Analysis of xx-ph-00014811-kz1a-base.sdk

Contents

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

Original Sudoku

level: deep

position: 98.7..6..5..........4.9..8.4...5..9..9...73....6..2..1.4.....6....1....2.....37.. initial

Autosolve

position: 98.7..6..5..........4.9..8.4...5..9..9...73....69.2..1.4.....6....1....2.....37.. 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: 0:00:06.222673

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

Deep Constraint Pair Analysis

Time used: 0:00:00.000015

List of important HDP chains detected for D4,E6: 3..:

* DIS # E6: 3 # F4: 6,8 => CTR => F4: 1
* CNT   1 HDP CHAINS /  60 HYP OPENED

List of important HDP chains detected for G4,H5: 2..:

* DIS # H5: 2 # C5: 1,8 => CTR => C5: 5
* DIS # H5: 2 + C5: 5 # B4: 3,7 => CTR => B4: 1,2
* DIS # G4: 2 # H6: 4,5 => CTR => H6: 7
* DIS # G4: 2 + H6: 7 # H1: 4,5 => CTR => H1: 1,2,3
* CNT   4 HDP CHAINS /  95 HYP OPENED

List of important HDP chains detected for H2,H6: 7..:

* DIS # H2: 7 # H1: 3,5 => CTR => H1: 1,2,4
* DIS # H2: 7 + H1: 1,2,4 # H5: 4,5 => CTR => H5: 2
* DIS # H2: 7 + H1: 1,2,4 + H5: 2 # B2: 2,3 => CTR => B2: 1,6
* DIS # H2: 7 + H1: 1,2,4 + H5: 2 + B2: 1,6 # C2: 2,3 => CTR => C2: 1
* PRF # H2: 7 + H1: 1,2,4 + H5: 2 + B2: 1,6 + C2: 1 => SOL
* STA H2: 7
* CNT   5 HDP CHAINS /  16 HYP OPENED

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

Details

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

Positions

`98.7..6..5..........4.9..8.4...5..9..9...73....6..2..1.4.....6....1....2.....37..`	initial
`98.7..6..5..........4.9..8.4...5..9..9...73....69.2..1.4.....6....1....2.....37..`	autosolve

Classification

level: deep

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
G4: 2,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F4,E5: 1.. / F4 = 1  =>  3 pairs (_) / E5 = 1  =>  3 pairs (_)
G7,H9: 1.. / G7 = 1  =>  3 pairs (_) / H9 = 1  =>  1 pairs (_)
G4,H5: 2.. / G4 = 2  =>  2 pairs (_) / H5 = 2  =>  5 pairs (_)
D4,E6: 3.. / D4 = 3  =>  2 pairs (_) / E6 = 3  =>  5 pairs (_)
I7,H8: 3.. / I7 = 3  =>  4 pairs (_) / H8 = 3  =>  1 pairs (_)
C5,B6: 5.. / C5 = 5  =>  3 pairs (_) / B6 = 5  =>  3 pairs (_)
I4,I5: 6.. / I4 = 6  =>  5 pairs (_) / I5 = 6  =>  3 pairs (_)
I4,H6: 7.. / I4 = 7  =>  4 pairs (_) / H6 = 7  =>  4 pairs (_)
E7,E8: 7.. / E7 = 7  =>  1 pairs (_) / E8 = 7  =>  2 pairs (_)
H2,H6: 7.. / H2 = 7  =>  4 pairs (_) / H6 = 7  =>  4 pairs (_)
G2,I2: 9.. / G2 = 9  =>  1 pairs (_) / I2 = 9  =>  1 pairs (_)
F7,F8: 9.. / F7 = 9  =>  1 pairs (_) / F8 = 9  =>  2 pairs (_)
C9,I9: 9.. / C9 = 9  =>  1 pairs (_) / I9 = 9  =>  1 pairs (_)
* DURATION: 0:00:08.643269  START: 10:08:30.080559  END: 10:08:38.723828 2020-12-03
* CP COUNT: (13)
* INCONCLUSIVE

