Analysis of xx-ph-00000159-127-base.sdk

Contents

Original Sudoku

level: very deep

Original Sudoku

position: ...4.....4...891...9..31........5..6.8.3..4..6.7....5..1.9..8....2......9...2...7 initial

Autosolve

position: ...4.....4...891...9..31........5..6.8.3..4..6.7....5..1.9..8....2......9...2...7 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

Time used: 0:00:00.000007

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

Very Deep Constraint Pair Analysis

Very Deep Constraint Pair Analysis

Time used: 0:01:23.597684

List of important HDP chains detected for A1,C1: 1..:

* DIS # A1: 1 # G4: 2,3 # H5: 1,9 => CTR => H5: 2,7
* DIS # A1: 1 # H4: 2,3 # E8: 6,7 => CTR => E8: 1,4,5
* DIS # A1: 1 # H4: 2,3 + E8: 1,4,5 # H1: 2,3 => CTR => H1: 6,7,8,9
* PRF # A1: 1 # H4: 2,3 + E8: 1,4,5 + H1: 6,7,8,9 # H2: 2,3 => SOL
* STA # A1: 1 # H4: 2,3 + E8: 1,4,5 + H1: 6,7,8,9 + H2: 2,3
* CNT   4 HDP CHAINS / 110 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

...4.....4...891...9..31........5..6.8.3..4..6.7....5..1.9..8....2......9...2...7 initial
...4.....4...891...9..31........5..6.8.3..4..6.7....5..1.9..8....2......9...2...7 autosolve

Classification

level: very deep

Pairing Analysis

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,C1: 1.. / A1 = 1  =>  4 pairs (_) / C1 = 1  =>  1 pairs (_)
D9,H9: 1.. / D9 = 1  =>  1 pairs (_) / H9 = 1  =>  0 pairs (_)
H7,I7: 2.. / H7 = 2  =>  0 pairs (_) / I7 = 2  =>  2 pairs (_)
H3,I3: 4.. / H3 = 4  =>  0 pairs (_) / I3 = 4  =>  0 pairs (_)
A5,C5: 5.. / A5 = 5  =>  2 pairs (_) / C5 = 5  =>  3 pairs (_)
E5,F5: 6.. / E5 = 6  =>  2 pairs (_) / F5 = 6  =>  1 pairs (_)
H4,I6: 8.. / H4 = 8  =>  0 pairs (_) / I6 = 8  =>  2 pairs (_)
A8,C9: 8.. / A8 = 8  =>  0 pairs (_) / C9 = 8  =>  1 pairs (_)
D4,H4: 8.. / D4 = 8  =>  2 pairs (_) / H4 = 8  =>  0 pairs (_)
C4,C5: 9.. / C4 = 9  =>  1 pairs (_) / C5 = 9  =>  2 pairs (_)
* DURATION: 0:00:06.760892  START: 22:21:08.962419  END: 22:21:15.723311 2020-09-28
* CP COUNT: (10)
* INCONCLUSIVE

--------------------------------------------------
* DEEP CONSTRAINT PAIRS (PAIR REDUCTION)
A1,C1: 1.. / A1 = 1 ==>  4 pairs (_) / C1 = 1 ==>  1 pairs (_)
A5,C5: 5.. / A5 = 5 ==>  2 pairs (_) / C5 = 5 ==>  3 pairs (_)
C4,C5: 9.. / C4 = 9 ==>  1 pairs (_) / C5 = 9 ==>  2 pairs (_)
E5,F5: 6.. / E5 = 6 ==>  2 pairs (_) / F5 = 6 ==>  1 pairs (_)
D4,H4: 8.. / D4 = 8 ==>  2 pairs (_) / H4 = 8 ==>  0 pairs (_)
H4,I6: 8.. / H4 = 8 ==>  0 pairs (_) / I6 = 8 ==>  2 pairs (_)
H7,I7: 2.. / H7 = 2 ==>  0 pairs (_) / I7 = 2 ==>  2 pairs (_)
A8,C9: 8.. / A8 = 8 ==>  0 pairs (_) / C9 = 8 ==>  1 pairs (_)
D9,H9: 1.. / D9 = 1 ==>  1 pairs (_) / H9 = 1 ==>  0 pairs (_)
H3,I3: 4.. / H3 = 4 ==>  0 pairs (_) / I3 = 4 ==>  0 pairs (_)
* DURATION: 0:00:57.860749  START: 22:21:15.723918  END: 22:22:13.584667 2020-09-28
* DCP COUNT: (10)
* INCONCLUSIVE

