Analysis of xx-ph-00442753-12_12_03-base.sdk

Contents

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

Original Sudoku

level: hard

position: ........1.......23..2.134.....5.......3.26.4..7.8..1.2..1.62..4.2..8.6..9........ initial

Autosolve

position: ...2....1.......23..2.134..2..5.......3.26.4..7.8..1.2..1.62..4.2..8.6..9.....2.. 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: 0:00:52.767916

The following important HDP chains were detected:

* DIS # E6: 4,9 # A1: 5,6 => CTR => A1: 3,4,7,8
* DIS # E6: 4,9 + A1: 3,4,7,8 # D9: 1,7 => CTR => D9: 3,4
* PRF # E6: 4,9 + A1: 3,4,7,8 + D9: 3,4 # D8: 3,4,9 => SOL
* STA # E6: 4,9 + A1: 3,4,7,8 + D9: 3,4 + D8: 3,4,9
* CNT   3 HDP CHAINS /  62 HYP OPENED

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

Details

Positions

`........1.......23..2.134.....5.......3.26.4..7.8..1.2..1.62..4.2..8.6..9........`	initial
`...2....1.......23..2.134..2..5.......3.26.4..7.8..1.2..1.62..4.2..8.6..9.....2..`	autosolve
`369248751148675923752913486214537869893126547675894132581762394427389615936451278`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
F6: 4,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A2,B2: 1.. / A2 = 1  =>  2 pairs (_) / B2 = 1  =>  2 pairs (_)
F4,D5: 1.. / F4 = 1  =>  2 pairs (_) / D5 = 1  =>  2 pairs (_)
H8,H9: 1.. / H8 = 1  =>  1 pairs (_) / H9 = 1  =>  1 pairs (_)
B4,F4: 1.. / B4 = 1  =>  2 pairs (_) / F4 = 1  =>  2 pairs (_)
A2,A5: 1.. / A2 = 1  =>  2 pairs (_) / A5 = 1  =>  2 pairs (_)
A1,B1: 3.. / A1 = 3  =>  1 pairs (_) / B1 = 3  =>  2 pairs (_)
E4,E6: 3.. / E4 = 3  =>  9 pairs (_) / E6 = 3  =>  1 pairs (_)
E6,H6: 3.. / E6 = 3  =>  1 pairs (_) / H6 = 3  =>  9 pairs (_)
G4,G7: 3.. / G4 = 3  =>  1 pairs (_) / G7 = 3  =>  3 pairs (_)
D2,D3: 6.. / D2 = 6  =>  3 pairs (_) / D3 = 6  =>  1 pairs (_)
B9,C9: 6.. / B9 = 6  =>  1 pairs (_) / C9 = 6  =>  1 pairs (_)
I3,I4: 6.. / I3 = 6  =>  3 pairs (_) / I4 = 6  =>  1 pairs (_)
F1,F2: 8.. / F1 = 8  =>  1 pairs (_) / F2 = 8  =>  1 pairs (_)
* DURATION: 0:00:10.164805  START: 00:10:00.891512  END: 00:10:11.056317 2020-12-27
* CP COUNT: (13)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:52.270688  START: 00:10:19.515782  END: 00:11:11.786470 2020-12-27
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00442753-12_12_03-base-pr-002.dot
* REASONING
* DIS # E6: 4,9 # A1: 5,6 => CTR => A1: 3,4,7,8
* DIS # E6: 4,9 + A1: 3,4,7,8 # D9: 1,7 => CTR => D9: 3,4
* PRF # E6: 4,9 + A1: 3,4,7,8 + D9: 3,4 # D8: 3,4,9 => SOL
* STA # E6: 4,9 + A1: 3,4,7,8 + D9: 3,4 + D8: 3,4,9
* CNT   3 HDP CHAINS /  62 HYP OPENED