--------------------------------------------------
* DEEP CONSTRAINT PAIRS (PAIR REDUCTION)
I4,I5: 6.. / I4 = 6 ==>  5 pairs (_) / I5 = 6 ==>  3 pairs (_)
D4,E6: 3.. / D4 = 3 ==>  2 pairs (_) / E6 = 3 ==>  7 pairs (_)
G4,H5: 2.. / G4 = 2 ==>  5 pairs (_) / H5 = 2 ==>  8 pairs (_)
H2,H6: 7.. / H2 = 7 ==>  0 pairs (*) / H6 = 7  =>  0 pairs (X)
* DURATION: 0:01:46.066803  START: 10:08:46.935735  END: 10:10:33.002538 2020-12-03
* REASONING D4,E6: 3..
* DIS # E6: 3 # F4: 6,8 => CTR => F4: 1
* CNT   1 HDP CHAINS /  60 HYP OPENED
* REASONING G4,H5: 2..
* DIS # H5: 2 # C5: 1,8 => CTR => C5: 5
* DIS # H5: 2 + C5: 5 # B4: 3,7 => CTR => B4: 1,2
* DIS # G4: 2 # H6: 4,5 => CTR => H6: 7
* DIS # G4: 2 + H6: 7 # H1: 4,5 => CTR => H1: 1,2,3
* CNT   4 HDP CHAINS /  95 HYP OPENED
* REASONING H2,H6: 7..
* DIS # H2: 7 # H1: 3,5 => CTR => H1: 1,2,4
* DIS # H2: 7 + H1: 1,2,4 # H5: 4,5 => CTR => H5: 2
* DIS # H2: 7 + H1: 1,2,4 + H5: 2 # B2: 2,3 => CTR => B2: 1,6
* DIS # H2: 7 + H1: 1,2,4 + H5: 2 + B2: 1,6 # C2: 2,3 => CTR => C2: 1
* PRF # H2: 7 + H1: 1,2,4 + H5: 2 + B2: 1,6 + C2: 1 => SOL
* STA H2: 7
* CNT   5 HDP CHAINS /  16 HYP OPENED
* DCP COUNT: (4)
* SOLUTION FOUND

Header Info

14811;kz1a;GP;23;11.30;1.20;1.20

Appendix: Full HDP Chains

A1. Pair Reduction Analysis

Full list of HDP chains traversed:

* INC # C4: 2,8 => UNS
* INC # C4: 1,3,7 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C4: 2,8 => UNS
* INC # C4: 1,3,7 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # C4: 2,8 => UNS
* INC # C4: 1,3,7 => UNS
* INC # C4: 2,8 # A5: 2,8 => UNS
* INC # C4: 2,8 # C5: 2,8 => UNS
* INC # C4: 2,8 # C7: 2,8 => UNS
* INC # C4: 2,8 # C9: 2,8 => UNS
* INC # C4: 2,8 # D2: 3,6 => UNS
* INC # C4: 2,8 # D3: 3,6 => UNS
* INC # C4: 2,8 # E5: 1,6 => UNS
* INC # C4: 2,8 # E5: 4,8 => UNS
* INC # C4: 2,8 # F2: 1,6 => UNS
* INC # C4: 2,8 # F3: 1,6 => UNS
* INC # C4: 2,8 => UNS
* INC # C4: 1,3,7 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A4. Deep Constraint Pair Analysis

Full list of HDP chains traversed for I4,I5: 6..:

