H3: 2,3 => UNS
* INC # I6: 4 # I3: 2,3 => UNS
* INC # I6: 4 # E1: 2,3 => UNS
* INC # I6: 4 # E1: 1 => UNS
* INC # I6: 4 # I7: 2,3 => UNS
* INC # I6: 4 # I7: 7,8,9 => UNS
* INC # I6: 4 => UNS
* INC # H4: 4 => UNS
* CNT  13 HDP CHAINS /  13 HYP OPENED

Full list of HDP chains traversed for G2,I2: 7..:

* INC # I2: 7 # E1: 1,3 => UNS
* INC # I2: 7 # F2: 1,3 => UNS
* INC # I2: 7 # E3: 1,3 => UNS
* INC # I2: 7 # F3: 1,3 => UNS
* INC # I2: 7 # H1: 1,3 => UNS
* INC # I2: 7 # H1: 2,4 => UNS
* INC # I2: 7 # F7: 1,3 => UNS
* INC # I2: 7 # F9: 1,3 => UNS
* INC # I2: 7 # H1: 1,2 => UNS
* INC # I2: 7 # H3: 1,2 => UNS
* INC # I2: 7 # B2: 1,2 => UNS
* INC # I2: 7 # C2: 1,2 => UNS
* INC # I2: 7 # D2: 1,2 => UNS
* INC # I2: 7 # G4: 1,2 => UNS
* INC # I2: 7 # G6: 1,2 => UNS
* INC # I2: 7 => UNS
* INC # G2: 7 # I7: 8,9 => UNS
* INC # G2: 7 # G9: 8,9 => UNS
* INC # G2: 7 # C8: 8,9 => UNS
* INC # G2: 7 # D8: 8,9 => UNS
* INC # G2: 7 # G4: 8,9 => UNS
* INC # G2: 7 # G6: 8,9 => UNS
* INC # G2: 7 => UNS
* CNT  23 HDP CHAINS /  23 HYP OPENED

Full list of HDP chains traversed for B8,B9: 4..:

* INC # B8: 4 # B2: 1,2 => UNS
* INC # B8: 4 # A3: 1,2 => UNS
* INC # B8: 4 # B3: 1,2 => UNS
* INC # B8: 4 # D2: 1,2 => UNS
* INC # B8: 4 # G2: 1,2 => UNS
* INC # B8: 4 # C4: 1,2 => UNS
* INC # B8: 4 # C5: 1,2 => UNS
* INC # B8: 4 # C9: 1,2 => UNS
* INC # B8: 4 # F7: 8,9 => UNS
* INC # B8: 4 # D9: 8,9 => UNS
* INC # B8: 4 # F9: 8,9 => UNS
* INC # B8: 4 # G8: 8,9 => UNS
* INC # B8: 4 # G8: 7 => UNS
* INC # B8: 4 # D5: 8,9 => UNS
* INC # B8: 4 # D6: 8,9 => UNS
* INC # B8: 4 => UNS
* INC # B9: 4 => UNS
* CNT  17 HDP CHAINS /  17 HYP OPENED

Full list of HDP chains traversed for C2,C8: 5..:

* INC # C2: 5 # C9: 8,9 => UNS
* INC # C2: 5 # C9: 1,2 => UNS
* INC # C2: 5 # D8: 8,9 => UNS
* INC # C2: 5 # G8: 8,9 => UNS
* INC # C2: 5 # C4: 8,9 => UNS
* INC # C2: 5 # C5: 8,9 => UNS
* INC # C2: 5 => UNS
* INC # C8: 5 # B2: 1,2 => UNS
* INC # C8: 5 # A3: 1,2 => UNS
* INC # C8: 5 # B3: 1,2 => UNS
* INC # C8: 5 # D2: 1,2 => UNS
* INC # C8: 5 # G2: 1,2 => UNS
* INC # C8: 5 # C4: 1,2 => UNS
* INC # C8: 5 # C5: 1,2 => UNS
* INC # C8: 5 # C9: 1,2 => UNS
* INC # C8: 5 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

