Analysis of xx-ph-02236726-2018_12_25-base.sdk

Contents

Original Sudoku

level: very deep

Original Sudoku

position: 9876..5..4..9..6......8..7.6..5..4.......3..2........51.........951....6.64.5.1.. initial

Autosolve

position: 9876..5..4..9..6....6.8..7.6..5..4.......3..2........51......5..951....6.64.5.1.. 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: 0:00:45.487294

List of important HDP chains detected for H1,H8: 4..:

* DIS # H1: 4 # E1: 3 # F6: 7,8 => CTR => F6: 1,4,6,9
* PRF # H1: 4 # E1: 3 + F6: 1,4,6,9 # A5: 7,8 => SOL
* STA # H1: 4 # E1: 3 + F6: 1,4,6,9 + A5: 7,8
* 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..4..9..6......8..7.6..5..4.......3..2........51.........951....6.64.5.1.. initial
9876..5..4..9..6....6.8..7.6..5..4.......3..2........51......5..951....6.64.5.1.. autosolve

Classification

level: very deep

Pairing Analysis

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B5,B6: 4.. / B5 = 4  =>  2 pairs (_) / B6 = 4  =>  0 pairs (_)
I7,H8: 4.. / I7 = 4  =>  3 pairs (_) / H8 = 4  =>  0 pairs (_)
H1,H8: 4.. / H1 = 4  =>  3 pairs (_) / H8 = 4  =>  0 pairs (_)
F2,F3: 5.. / F2 = 5  =>  0 pairs (_) / F3 = 5  =>  1 pairs (_)
A5,B5: 5.. / A5 = 5  =>  1 pairs (_) / B5 = 5  =>  1 pairs (_)
B2,F2: 5.. / B2 = 5  =>  1 pairs (_) / F2 = 5  =>  0 pairs (_)
A3,A5: 5.. / A3 = 5  =>  1 pairs (_) / A5 = 5  =>  1 pairs (_)
H5,H6: 6.. / H5 = 6  =>  0 pairs (_) / H6 = 6  =>  0 pairs (_)
E7,F7: 6.. / E7 = 6  =>  0 pairs (_) / F7 = 6  =>  0 pairs (_)
E5,H5: 6.. / E5 = 6  =>  0 pairs (_) / H5 = 6  =>  0 pairs (_)
F6,F7: 6.. / F6 = 6  =>  0 pairs (_) / F7 = 6  =>  0 pairs (_)
E2,F2: 7.. / E2 = 7  =>  0 pairs (_) / F2 = 7  =>  1 pairs (_)
H2,I2: 8.. / H2 = 8  =>  1 pairs (_) / I2 = 8  =>  0 pairs (_)
G3,I3: 9.. / G3 = 9  =>  1 pairs (_) / I3 = 9  =>  2 pairs (_)
* DURATION: 0:00:09.135884  START: 06:24:02.793126  END: 06:24:11.929010 2020-10-10
* CP COUNT: (14)
* INCONCLUSIVE

--------------------------------------------------
* DEEP CONSTRAINT PAIRS (PAIR REDUCTION)
H1,H8: 4.. / H1 = 4 ==>  3 pairs (_) / H8 = 4 ==>  0 pairs (_)
I7,H8: 4.. / I7 = 4 ==>  3 pairs (_) / H8 = 4 ==>  0 pairs (_)
G3,I3: 9.. / G3 = 9 ==>  1 pairs (_) / I3 = 9 ==>  2 pairs (_)
B5,B6: 4.. / B5 = 4 ==>  2 pairs (_) / B6 = 4 ==>  0 pairs (_)
A3,A5: 5.. / A3 = 5 ==>  1 pairs (_) / A5 = 5 ==>  1 pairs (_)
A5,B5: 5.. / A5 = 5 ==>  1 pairs (_) / B5 = 5 ==>  1 pairs (_)
H2,I2: 8.. / H2 = 8 ==>  1 pairs (_) / I2 = 8 ==>  0 pairs (_)
E2,F2: 7.. / E2 = 7 ==>  0 pairs (_) / F2 = 7 ==>  1 pairs (_)
B2,F2: 5.. / B2 = 5 ==>  1 pairs (_) / F2 = 5 ==>  0 pairs (_)
F2,F3: 5.. / F2 = 5 ==>  0 pairs (_) / F3 = 5 ==>  1 pairs (_)
F6,F7: 6.. / F6 = 6 ==>  0 pairs (_) / F7 = 6 ==>  0 pairs (_)
E5,H5: 6.. / E5 = 6 ==>  0 pairs (_) / H5 = 6 ==>  0 pairs (_)
E7,F7: 6.. / E7 = 6 ==>  0 pairs (_) / F7 = 6 ==>  0 pairs (_)
H5,H6: 6.. / H5 = 6 ==>  0 pairs (_) / H6 = 6 ==>  0 pairs (_)
* DURATION: 0:01:11.369550  START: 06:24:11.929619  END: 06:25:23.299169 2020-10-10
* DCP COUNT: (14)
* INCONCLUSIVE