Header Info

442753;12_12_03;dob;24;11.30;1.20;1.20

Solution

position: 369248751148675923752913486214537869893126547675894132581762394427389615936451278 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 # E4: 4,9 => UNS
* INC # F4: 4,9 => UNS
* INC # E6: 4,9 => UNS
* INC # C6: 4,9 => UNS
* INC # C6: 5,6 => UNS
* INC # F1: 4,9 => UNS
* INC # F2: 4,9 => UNS
* INC # F8: 4,9 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E4: 4,9 => UNS
* INC # F4: 4,9 => UNS
* INC # E6: 4,9 => UNS
* INC # C6: 4,9 => UNS
* INC # C6: 5,6 => UNS
* INC # F1: 4,9 => UNS
* INC # F2: 4,9 => UNS
* INC # F8: 4,9 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # E4: 4,9 => UNS
* INC # F4: 4,9 => UNS
* INC # E6: 4,9 => UNS
* INC # C6: 4,9 => UNS
* INC # C6: 5,6 => UNS
* INC # F1: 4,9 => UNS
* INC # F2: 4,9 => UNS
* INC # F8: 4,9 => UNS
* INC # E4: 4,9 # B4: 4,9 => UNS
* INC # E4: 4,9 # C4: 4,9 => UNS
* INC # E4: 4,9 # E1: 4,9 => UNS
* INC # E4: 4,9 # E2: 4,9 => UNS
* INC # E4: 4,9 # F8: 1,7 => UNS
* INC # E4: 4,9 # F9: 1,7 => UNS
* INC # E4: 4,9 # D8: 1,7 => UNS
* INC # E4: 4,9 # D9: 1,7 => UNS
* INC # E4: 4,9 # C6: 4,9 => UNS
* INC # E4: 4,9 # C6: 5,6 => UNS
* INC # E4: 4,9 # F1: 4,9 => UNS
* INC # E4: 4,9 # F2: 4,9 => UNS
* INC # E4: 4,9 # F8: 4,9 => UNS
* INC # E4: 4,9 => UNS
* INC # F4: 4,9 # D2: 6,7 => UNS
* INC # F4: 4,9 # D2: 4 => UNS
* INC # F4: 4,9 # A3: 6,7 => UNS
* INC # F4: 4,9 # H3: 6,7 => UNS
* INC # F4: 4,9 # I3: 6,7 => UNS
* INC # F4: 4,9 # B5: 5,8 => UNS
* INC # F4: 4,9 # B5: 9 => UNS
* INC # F4: 4,9 # G5: 5,8 => UNS
* INC # F4: 4,9 # I5: 5,8 => UNS
* INC # F4: 4,9 # A1: 5,8 => UNS
* INC # F4: 4,9 # A3: 5,8 => UNS
* INC # F4: 4,9 # A7: 5,8 => UNS
* INC # F4: 4,9 # C4: 4,9 => UNS
* INC # F4: 4,9 # C4: 6,8 => UNS
* INC # F4: 4,9 # C6: 4,9 => UNS
* INC # F4: 4,9 # C6: 5,6 => UNS
* INC # F4: 4,9 # B9: 4,5 => UNS
* INC # F4: 4,9 # C9: 4,5 => UNS
* INC # F4: 4,9 # E1: 4,5 => UNS
* INC # F4: 4,9 # E2: 4,5 => UNS
* INC # F4: 4,9 => UNS
* INC # E6: 4,9 # B4: 1,8 => UNS
* INC # E6: 4,9 # B5: 1,8 => UNS
* INC # E6: 4,9 # A2: 1,8 => UNS
* INC # E6: 4,9 # A2: 4,5,6,7 => UNS
* DIS # E6: 4,9 # A1: 5,6 => CTR => A1: 3,4,7,8
* INC # E6: 4,9 + A1: 3,4,7,8 # A2: 5,6 => UNS
* INC # E6: 4,9 + A1: 3,4,7,8 # A3: 5,6 => UNS
* INC # E6: 4,9 + A1: 3,4,7,8 # A2: 5,6 => UNS
* INC # E6: 4,9 + A1: 3,4,7,8 # A3: 5,6 => UNS
* INC # E6: 4,9 + A1: 3,4,7,8 # C1: 5,6 => UNS
* INC # E6: 4,9 + A1: 3,4,7,8 # C2: 5,6 => UNS
* INC # E6: 4,9 + A1: 3,4,7,8 # C9: 5,6 => UNS
* INC # E6: 4,9 + A1: 3,4,7,8 # F8: 1,7 => UNS
* INC # E6: 4,9 + A1: 3,4,7,8 # F9: 1,7 => UNS
* INC # E6: 4,9 + A1: 3,4,7,8 # D8: 1,7 => UNS
* DIS # E6: 4,9 + A1: 3,4,7,8 # D9: 1,7 => CTR => D9: 3,4
* INC # E6: 4,9 + A1: 3,4,7,8 + D9: 3,4 # D8: 1,7 => UNS
* PRF # E6: 4,9 + A1: 3,4,7,8 + D9: 3,4 # D8: 3,4,9 => SOL
* STA # E6: 4,9 + A1: 3,4,7,8 + D9: 3,4 + D8: 3,4,9
* CNT  61 HDP CHAINS /  62 HYP OPENED