* INC # I4: 6 # C4: 3,8 => UNS
* INC # I4: 6 # C4: 1,2,7 => UNS
* INC # I4: 6 # E6: 3,8 => UNS
* INC # I4: 6 # E6: 4 => UNS
* INC # I4: 6 # A7: 3,8 => UNS
* INC # I4: 6 # A8: 3,8 => UNS
* INC # I4: 6 # B8: 3,5 => UNS
* INC # I4: 6 # B8: 6,7 => UNS
* INC # I4: 6 # E6: 3,8 => UNS
* INC # I4: 6 # E6: 4 => UNS
* INC # I4: 6 # C4: 3,8 => UNS
* INC # I4: 6 # C4: 1,2,7 => UNS
* INC # I4: 6 # D2: 3,8 => UNS
* INC # I4: 6 # D2: 2,4,6 => UNS
* INC # I4: 6 # E5: 1,8 => UNS
* INC # I4: 6 # E5: 4,6 => UNS
* INC # I4: 6 # C4: 1,8 => UNS
* INC # I4: 6 # C4: 2,3,7 => UNS
* INC # I4: 6 # F2: 1,8 => UNS
* INC # I4: 6 # F2: 4,6 => UNS
* INC # I4: 6 # C4: 2,8 => UNS
* INC # I4: 6 # C4: 1,3,7 => UNS
* INC # I4: 6 => UNS
* INC # I5: 6 # E5: 4,8 => UNS
* INC # I5: 6 # E6: 4,8 => UNS
* INC # I5: 6 # D2: 4,8 => UNS
* INC # I5: 6 # D9: 4,8 => UNS
* INC # I5: 6 # C4: 2,8 => UNS
* INC # I5: 6 # C4: 1,3,7 => UNS
* INC # I5: 6 # C4: 7,8 => UNS
* INC # I5: 6 # C4: 1,2,3 => UNS
* INC # I5: 6 => UNS
* CNT  32 HDP CHAINS /  32 HYP OPENED

Full list of HDP chains traversed for D4,E6: 3..:

* INC # E6: 3 # C4: 7,8 => UNS
* INC # E6: 3 # C4: 1,2,3 => UNS
* INC # E6: 3 # A7: 7,8 => UNS
* INC # E6: 3 # A8: 7,8 => UNS
* INC # E6: 3 # H6: 5,7 => UNS
* INC # E6: 3 # H6: 4 => UNS
* INC # E6: 3 # B8: 5,7 => UNS
* INC # E6: 3 # B8: 3,6 => UNS
* DIS # E6: 3 # F4: 6,8 => CTR => F4: 1
* INC # E6: 3 + F4: 1 # D5: 6,8 => UNS
* INC # E6: 3 + F4: 1 # E5: 6,8 => UNS
* INC # E6: 3 + F4: 1 # I4: 6,8 => UNS
* INC # E6: 3 + F4: 1 # I4: 7 => UNS
* INC # E6: 3 + F4: 1 # D2: 6,8 => UNS
* INC # E6: 3 + F4: 1 # D9: 6,8 => UNS
* INC # E6: 3 + F4: 1 # C4: 2,8 => UNS