--------------------------------------------------
* VERY DEEP CONSTRAINT PAIRS (PAIR REDUCTION, RECURSIVE)
H1,H8: 4.. / H1 = 4 ==>  0 pairs (*) / H8 = 4  =>  0 pairs (X)
* DURATION: 0:00:45.484320  START: 06:25:23.472391  END: 06:26:08.956711 2020-10-10
* REASONING H1,H8: 4..
* DIS # H1: 4 # E1: 3 # F6: 7,8 => CTR => F6: 1,4,6,9
* PRF # H1: 4 # E1: 3 + F6: 1,4,6,9 # A5: 7,8 => SOL
* STA # H1: 4 # E1: 3 + F6: 1,4,6,9 + A5: 7,8
* CNT   2 HDP CHAINS /  49 HYP OPENED
* VDCP COUNT: (1)
* SOLUTION FOUND

Header Info

2236726;2018_12_25;PAQ;25;11.50;1.20;1.20

Appendix: Full HDP Chains

A1. Deep Constraint Pair Analysis

Full list of HDP chains traversed for H1,H8: 4..:

* INC # H1: 4 # E1: 1,2 => UNS
* INC # H1: 4 # E1: 3 => UNS
* INC # H1: 4 # F4: 1,2 => UNS
* INC # H1: 4 # F6: 1,2 => UNS
* INC # H1: 4 # H2: 1,3 => UNS
* INC # H1: 4 # I2: 1,3 => UNS
* INC # H1: 4 # I3: 1,3 => UNS
* INC # H1: 4 # E1: 1,3 => UNS
* INC # H1: 4 # E1: 2 => UNS
* INC # H1: 4 # I4: 1,3 => UNS
* INC # H1: 4 # I4: 7,8,9 => UNS
* INC # H1: 4 => UNS
* INC # H8: 4 => UNS
* CNT  13 HDP CHAINS /  13 HYP OPENED

Full list of HDP chains traversed for I7,H8: 4..:

* INC # I7: 4 # E1: 1,2 => UNS
* INC # I7: 4 # E1: 3 => UNS
* INC # I7: 4 # F4: 1,2 => UNS
* INC # I7: 4 # F6: 1,2 => UNS
* INC # I7: 4 # H2: 1,3 => UNS
* INC # I7: 4 # I2: 1,3 => UNS
* INC # I7: 4 # I3: 1,3 => UNS
* INC # I7: 4 # E1: 1,3 => UNS
* INC # I7: 4 # E1: 2 => UNS
* INC # I7: 4 # I4: 1,3 => UNS
* INC # I7: 4 # I4: 7,8,9 => UNS
* INC # I7: 4 => UNS
* INC # H8: 4 => UNS
* CNT  13 HDP CHAINS /  13 HYP OPENED

Full list of HDP chains traversed for G3,I3: 9..:

* INC # I3: 9 # E1: 1,2 => UNS
* INC # I3: 9 # E2: 1,2 => UNS
* INC # I3: 9 # F2: 1,2 => UNS
* INC # I3: 9 # F3: 1,2 => UNS
* INC # I3: 9 # H1: 1,2 => UNS
* INC # I3: 9 # H1: 3,4 => UNS
* INC # I3: 9 # F4: 1,2 => UNS
* INC # I3: 9 # F6: 1,2 => UNS
* INC # I3: 9 # H1: 2,3 => UNS
* INC # I3: 9 # H2: 2,3 => UNS
* INC # I3: 9 # A3: 2,3 => UNS
* INC # I3: 9 # B3: 2,3 => UNS
* INC # I3: 9 # D3: 2,3 => UNS
* INC # I3: 9 # G7: 2,3 => UNS
* INC # I3: 9 # G8: 2,3 => UNS
* INC # I3: 9 => UNS
* INC # G3: 9 # I4: 7,8 => UNS
* INC # G3: 9 # G6: 7,8 => UNS
* INC # G3: 9 # A5: 7,8 => UNS
* INC # G3: 9 # D5: 7,8 => UNS
* INC # G3: 9 # G7: 7,8 => UNS
* INC # G3: 9 # G8: 7,8 => UNS
* INC # G3: 9 => UNS
* CNT  23 HDP CHAINS /  23 HYP OPENED

Full list of HDP chains traversed for B5,B6: 4..:

