Analysis of xx-ph-01628109-14_09-base.sdk

Contents

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

Original Sudoku

level: hard

position: 98.76.5..7.45..8...3..9....6...57.8..4.6.......7..96..4..9..7......7..21......... initial

Autosolve

position: 98.76.5..7.45..8...3..9....6...57.8..4.6.......7..96..4..9..7......7..21.7....... 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: 0:00:41.402996

The following important HDP chains were detected:

* DIS # B2: 1,2 # C5: 1,2 => CTR => C5: 3,5,8,9
* DIS # B2: 1,2 + C5: 3,5,8,9 # A9: 3,8 => CTR => A9: 1,2
* DIS # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 # F8: 3,8 => CTR => F8: 4,5,6
* PRF # A3: 1,2 # D3: 1,2 => SOL
* STA # A3: 1,2 + D3: 1,2
* CNT   4 HDP CHAINS /  84 HYP OPENED

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

Details

Positions

`98.76.5..7.45..8...3..9....6...57.8..4.6.......7..96..4..9..7......7..21.........`	initial
`98.76.5..7.45..8...3..9....6...57.8..4.6.......7..96..4..9..7......7..21.7.......`	autosolve
`982764513764531892135298467691357284543682179827149635416923758358476921279815346`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
C1: 1,2

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E6,E9: 4.. / E6 = 4  =>  1 pairs (_) / E9 = 4  =>  4 pairs (_)
A3,C3: 5.. / A3 = 5  =>  2 pairs (_) / C3 = 5  =>  5 pairs (_)
B2,C3: 6.. / B2 = 6  =>  4 pairs (_) / C3 = 6  =>  5 pairs (_)
H3,I3: 7.. / H3 = 7  =>  1 pairs (_) / I3 = 7  =>  1 pairs (_)
H5,I5: 7.. / H5 = 7  =>  1 pairs (_) / I5 = 7  =>  1 pairs (_)
H3,H5: 7.. / H3 = 7  =>  1 pairs (_) / H5 = 7  =>  1 pairs (_)
I3,I5: 7.. / I3 = 7  =>  1 pairs (_) / I5 = 7  =>  1 pairs (_)
D3,F3: 8.. / D3 = 8  =>  2 pairs (_) / F3 = 8  =>  1 pairs (_)
I7,I9: 8.. / I7 = 8  =>  1 pairs (_) / I9 = 8  =>  1 pairs (_)
H2,I2: 9.. / H2 = 9  =>  1 pairs (_) / I2 = 9  =>  1 pairs (_)
B4,B8: 9.. / B4 = 9  =>  2 pairs (_) / B8 = 9  =>  3 pairs (_)
* DURATION: 0:00:06.642769  START: 13:52:33.839258  END: 13:52:40.482027 2020-11-02
* CP COUNT: (11)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:41.162623  START: 13:52:47.509413  END: 13:53:28.672036 2020-11-02
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-01628109-14_09-base-pr-002.dot
* REASONING
* DIS # B2: 1,2 # C5: 1,2 => CTR => C5: 3,5,8,9
* DIS # B2: 1,2 + C5: 3,5,8,9 # A9: 3,8 => CTR => A9: 1,2
* DIS # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 # F8: 3,8 => CTR => F8: 4,5,6
* PRF # A3: 1,2 # D3: 1,2 => SOL
* STA # A3: 1,2 + D3: 1,2
* CNT   4 HDP CHAINS /  84 HYP OPENED

Header Info

1628109;14_09;GP;26;11.40;1.20;1.20

Solution

position: 982764513764531892135298467691357284543682179827149635416923758358476921279815346 solved

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 # A3: 1,2 => UNS
* INC # C3: 1,2 => UNS
* INC # F1: 1,2 => UNS
* INC # F1: 3,4 => UNS
* INC # C4: 1,2 => UNS
* INC # C5: 1,2 => UNS
* INC # C7: 1,2 => UNS
* INC # C9: 1,2 => UNS
* CNT   9 HDP CHAINS /   9 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 1,2 => UNS
* INC # A3: 1,2 => UNS
* INC # C3: 1,2 => UNS
* INC # F1: 1,2 => UNS
* INC # F1: 3,4 => UNS
* INC # C4: 1,2 => UNS
* INC # C5: 1,2 => UNS
* INC # C7: 1,2 => UNS
* INC # C9: 1,2 => UNS
* CNT   9 HDP CHAINS /   9 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 1,2 => UNS
* INC # A3: 1,2 => UNS
* INC # C3: 1,2 => UNS
* INC # F1: 1,2 => UNS
* INC # F1: 3,4 => UNS
* INC # C4: 1,2 => UNS
* INC # C5: 1,2 => UNS
* INC # C7: 1,2 => UNS
* INC # C9: 1,2 => UNS
* INC # B2: 1,2 # F1: 1,2 => UNS
* INC # B2: 1,2 # F1: 4 => UNS
* INC # B2: 1,2 # C4: 1,2 => UNS
* DIS # B2: 1,2 # C5: 1,2 => CTR => C5: 3,5,8,9
* INC # B2: 1,2 + C5: 3,5,8,9 # C7: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 # C9: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 # F1: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 # F1: 4 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 # C4: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 # C7: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 # C9: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 # E2: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 # F2: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 # B4: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 # B6: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 # B7: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 # H9: 6,9 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 # H9: 3,4,5 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 # I9: 6,9 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 # I9: 3,4,5,8 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 # C7: 3,8 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 # C8: 3,8 => UNS
* DIS # B2: 1,2 + C5: 3,5,8,9 # A9: 3,8 => CTR => A9: 1,2
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 # C9: 3,8 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 # D8: 3,8 => UNS
* DIS # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 # F8: 3,8 => CTR => F8: 4,5,6
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # D8: 3,8 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # D8: 4 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # A5: 3,8 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # A6: 3,8 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # C7: 3,8 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # C8: 3,8 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # C9: 3,8 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # D8: 3,8 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # D8: 4 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # A5: 3,8 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # A6: 3,8 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # F1: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # F1: 4 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # C4: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # C7: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # C9: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # E2: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # F2: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # B4: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # B6: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # B7: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # H9: 6,9 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # H9: 3,4,5 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # I9: 6,9 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # I9: 3,4,5,8 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # C7: 3,8 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # C8: 3,8 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # C9: 3,8 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # D8: 3,8 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # D8: 4 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # A5: 3,8 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # A6: 3,8 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # B7: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # C7: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # C9: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # D9: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # E9: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # F9: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # A5: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 # A6: 1,2 => UNS
* INC # B2: 1,2 + C5: 3,5,8,9 + A9: 1,2 + F8: 4,5,6 => UNS
* INC # A3: 1,2 # F1: 1,2 => UNS
* INC # A3: 1,2 # F1: 3,4 => UNS
* INC # A3: 1,2 # C4: 1,2 => UNS
* INC # A3: 1,2 # C5: 1,2 => UNS
* INC # A3: 1,2 # C7: 1,2 => UNS
* INC # A3: 1,2 # C9: 1,2 => UNS
* PRF # A3: 1,2 # D3: 1,2 => SOL
* STA # A3: 1,2 + D3: 1,2
* CNT  83 HDP CHAINS /  84 HYP OPENED