--------------------------------------------------
* VERY DEEP CONSTRAINT PAIRS (PAIR REDUCTION, RECURSIVE)
A1,C1: 1.. / A1 = 1 ==>  0 pairs (*) / C1 = 1  =>  0 pairs (X)
* DURATION: 0:01:23.596481  START: 22:22:13.701605  END: 22:23:37.298086 2020-09-28
* REASONING A1,C1: 1..
* DIS # A1: 1 # G4: 2,3 # H5: 1,9 => CTR => H5: 2,7
* DIS # A1: 1 # H4: 2,3 # E8: 6,7 => CTR => E8: 1,4,5
* DIS # A1: 1 # H4: 2,3 + E8: 1,4,5 # H1: 2,3 => CTR => H1: 6,7,8,9
* PRF # A1: 1 # H4: 2,3 + E8: 1,4,5 + H1: 6,7,8,9 # H2: 2,3 => SOL
* STA # A1: 1 # H4: 2,3 + E8: 1,4,5 + H1: 6,7,8,9 + H2: 2,3
* CNT   4 HDP CHAINS / 110 HYP OPENED
* VDCP COUNT: (1)
* SOLUTION FOUND

Header Info

159;127;elev;23;11.50;11.50;10.60

Appendix: Full HDP Chains

A1. Deep Constraint Pair Analysis

Full list of HDP chains traversed for A1,C1: 1..:

* INC # A1: 1 # B4: 2,3 => UNS
* INC # A1: 1 # B6: 2,3 => UNS
* INC # A1: 1 # G4: 2,3 => UNS
* INC # A1: 1 # H4: 2,3 => UNS
* INC # A1: 1 # E4: 1,9 => UNS
* INC # A1: 1 # H4: 1,9 => UNS
* INC # A1: 1 # E5: 1,9 => UNS
* INC # A1: 1 # H5: 1,9 => UNS
* INC # A1: 1 # I5: 1,9 => UNS
* INC # A1: 1 # A8: 3,7 => UNS
* INC # A1: 1 # B8: 3,7 => UNS
* INC # A1: 1 # F7: 3,7 => UNS
* INC # A1: 1 # F7: 4,6 => UNS
* INC # A1: 1 => UNS
* INC # C1: 1 => UNS
* CNT  15 HDP CHAINS /  15 HYP OPENED

Full list of HDP chains traversed for A5,C5: 5..:

* INC # C5: 5 # B1: 3,6 => UNS
* INC # C5: 5 # B2: 3,6 => UNS
* INC # C5: 5 # H2: 3,6 => UNS
* INC # C5: 5 # H2: 2,7 => UNS
* INC # C5: 5 # C7: 3,6 => UNS
* INC # C5: 5 # C9: 3,6 => UNS
* INC # C5: 5 # H3: 6,8 => UNS
* INC # C5: 5 # H3: 2,4,7 => UNS
* INC # C5: 5 # C9: 6,8 => UNS
* INC # C5: 5 # C9: 3,4 => UNS
* INC # C5: 5 # A4: 1,2 => UNS
* INC # C5: 5 # A4: 3 => UNS
* INC # C5: 5 # H5: 1,2 => UNS
* INC # C5: 5 # I5: 1,2 => UNS
* INC # C5: 5 => UNS
* INC # A5: 5 # C4: 1,9 => UNS
* INC # A5: 5 # C4: 3,4 => UNS
* INC # A5: 5 # E5: 1,9 => UNS
* INC # A5: 5 # H5: 1,9 => UNS
* INC # A5: 5 # I5: 1,9 => UNS
* INC # A5: 5 # A8: 3,7 => UNS
* INC # A5: 5 # B8: 3,7 => UNS
* INC # A5: 5 # F7: 3,7 => UNS
* INC # A5: 5 # F7: 4,6 => UNS
* INC # A5: 5 # A1: 3,7 => UNS
* INC # A5: 5 # A1: 1,2,8 => UNS
* INC # A5: 5 => UNS
* CNT  27 HDP CHAINS /  27 HYP OPENED