* INC # B5: 4 # B2: 2,3 => UNS
* INC # B5: 4 # C2: 2,3 => UNS
* INC # B5: 4 # B3: 2,3 => UNS
* INC # B5: 4 # D3: 2,3 => UNS
* INC # B5: 4 # G3: 2,3 => UNS
* INC # B5: 4 # A6: 2,3 => UNS
* INC # B5: 4 # A8: 2,3 => UNS
* INC # B5: 4 # A9: 2,3 => UNS
* INC # B5: 4 # F4: 7,8 => UNS
* INC # B5: 4 # D6: 7,8 => UNS
* INC # B5: 4 # F6: 7,8 => UNS
* INC # B5: 4 # G5: 7,8 => UNS
* INC # B5: 4 # G5: 9 => UNS
* INC # B5: 4 # D7: 7,8 => UNS
* INC # B5: 4 # D9: 7,8 => UNS
* INC # B5: 4 => UNS
* INC # B6: 4 => UNS
* CNT  17 HDP CHAINS /  17 HYP OPENED

Full list of HDP chains traversed for A3,A5: 5..:

* INC # A3: 5 # A6: 7,8 => UNS
* INC # A3: 5 # A6: 2,3 => UNS
* INC # A3: 5 # D5: 7,8 => UNS
* INC # A3: 5 # G5: 7,8 => UNS
* INC # A3: 5 # A8: 7,8 => UNS
* INC # A3: 5 # A9: 7,8 => UNS
* INC # A3: 5 => UNS
* INC # A5: 5 # B2: 2,3 => UNS
* INC # A5: 5 # C2: 2,3 => UNS
* INC # A5: 5 # B3: 2,3 => UNS
* INC # A5: 5 # D3: 2,3 => UNS
* INC # A5: 5 # G3: 2,3 => UNS
* INC # A5: 5 # A6: 2,3 => UNS
* INC # A5: 5 # A8: 2,3 => UNS
* INC # A5: 5 # A9: 2,3 => UNS
* INC # A5: 5 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

Full list of HDP chains traversed for A5,B5: 5..:

* INC # A5: 5 # B2: 2,3 => UNS
* INC # A5: 5 # C2: 2,3 => UNS
* INC # A5: 5 # B3: 2,3 => UNS
* INC # A5: 5 # D3: 2,3 => UNS
* INC # A5: 5 # G3: 2,3 => UNS
* INC # A5: 5 # A6: 2,3 => UNS
* INC # A5: 5 # A8: 2,3 => UNS
* INC # A5: 5 # A9: 2,3 => UNS
* INC # A5: 5 => UNS
* INC # B5: 5 # A6: 7,8 => UNS
* INC # B5: 5 # A6: 2,3 => UNS
* INC # B5: 5 # D5: 7,8 => UNS
* INC # B5: 5 # G5: 7,8 => UNS
* INC # B5: 5 # A8: 7,8 => UNS
* INC # B5: 5 # A9: 7,8 => UNS
* INC # B5: 5 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

Full list of HDP chains traversed for H2,I2: 8..:

* INC # H2: 8 # H1: 1,3 => UNS
* INC # H2: 8 # I1: 1,3 => UNS
* INC # H2: 8 # I3: 1,3 => UNS
* INC # H2: 8 # B2: 1,3 => UNS
* INC # H2: 8 # C2: 1,3 => UNS
* INC # H2: 8 # E2: 1,3 => UNS
* INC # H2: 8 # I4: 1,3 => UNS
* INC # H2: 8 # I4: 7,8,9 => UNS
* INC # H2: 8 => UNS
* INC # I2: 8 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

Full list of HDP chains traversed for E2,F2: 7..:

* INC # F2: 7 # C2: 2,3 => UNS
* INC # F2: 7 # B3: 2,3 => UNS
* INC # F2: 7 # D3: 2,3 => UNS
* INC # F2: 7 # G3: 2,3 => UNS
* INC # F2: 7 # A6: 2,3 => UNS
* INC # F2: 7 # A8: 2,3 => UNS
* INC # F2: 7 # A9: 2,3 => UNS
* INC # F2: 7 => UNS
* INC # E2: 7 => UNS
* CNT   9 HDP CHAINS /   9 HYP OPENED

Full list of HDP chains traversed for B2,F2: 5..:

* INC # B2: 5 # C2: 2,3 => UNS
* INC # B2: 5 # B3: 2,3 => UNS
* INC # B2: 5 # D3: 2,3 => UNS
* INC # B2: 5 # G3: 2,3 => UNS
* INC # B2: 5 # A6: 2,3 => UNS
* INC # B2: 5 # A8: 2,3 => UNS
* INC # B2: 5 # A9: 2,3 => UNS
* INC # B2: 5 => UNS
* INC # F2: 5 => UNS
* CNT   9 HDP CHAINS /   9 HYP OPENED