* INC # E6: 3 + F4: 1 # C4: 3,7 => UNS
* INC # E6: 3 + F4: 1 # C5: 2,5 => UNS
* INC # E6: 3 + F4: 1 # C5: 1,8 => UNS
* INC # E6: 3 + F4: 1 # H1: 2,5 => UNS
* INC # E6: 3 + F4: 1 # H1: 1,3,4 => UNS
* INC # E6: 3 + F4: 1 # H1: 4,5 => UNS
* INC # E6: 3 + F4: 1 # I1: 4,5 => UNS
* INC # E6: 3 + F4: 1 # F8: 4,5 => UNS
* INC # E6: 3 + F4: 1 # F8: 6,8,9 => UNS
* INC # E6: 3 + F4: 1 # D3: 5,6 => UNS
* INC # E6: 3 + F4: 1 # D3: 2,3 => UNS
* INC # E6: 3 + F4: 1 # F8: 5,6 => UNS
* INC # E6: 3 + F4: 1 # F8: 4,8,9 => UNS
* INC # E6: 3 + F4: 1 # C4: 7,8 => UNS
* INC # E6: 3 + F4: 1 # C4: 2,3 => UNS
* INC # E6: 3 + F4: 1 # A7: 7,8 => UNS
* INC # E6: 3 + F4: 1 # A8: 7,8 => UNS
* INC # E6: 3 + F4: 1 # H6: 5,7 => UNS
* INC # E6: 3 + F4: 1 # H6: 4 => UNS
* INC # E6: 3 + F4: 1 # B8: 5,7 => UNS
* INC # E6: 3 + F4: 1 # B8: 3,6 => UNS
* INC # E6: 3 + F4: 1 # D5: 6,8 => UNS
* INC # E6: 3 + F4: 1 # E5: 6,8 => UNS
* INC # E6: 3 + F4: 1 # I4: 6,8 => UNS
* INC # E6: 3 + F4: 1 # I4: 7 => UNS
* INC # E6: 3 + F4: 1 # D2: 6,8 => UNS
* INC # E6: 3 + F4: 1 # D9: 6,8 => UNS
* INC # E6: 3 + F4: 1 # C4: 2,8 => UNS
* INC # E6: 3 + F4: 1 # C4: 3,7 => UNS
* INC # E6: 3 + F4: 1 # C5: 2,5 => UNS
* INC # E6: 3 + F4: 1 # C5: 1,8 => UNS
* INC # E6: 3 + F4: 1 # H1: 2,5 => UNS
* INC # E6: 3 + F4: 1 # H1: 1,3,4 => UNS
* INC # E6: 3 + F4: 1 => UNS
* INC # D4: 3 # D5: 4,8 => UNS
* INC # D4: 3 # E5: 4,8 => UNS
* INC # D4: 3 # G6: 4,8 => UNS
* INC # D4: 3 # G6: 5 => UNS
* INC # D4: 3 # E2: 4,8 => UNS
* INC # D4: 3 # E8: 4,8 => UNS
* INC # D4: 3 # E9: 4,8 => UNS
* INC # D4: 3 # C4: 2,8 => UNS
* INC # D4: 3 # C4: 1,7 => UNS
* INC # D4: 3 => UNS
* CNT  60 HDP CHAINS /  60 HYP OPENED