Full list of HDP chains traversed for C4,C5: 9..:

* INC # C5: 9 # H5: 1,2 => UNS
* INC # C5: 9 # I6: 1,2 => UNS
* INC # C5: 9 # A8: 3,7 => UNS
* INC # C5: 9 # B8: 3,7 => UNS
* INC # C5: 9 # F7: 3,7 => UNS
* INC # C5: 9 # F7: 4,6 => UNS
* INC # C5: 9 # A1: 3,7 => UNS
* INC # C5: 9 # A1: 1,2,8 => UNS
* INC # C5: 9 => UNS
* INC # C4: 9 # A5: 1,5 => UNS
* INC # C4: 9 # A5: 2 => UNS
* INC # C4: 9 # C1: 1,5 => UNS
* INC # C4: 9 # C1: 3,6,8 => UNS
* INC # C4: 9 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

Full list of HDP chains traversed for E5,F5: 6..:

* INC # E5: 6 # D2: 5,7 => UNS
* INC # E5: 6 # D3: 5,7 => UNS
* INC # E5: 6 # A1: 5,7 => UNS
* INC # E5: 6 # B1: 5,7 => UNS
* INC # E5: 6 # G1: 5,7 => UNS
* INC # E5: 6 # E7: 5,7 => UNS
* INC # E5: 6 # E8: 5,7 => UNS
* INC # E5: 6 # D4: 2,7 => UNS
* INC # E5: 6 # D4: 1,8 => UNS
* INC # E5: 6 # H5: 2,7 => UNS
* INC # E5: 6 # H5: 1,9 => UNS
* INC # E5: 6 # F1: 2,7 => UNS
* INC # E5: 6 # F1: 6 => UNS
* INC # E5: 6 => UNS
* INC # F5: 6 # D2: 2,7 => UNS
* INC # F5: 6 # D3: 2,7 => UNS
* INC # F5: 6 # A1: 2,7 => UNS
* INC # F5: 6 # B1: 2,7 => UNS
* INC # F5: 6 # G1: 2,7 => UNS
* INC # F5: 6 # H1: 2,7 => UNS
* INC # F5: 6 => UNS
* CNT  21 HDP CHAINS /  21 HYP OPENED

Full list of HDP chains traversed for D4,H4: 8..:

* INC # D4: 8 # B6: 2,4 => UNS
* INC # D4: 8 # B6: 3 => UNS
* INC # D4: 8 => UNS
* INC # H4: 8 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

Full list of HDP chains traversed for H4,I6: 8..:

* INC # I6: 8 # B6: 2,4 => UNS
* INC # I6: 8 # B6: 3 => UNS
* INC # I6: 8 => UNS
* INC # H4: 8 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

Full list of HDP chains traversed for H7,I7: 2..:

* INC # I7: 2 # G1: 3,5 => UNS
* INC # I7: 2 # I1: 3,5 => UNS
* INC # I7: 2 # B2: 3,5 => UNS
* INC # I7: 2 # C2: 3,5 => UNS
* INC # I7: 2 # I8: 3,5 => UNS
* INC # I7: 2 # I8: 1,4,9 => UNS
* INC # I7: 2 # H4: 1,9 => UNS
* INC # I7: 2 # H5: 1,9 => UNS
* INC # I7: 2 # I6: 1,9 => UNS
* INC # I7: 2 # C5: 1,9 => UNS
* INC # I7: 2 # E5: 1,9 => UNS
* INC # I7: 2 # I8: 1,9 => UNS
* INC # I7: 2 # I8: 3,4,5 => UNS
* INC # I7: 2 => UNS
* INC # H7: 2 => UNS
* CNT  15 HDP CHAINS /  15 HYP OPENED

Full list of HDP chains traversed for A8,C9: 8..:

* INC # C9: 8 # B1: 5,6 => UNS
* INC # C9: 8 # C1: 5,6 => UNS
* INC # C9: 8 # B2: 5,6 => UNS
* INC # C9: 8 # C2: 5,6 => UNS
* INC # C9: 8 # D3: 5,6 => UNS
* INC # C9: 8 # G3: 5,6 => UNS
* INC # C9: 8 # C7: 5,6 => UNS
* INC # C9: 8 # C7: 3,4 => UNS
* INC # C9: 8 => UNS
* INC # A8: 8 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

Full list of HDP chains traversed for D9,H9: 1..:

* INC # D9: 1 # D4: 2,8 => UNS
* INC # D9: 1 # F6: 2,8 => UNS
* INC # D9: 1 # I6: 2,8 => UNS
* INC # D9: 1 # I6: 1,3,9 => UNS
* INC # D9: 1 => UNS
* INC # H9: 1 => UNS
* CNT   6 HDP CHAINS /   6 HYP OPENED

Full list of HDP chains traversed for H3,I3: 4..:

* INC # H3: 4 => UNS
* INC # I3: 4 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED

A2. Very Deep Constraint Pair Analysis

Full list of HDP chains traversed for A1,C1: 1..:

* INC # A1: 1 # B4: 2,3 => UNS
* INC # A1: 1 # B6: 2,3 => UNS
* INC # A1: 1 # G4: 2,3 => UNS
* INC # A1: 1 # H4: 2,3 => UNS
* INC # A1: 1 # E4: 1,9 => UNS
* INC # A1: 1 # H4: 1,9 => UNS
* INC # A1: 1 # E5: 1,9 => UNS
* INC # A1: 1 # H5: 1,9 => UNS
* INC # A1: 1 # I5: 1,9 => UNS
* INC # A1: 1 # A8: 3,7 => UNS
* INC # A1: 1 # B8: 3,7 => UNS
* INC # A1: 1 # F7: 3,7 => UNS
* INC # A1: 1 # F7: 4,6 => UNS
* INC # A1: 1 # B4: 2,3 # B1: 2,3 => UNS
* INC # A1: 1 # B4: 2,3 # B2: 2,3 => UNS
* INC # A1: 1 # B4: 2,3 # H4: 1,9 => UNS
* INC # A1: 1 # B4: 2,3 # H4: 7,8 => UNS
* INC # A1: 1 # B4: 2,3 # E5: 1,9 => UNS
* INC # A1: 1 # B4: 2,3 # H5: 1,9 => UNS
* INC # A1: 1 # B4: 2,3 # I5: 1,9 => UNS
* INC # A1: 1 # B4: 2,3 # E5: 1,9 => UNS
* INC # A1: 1 # B4: 2,3 # E5: 6,7 => UNS
* INC # A1: 1 # B4: 2,3 # I6: 1,9 => UNS
* INC # A1: 1 # B4: 2,3 # I6: 2,3,8 => UNS
* INC # A1: 1 # B4: 2,3 # D6: 2,8 => UNS
* INC # A1: 1 # B4: 2,3 # D6: 1 => UNS
* INC # A1: 1 # B4: 2,3 # I6: 2,8 => UNS
* INC # A1: 1 # B4: 2,3 # I6: 1,3,9 => UNS
* INC # A1: 1 # B4: 2,3 # H4: 7,9 => UNS
* INC # A1: 1 # B4: 2,3 # H5: 7,9 => UNS
* INC # A1: 1 # B4: 2,3 # G1: 7,9 => UNS
* INC # A1: 1 # B4: 2,3 # G1: 2,3,5,6 => UNS
* INC # A1: 1 # B4: 2,3 # A8: 3,7 => UNS
* INC # A1: 1 # B4: 2,3 # B8: 3,7 => UNS
* INC # A1: 1 # B4: 2,3 # F7: 3,7 => UNS
* INC # A1: 1 # B4: 2,3 # F7: 4,6 => UNS
* INC # A1: 1 # B4: 2,3 => UNS
* INC # A1: 1 # B6: 2,3 # G4: 2,3 => UNS
* INC # A1: 1 # B6: 2,3 # H4: 2,3 => UNS
* INC # A1: 1 # B6: 2,3 # E4: 1,9 => UNS
* INC # A1: 1 # B6: 2,3 # H4: 1,9 => UNS
* INC # A1: 1 # B6: 2,3 # E5: 1,9 => UNS
* INC # A1: 1 # B6: 2,3 # H5: 1,9 => UNS
* INC # A1: 1 # B6: 2,3 # I5: 1,9 => UNS
* INC # A1: 1 # B6: 2,3 # G6: 2,3 => UNS
* INC # A1: 1 # B6: 2,3 # I6: 2,3 => UNS
* INC # A1: 1 # B6: 2,3 # B1: 2,3 => UNS
* INC # A1: 1 # B6: 2,3 # B2: 2,3 => UNS
* INC # A1: 1 # B6: 2,3 # A8: 3,7 => UNS
* INC # A1: 1 # B6: 2,3 # B8: 3,7 => UNS
* INC # A1: 1 # B6: 2,3 # F7: 3,7 => UNS
* INC # A1: 1 # B6: 2,3 # F7: 4,6 => UNS
* INC # A1: 1 # B6: 2,3 => UNS
* INC # A1: 1 # G4: 2,3 # E4: 1,9 => UNS
* INC # A1: 1 # G4: 2,3 # H4: 1,9 => UNS
* INC # A1: 1 # G4: 2,3 # E5: 1,9 => UNS
* DIS # A1: 1 # G4: 2,3 # H5: 1,9 => CTR => H5: 2,7