Full list of HDP chains traversed for B8,C8: 5..:

* INC # B8: 5 # C9: 8,9 => UNS
* INC # B8: 5 # C9: 1,2 => UNS
* INC # B8: 5 # D8: 8,9 => UNS
* INC # B8: 5 # G8: 8,9 => UNS
* INC # B8: 5 # C4: 8,9 => UNS
* INC # B8: 5 # C5: 8,9 => UNS
* INC # B8: 5 => UNS
* INC # C8: 5 # B2: 1,2 => UNS
* INC # C8: 5 # A3: 1,2 => UNS
* INC # C8: 5 # B3: 1,2 => UNS
* INC # C8: 5 # D2: 1,2 => UNS
* INC # C8: 5 # G2: 1,2 => UNS
* INC # C8: 5 # C4: 1,2 => UNS
* INC # C8: 5 # C5: 1,2 => UNS
* INC # C8: 5 # C9: 1,2 => UNS
* INC # C8: 5 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

Full list of HDP chains traversed for E3,F3: 9..:

* INC # F3: 9 # B2: 1,2 => UNS
* INC # F3: 9 # A3: 1,2 => UNS
* INC # F3: 9 # D2: 1,2 => UNS
* INC # F3: 9 # G2: 1,2 => UNS
* INC # F3: 9 # C4: 1,2 => UNS
* INC # F3: 9 # C5: 1,2 => UNS
* INC # F3: 9 # C9: 1,2 => UNS
* INC # F3: 9 => UNS
* INC # E3: 9 => UNS
* CNT   9 HDP CHAINS /   9 HYP OPENED

Full list of HDP chains traversed for H3,I3: 8..:

* INC # H3: 8 # H1: 2,3 => UNS
* INC # H3: 8 # I1: 2,3 => UNS
* INC # H3: 8 # I2: 2,3 => UNS
* INC # H3: 8 # A3: 2,3 => UNS
* INC # H3: 8 # B3: 2,3 => UNS
* INC # H3: 8 # E3: 2,3 => UNS
* INC # H3: 8 # I7: 2,3 => UNS
* INC # H3: 8 # I7: 7,8,9 => UNS
* INC # H3: 8 => UNS
* INC # I3: 8 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

Full list of HDP chains traversed for B3,F3: 5..:

* INC # B3: 5 # B2: 1,2 => UNS
* INC # B3: 5 # A3: 1,2 => UNS
* INC # B3: 5 # D2: 1,2 => UNS
* INC # B3: 5 # G2: 1,2 => UNS
* INC # B3: 5 # C4: 1,2 => UNS
* INC # B3: 5 # C5: 1,2 => UNS
* INC # B3: 5 # C9: 1,2 => UNS
* INC # B3: 5 => UNS
* INC # F3: 5 => UNS
* CNT   9 HDP CHAINS /   9 HYP OPENED

Full list of HDP chains traversed for F2,F3: 5..:

* INC # F2: 5 # B2: 1,2 => UNS
* INC # F2: 5 # A3: 1,2 => UNS
* INC # F2: 5 # D2: 1,2 => UNS
* INC # F2: 5 # G2: 1,2 => UNS
* INC # F2: 5 # C4: 1,2 => UNS
* INC # F2: 5 # C5: 1,2 => UNS
* INC # F2: 5 # C9: 1,2 => UNS
* INC # F2: 5 => UNS
* INC # F3: 5 => UNS
* CNT   9 HDP CHAINS /   9 HYP OPENED

Full list of HDP chains traversed for F6,F9: 6..:

* INC # F6: 6 => UNS
* INC # F9: 6 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED

Full list of HDP chains traversed for E6,E9: 6..:

* INC # E6: 6 => UNS
* INC # E9: 6 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED

Full list of HDP chains traversed for E9,F9: 6..:

* INC # E9: 6 => UNS
* INC # F9: 6 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED

Full list of HDP chains traversed for E6,F6: 6..:

* INC # E6: 6 => UNS
* INC # F6: 6 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED

A2. Very Deep Constraint Pair Analysis

Full list of HDP chains traversed for H1,H4: 4..:

* INC # H1: 4 # E1: 1,3 => UNS
* INC # H1: 4 # E1: 2 => UNS
* INC # H1: 4 # F7: 1,3 => UNS
* INC # H1: 4 # F9: 1,3 => UNS
* INC # H1: 4 # I2: 2,3 => UNS
* INC # H1: 4 # H3: 2,3 => UNS
* INC # H1: 4 # I3: 2,3 => UNS
* INC # H1: 4 # E1: 2,3 => UNS
* INC # H1: 4 # E1: 1 => UNS
* INC # H1: 4 # I7: 2,3 => UNS
* INC # H1: 4 # I7: 7,8,9 => UNS
* INC # H1: 4 # E1: 1,3 # E7: 1,3 => UNS
* INC # H1: 4 # E1: 1,3 # E9: 1,3 => UNS
* INC # H1: 4 # E1: 1,3 # F7: 1,3 => UNS
* INC # H1: 4 # E1: 1,3 # F9: 1,3 => UNS
* INC # H1: 4 # E1: 1,3 # E4: 2,9 => UNS
* INC # H1: 4 # E1: 1,3 # E6: 2,9 => UNS
* INC # H1: 4 # E1: 1,3 # G6: 1,7 => UNS
* INC # H1: 4 # E1: 1,3 # G6: 2,8,9 => UNS
* INC # H1: 4 # E1: 1,3 # I7: 3,7 => UNS
* INC # H1: 4 # E1: 1,3 # I7: 8,9 => UNS
* INC # H1: 4 # E1: 1,3 # H3: 3,8 => UNS
* INC # H1: 4 # E1: 1,3 # H3: 1 => UNS
* INC # H1: 4 # E1: 1,3 # I7: 3,8 => UNS
* INC # H1: 4 # E1: 1,3 # I7: 7,9 => UNS
* INC # H1: 4 # E1: 1,3 => UNS
* INC # H1: 4 # E1: 2 # F3: 3,5 => UNS
* INC # H1: 4 # E1: 2 # F3: 9 => UNS
* INC # H1: 4 # E1: 2 # B2: 3,5 => UNS
* INC # H1: 4 # E1: 2 # B2: 1,2 => UNS
* INC # H1: 4 # E1: 2 # F3: 3,9 => UNS
* INC # H1: 4 # E1: 2 # F3: 5 => UNS
* INC # H1: 4 # E1: 2 # E7: 3,9 => UNS
* INC # H1: 4 # E1: 2 # E8: 3,9 => UNS
* INC # H1: 4 # E1: 2 # E9: 3,9 => UNS
* INC # H1: 4 # E1: 2 # G2: 2,7 => UNS
* INC # H1: 4 # E1: 2 # G2: 1 => UNS
* INC # H1: 4 # E1: 2 # I5: 2,7 => UNS
* INC # H1: 4 # E1: 2 # I7: 2,7 => UNS
* INC # H1: 4 # E1: 2 # H3: 2,8 => UNS
* INC # H1: 4 # E1: 2 # H3: 1 => UNS
* INC # H1: 4 # E1: 2 # I5: 2,8 => UNS
* INC # H1: 4 # E1: 2 # I7: 2,8 => UNS
* INC # H1: 4 # E1: 2 # F7: 8,9 => UNS
* INC # H1: 4 # E1: 2 # D9: 8,9 => UNS
* DIS # H1: 4 # E1: 2 # F9: 8,9 => CTR => F9: 3,4,6,7
* PRF # H1: 4 # E1: 2 + F9: 3,4,6,7 # C8: 8,9 => SOL
* STA # H1: 4 # E1: 2 + F9: 3,4,6,7 + C8: 8,9
* CNT  47 HDP CHAINS /  49 HYP OPENED