Full list of HDP chains traversed for G4,H5: 2..:

* DIS # H5: 2 # C5: 1,8 => CTR => C5: 5
* INC # H5: 2 + C5: 5 # E5: 1,8 => UNS
* INC # H5: 2 + C5: 5 # E5: 4,6 => UNS
* INC # H5: 2 + C5: 5 # D2: 3,6 => UNS
* INC # H5: 2 + C5: 5 # D3: 3,6 => UNS
* INC # H5: 2 + C5: 5 # E5: 1,6 => UNS
* INC # H5: 2 + C5: 5 # E5: 4,8 => UNS
* INC # H5: 2 + C5: 5 # F2: 1,6 => UNS
* INC # H5: 2 + C5: 5 # F3: 1,6 => UNS
* INC # H5: 2 + C5: 5 # H6: 4,5 => UNS
* INC # H5: 2 + C5: 5 # H6: 7 => UNS
* INC # H5: 2 + C5: 5 # G8: 4,5 => UNS
* INC # H5: 2 + C5: 5 # G8: 9 => UNS
* INC # H5: 2 + C5: 5 # E5: 1,8 => UNS
* INC # H5: 2 + C5: 5 # E5: 4,6 => UNS
* DIS # H5: 2 + C5: 5 # B4: 3,7 => CTR => B4: 1,2
* INC # H5: 2 + C5: 5 + B4: 1,2 # C4: 3,7 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # A6: 3,7 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # B2: 3,7 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # B3: 3,7 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # B8: 3,7 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # D2: 3,6 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # D3: 3,6 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # E5: 1,6 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # E5: 4,8 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # F2: 1,6 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # F3: 1,6 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # D5: 4,6 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # E5: 4,6 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # H6: 4,5 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # H6: 7 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # G8: 4,5 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # G8: 9 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # C4: 1,2 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # C4: 3,7 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # B2: 1,2 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # B3: 1,2 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # B9: 1,2 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # E5: 1,8 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # E5: 4,6 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # C4: 3,7 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # A6: 3,7 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # B2: 3,7 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # B3: 3,7 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # B8: 3,7 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # D2: 3,6 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # D3: 3,6 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # E5: 1,6 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # E5: 4,8 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # F2: 1,6 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # F3: 1,6 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # D5: 4,6 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # E5: 4,6 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # H6: 4,5 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # H6: 7 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # G8: 4,5 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 # G8: 9 => UNS
* INC # H5: 2 + C5: 5 + B4: 1,2 => UNS
* INC # G4: 2 # H1: 1,5 => UNS
* INC # G4: 2 # H1: 2,3,4 => UNS
* INC # G4: 2 # F3: 1,5 => UNS
* INC # G4: 2 # F3: 6 => UNS
* INC # G4: 2 # G7: 1,5 => UNS
* INC # G4: 2 # G7: 8,9 => UNS
* INC # G4: 2 # I5: 4,5 => UNS
* INC # G4: 2 # G6: 4,5 => UNS
* DIS # G4: 2 # H6: 4,5 => CTR => H6: 7
* DIS # G4: 2 + H6: 7 # H1: 4,5 => CTR => H1: 1,2,3
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # H8: 4,5 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # H9: 4,5 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # I5: 4,5 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # G6: 4,5 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # H8: 4,5 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # H9: 4,5 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # F3: 1,5 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # F3: 6 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # G7: 1,5 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # G7: 8,9 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # C4: 3,8 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # C4: 1,7 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # E6: 3,8 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # E6: 4 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # A7: 3,8 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # A8: 3,8 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # B8: 3,5 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # B8: 6,7 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # I5: 6,8 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # I5: 4,5 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # D4: 6,8 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # F4: 6,8 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # I5: 4,5 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # G6: 4,5 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # H8: 4,5 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 # H9: 4,5 => UNS
* INC # G4: 2 + H6: 7 + H1: 1,2,3 => UNS
* CNT  95 HDP CHAINS /  95 HYP OPENED

Full list of HDP chains traversed for H2,H6: 7..:

* DIS # H2: 7 # H1: 3,5 => CTR => H1: 1,2,4
* INC # H2: 7 + H1: 1,2,4 # I1: 3,5 => UNS
* INC # H2: 7 + H1: 1,2,4 # I1: 3,5 => UNS
* INC # H2: 7 + H1: 1,2,4 # I1: 4 => UNS
* INC # H2: 7 + H1: 1,2,4 # D3: 3,5 => UNS
* INC # H2: 7 + H1: 1,2,4 # D3: 2,6 => UNS
* INC # H2: 7 + H1: 1,2,4 # E5: 4,8 => UNS
* INC # H2: 7 + H1: 1,2,4 # E6: 4,8 => UNS
* INC # H2: 7 + H1: 1,2,4 # D2: 4,8 => UNS
* INC # H2: 7 + H1: 1,2,4 # D9: 4,8 => UNS
* INC # H2: 7 + H1: 1,2,4 # C4: 2,8 => UNS
* INC # H2: 7 + H1: 1,2,4 # C4: 1,3 => UNS
* DIS # H2: 7 + H1: 1,2,4 # H5: 4,5 => CTR => H5: 2
* DIS # H2: 7 + H1: 1,2,4 + H5: 2 # B2: 2,3 => CTR => B2: 1,6
* DIS # H2: 7 + H1: 1,2,4 + H5: 2 + B2: 1,6 # C2: 2,3 => CTR => C2: 1
* PRF # H2: 7 + H1: 1,2,4 + H5: 2 + B2: 1,6 + C2: 1 => SOL
* STA H2: 7
* CNT  16 HDP CHAINS /  16 HYP OPENED