Analysis of xx-ph-00000401-240-base.sdk

Contents

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

Original Sudoku

level: hard

position: .2......94......3...8..75.......18..3...2..4..9......261...8......5..6....57..... initial

Autosolve

position: .2......94......3...8..75.......18..3...2..4..9......261...8......5..6....57..... 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: 0:00:18.082641

The following important HDP chains were detected:

* DIS # C2: 6,7 # B2: 6,7 => CTR => B2: 5
* PRF # C2: 6,7 + B2: 5 # C4: 6,7 => SOL
* STA # C2: 6,7 + B2: 5 + C4: 6,7
* CNT   2 HDP CHAINS /  29 HYP OPENED

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

Details

Positions

`.2......94......3...8..75.......18..3...2..4..9......261...8......5..6....57.....`	initial
`.2......94......3...8..75.......18..3...2..4..9......261...8......5..6....57.....`	autosolve
`123456789457189236968237514276941853381625947594873162612398475739514628845762391`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (2)
A3: 1,9
B3: 3,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E8,E9: 1.. / E8 = 1  =>  2 pairs (_) / E9 = 1  =>  3 pairs (_)
G2,H3: 2.. / G2 = 2  =>  3 pairs (_) / H3 = 2  =>  3 pairs (_)
A4,C4: 2.. / A4 = 2  =>  3 pairs (_) / C4 = 2  =>  3 pairs (_)
D3,H3: 2.. / D3 = 2  =>  3 pairs (_) / H3 = 2  =>  3 pairs (_)
C1,B3: 3.. / C1 = 3  =>  8 pairs (_) / B3 = 3  =>  2 pairs (_)
I4,G6: 3.. / I4 = 3  =>  3 pairs (_) / G6 = 3  =>  2 pairs (_)
G1,I3: 4.. / G1 = 4  =>  3 pairs (_) / I3 = 4  =>  3 pairs (_)
A1,B2: 5.. / A1 = 5  =>  4 pairs (_) / B2 = 5  =>  3 pairs (_)
H7,I7: 5.. / H7 = 5  =>  2 pairs (_) / I7 = 5  =>  2 pairs (_)
E9,F9: 6.. / E9 = 6  =>  2 pairs (_) / F9 = 6  =>  3 pairs (_)
E4,E6: 7.. / E4 = 7  =>  3 pairs (_) / E6 = 7  =>  3 pairs (_)
H1,I2: 8.. / H1 = 8  =>  2 pairs (_) / I2 = 8  =>  2 pairs (_)
B5,A6: 8.. / B5 = 8  =>  4 pairs (_) / A6 = 8  =>  3 pairs (_)
B5,D5: 8.. / B5 = 8  =>  4 pairs (_) / D5 = 8  =>  3 pairs (_)
C2,A3: 9.. / C2 = 9  =>  4 pairs (_) / A3 = 9  =>  2 pairs (_)
H4,G5: 9.. / H4 = 9  =>  3 pairs (_) / G5 = 9  =>  4 pairs (_)
* DURATION: 0:00:09.819373  START: 10:19:55.298548  END: 10:20:05.117921 2020-10-18
* CP COUNT: (16)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:17.946455  START: 10:20:11.383291  END: 10:20:29.329746 2020-10-18
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00000401-240-base-pr-002.dot
* REASONING
* DIS # C2: 6,7 # B2: 6,7 => CTR => B2: 5
* PRF # C2: 6,7 + B2: 5 # C4: 6,7 => SOL
* STA # C2: 6,7 + B2: 5 + C4: 6,7
* CNT   2 HDP CHAINS /  29 HYP OPENED

Header Info

401;240;elev;21;11.40;11.40;2.60

Solution

position: 123456789457189236968237514276941853381625947594873162612398475739514628845762391 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 # C2: 1,9 => UNS
* INC # C2: 6,7 => UNS
* INC # D3: 1,9 => UNS
* INC # D3: 2,3,4,6 => UNS
* INC # C1: 3,6 => UNS
* INC # C1: 1,7 => UNS
* INC # D3: 3,6 => UNS
* INC # E3: 3,6 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C2: 1,9 => UNS
* INC # C2: 6,7 => UNS
* INC # D3: 1,9 => UNS
* INC # D3: 2,3,4,6 => UNS
* INC # C1: 3,6 => UNS
* INC # C1: 1,7 => UNS
* INC # D3: 3,6 => UNS
* INC # E3: 3,6 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # C2: 1,9 => UNS
* INC # C2: 6,7 => UNS
* INC # D3: 1,9 => UNS
* INC # D3: 2,3,4,6 => UNS
* INC # C1: 3,6 => UNS
* INC # C1: 1,7 => UNS
* INC # D3: 3,6 => UNS
* INC # E3: 3,6 => UNS
* INC # C2: 1,9 # B2: 5,7 => UNS
* INC # C2: 1,9 # B2: 6 => UNS
* INC # C2: 1,9 # A4: 5,7 => UNS
* INC # C2: 1,9 # A6: 5,7 => UNS
* INC # C2: 1,9 # D2: 1,9 => UNS
* INC # C2: 1,9 # D2: 2,6,8 => UNS
* INC # C2: 1,9 # D3: 1,9 => UNS
* INC # C2: 1,9 # D3: 2,3,4,6 => UNS
* INC # C2: 1,9 # C1: 3,6 => UNS
* INC # C2: 1,9 # C1: 7 => UNS
* INC # C2: 1,9 # D3: 3,6 => UNS
* INC # C2: 1,9 # E3: 3,6 => UNS
* INC # C2: 1,9 => UNS
* INC # C2: 6,7 # C1: 6,7 => UNS
* DIS # C2: 6,7 # B2: 6,7 => CTR => B2: 5
* INC # C2: 6,7 + B2: 5 # C1: 6,7 => UNS
* INC # C2: 6,7 + B2: 5 # C1: 1,3 => UNS
* INC # C2: 6,7 + B2: 5 # I2: 6,7 => UNS
* INC # C2: 6,7 + B2: 5 # I2: 1,8 => UNS
* PRF # C2: 6,7 + B2: 5 # C4: 6,7 => SOL
* STA # C2: 6,7 + B2: 5 + C4: 6,7
* CNT  28 HDP CHAINS /  29 HYP OPENED