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # I5: 1,9 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # E5: 1,9 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # I5: 1,9 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # G6: 2,3 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # I6: 2,3 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # B1: 2,3 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # B2: 2,3 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # G6: 2,3 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # I6: 2,3 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # G1: 2,3 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # G1: 5,6,7,9 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # A8: 3,7 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # B8: 3,7 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # F7: 3,7 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # F7: 4,6 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # E4: 1,9 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # H4: 1,9 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # E5: 1,9 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # I5: 1,9 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # G6: 2,3 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # I6: 2,3 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # B1: 2,3 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # B2: 2,3 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # G6: 2,3 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # I6: 2,3 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # G1: 2,3 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # G1: 5,6,7,9 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # F5: 2,7 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # F5: 6 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # A8: 3,7 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # B8: 3,7 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # F7: 3,7 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 # F7: 4,6 => UNS
* INC # A1: 1 # G4: 2,3 + H5: 2,7 => UNS
* INC # A1: 1 # H4: 2,3 # G6: 2,3 => UNS
* INC # A1: 1 # H4: 2,3 # G6: 9 => UNS
* INC # A1: 1 # H4: 2,3 # B1: 2,3 => UNS
* INC # A1: 1 # H4: 2,3 # B2: 2,3 => UNS
* INC # A1: 1 # H4: 2,3 # F5: 6,7 => UNS
* INC # A1: 1 # H4: 2,3 # F5: 2 => UNS
* INC # A1: 1 # H4: 2,3 # E1: 6,7 => UNS
* INC # A1: 1 # H4: 2,3 # E7: 6,7 => UNS
* DIS # A1: 1 # H4: 2,3 # E8: 6,7 => CTR => E8: 1,4,5
* INC # A1: 1 # H4: 2,3 + E8: 1,4,5 # F5: 6,7 => UNS
* INC # A1: 1 # H4: 2,3 + E8: 1,4,5 # F5: 2 => UNS
* INC # A1: 1 # H4: 2,3 + E8: 1,4,5 # E1: 6,7 => UNS
* INC # A1: 1 # H4: 2,3 + E8: 1,4,5 # E7: 6,7 => UNS
* INC # A1: 1 # H4: 2,3 + E8: 1,4,5 # G6: 2,3 => UNS
* INC # A1: 1 # H4: 2,3 + E8: 1,4,5 # G6: 9 => UNS
* DIS # A1: 1 # H4: 2,3 + E8: 1,4,5 # H1: 2,3 => CTR => H1: 6,7,8,9
* PRF # A1: 1 # H4: 2,3 + E8: 1,4,5 + H1: 6,7,8,9 # H2: 2,3 => SOL
* STA # A1: 1 # H4: 2,3 + E8: 1,4,5 + H1: 6,7,8,9 + H2: 2,3
* CNT 108 HDP CHAINS / 110 HYP OPENED