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

* INC # F3: 5 # C2: 2,3 => UNS
* INC # F3: 5 # B3: 2,3 => UNS
* INC # F3: 5 # D3: 2,3 => UNS
* INC # F3: 5 # G3: 2,3 => UNS
* INC # F3: 5 # A6: 2,3 => UNS
* INC # F3: 5 # A8: 2,3 => UNS
* INC # F3: 5 # A9: 2,3 => UNS
* INC # F3: 5 => UNS
* INC # F2: 5 => UNS
* CNT   9 HDP CHAINS /   9 HYP OPENED

Full list of HDP chains traversed for F6,F7: 6..:

* INC # F6: 6 => UNS
* INC # F7: 6 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED

Full list of HDP chains traversed for E5,H5: 6..:

* INC # E5: 6 => UNS
* INC # H5: 6 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED

Full list of HDP chains traversed for E7,F7: 6..:

* INC # E7: 6 => UNS
* INC # F7: 6 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED

Full list of HDP chains traversed for H5,H6: 6..:

* INC # H5: 6 => UNS
* INC # H6: 6 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED

A2. Very Deep Constraint Pair Analysis

Full list of HDP chains traversed for H1,H8: 4..:

* INC # H1: 4 # E1: 1,2 => UNS
* INC # H1: 4 # E1: 3 => UNS
* INC # H1: 4 # F4: 1,2 => UNS
* INC # H1: 4 # F6: 1,2 => UNS
* INC # H1: 4 # H2: 1,3 => UNS
* INC # H1: 4 # I2: 1,3 => UNS
* INC # H1: 4 # I3: 1,3 => UNS
* INC # H1: 4 # E1: 1,3 => UNS
* INC # H1: 4 # E1: 2 => UNS
* INC # H1: 4 # I4: 1,3 => UNS
* INC # H1: 4 # I4: 7,8,9 => UNS
* INC # H1: 4 # E1: 1,2 # E4: 1,2 => UNS
* INC # H1: 4 # E1: 1,2 # E6: 1,2 => UNS
* INC # H1: 4 # E1: 1,2 # F4: 1,2 => UNS
* INC # H1: 4 # E1: 1,2 # F6: 1,2 => UNS
* INC # H1: 4 # E1: 1,2 # E7: 3,7 => UNS
* INC # H1: 4 # E1: 1,2 # E8: 3,7 => UNS
* INC # H1: 4 # E1: 1,2 # H2: 1,8 => UNS
* INC # H1: 4 # E1: 1,2 # H2: 2 => UNS
* INC # H1: 4 # E1: 1,2 # I4: 1,8 => UNS
* INC # H1: 4 # E1: 1,2 # I4: 7,9 => UNS
* INC # H1: 4 # E1: 1,2 # G7: 2,9 => UNS
* INC # H1: 4 # E1: 1,2 # G7: 3,7,8 => UNS
* INC # H1: 4 # E1: 1,2 # I4: 1,9 => UNS
* INC # H1: 4 # E1: 1,2 # I4: 7,8 => UNS
* INC # H1: 4 # E1: 1,2 => UNS
* INC # H1: 4 # E1: 3 # F2: 1,7 => UNS
* INC # H1: 4 # E1: 3 # F2: 5 => UNS
* INC # H1: 4 # E1: 3 # E4: 1,7 => UNS
* INC # H1: 4 # E1: 3 # E5: 1,7 => UNS
* INC # H1: 4 # E1: 3 # E6: 1,7 => UNS
* INC # H1: 4 # E1: 3 # F2: 1,5 => UNS
* INC # H1: 4 # E1: 3 # F2: 7 => UNS
* INC # H1: 4 # E1: 3 # B3: 1,5 => UNS
* INC # H1: 4 # E1: 3 # B3: 2,3 => UNS
* INC # H1: 4 # E1: 3 # H2: 3,8 => UNS
* INC # H1: 4 # E1: 3 # H2: 2 => UNS
* INC # H1: 4 # E1: 3 # I4: 3,8 => UNS
* INC # H1: 4 # E1: 3 # I9: 3,8 => UNS
* INC # H1: 4 # E1: 3 # G3: 3,9 => UNS
* INC # H1: 4 # E1: 3 # G3: 2 => UNS
* INC # H1: 4 # E1: 3 # I4: 3,9 => UNS
* INC # H1: 4 # E1: 3 # I9: 3,9 => UNS
* INC # H1: 4 # E1: 3 # F4: 7,8 => UNS
* INC # H1: 4 # E1: 3 # D6: 7,8 => UNS
* DIS # H1: 4 # E1: 3 # F6: 7,8 => CTR => F6: 1,4,6,9
* PRF # H1: 4 # E1: 3 + F6: 1,4,6,9 # A5: 7,8 => SOL
* STA # H1: 4 # E1: 3 + F6: 1,4,6,9 + A5: 7,8
* CNT  47 HDP CHAINS /  49 HYP OPENED