Analysis of xx-ph-00276983-12_12_03-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: ........1..2..3.4..3..5.6......6...7.8...2.9.2..1..5....37......49......8....9.3. initial

Autosolve

position: ......3.1..2..3.4..3..5.6......6...7.8...2.9.2..1..5....37......49......8....9.3. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

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

Pair Reduction

Pair Reduction

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

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:30.790719

The following important HDP chains were detected:

* DIS # G4: 1,4 # D1: 6,8 => CTR => D1: 2,4,9
* DIS # G4: 1,4 + D1: 2,4,9 # D8: 6,8 => CTR => D8: 2,3,5
* DIS # G4: 1,4 + D1: 2,4,9 + D8: 2,3,5 # H1: 7,8 => CTR => H1: 5
* PRF # G4: 1,4 + D1: 2,4,9 + D8: 2,3,5 + H1: 5 # E6: 4,7 => SOL
* STA # G4: 1,4 + D1: 2,4,9 + D8: 2,3,5 + H1: 5 + E6: 4,7
* CNT   4 HDP CHAINS /  28 HYP OPENED

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

Details

Positions

........1..2..3.4..3..5.6......6...7.8...2.9.2..1..5....37......49......8....9.3. initial
......3.1..2..3.4..3..5.6......6...7.8...2.9.2..1..5....37......49......8....9.3. autosolve
678294351152673849934851672315968427487532196296147583523786914749315268861429735 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (2)
G5: 1,4
H6: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E2,F3: 1.. / E2 = 1  =>  3 pairs (_) / F3 = 1  =>  2 pairs (_)
G4,H4: 2.. / G4 = 2  =>  3 pairs (_) / H4 = 2  =>  4 pairs (_)
B7,B9: 2.. / B7 = 2  =>  2 pairs (_) / B9 = 2  =>  3 pairs (_)
A4,A5: 3.. / A4 = 3  =>  2 pairs (_) / A5 = 3  =>  6 pairs (_)
I5,I6: 3.. / I5 = 3  =>  7 pairs (_) / I6 = 3  =>  3 pairs (_)
D8,E8: 3.. / D8 = 3  =>  3 pairs (_) / E8 = 3  =>  4 pairs (_)
A4,D4: 3.. / A4 = 3  =>  2 pairs (_) / D4 = 3  =>  6 pairs (_)
E6,I6: 3.. / E6 = 3  =>  7 pairs (_) / I6 = 3  =>  3 pairs (_)
H1,I2: 5.. / H1 = 5  =>  3 pairs (_) / I2 = 5  =>  2 pairs (_)
C1,C3: 8.. / C1 = 8  =>  2 pairs (_) / C3 = 8  =>  4 pairs (_)
D4,E6: 9.. / D4 = 9  =>  4 pairs (_) / E6 = 9  =>  4 pairs (_)
G7,I7: 9.. / G7 = 9  =>  3 pairs (_) / I7 = 9  =>  5 pairs (_)
B6,E6: 9.. / B6 = 9  =>  4 pairs (_) / E6 = 9  =>  4 pairs (_)
G2,G7: 9.. / G2 = 9  =>  5 pairs (_) / G7 = 9  =>  3 pairs (_)
* DURATION: 0:00:10.252367  START: 16:02:46.331777  END: 16:02:56.584144 2020-12-24
* CP COUNT: (14)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:30.608994  START: 16:03:05.633869  END: 16:03:36.242863 2020-12-24
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00276983-12_12_03-base-pr-002.dot
* REASONING
* DIS # G4: 1,4 # D1: 6,8 => CTR => D1: 2,4,9
* DIS # G4: 1,4 + D1: 2,4,9 # D8: 6,8 => CTR => D8: 2,3,5
* DIS # G4: 1,4 + D1: 2,4,9 + D8: 2,3,5 # H1: 7,8 => CTR => H1: 5
* PRF # G4: 1,4 + D1: 2,4,9 + D8: 2,3,5 + H1: 5 # E6: 4,7 => SOL
* STA # G4: 1,4 + D1: 2,4,9 + D8: 2,3,5 + H1: 5 + E6: 4,7
* CNT   4 HDP CHAINS /  28 HYP OPENED

Header Info

276983;12_12_03;dob;22;11.30;1.20;1.20

Solution

position: 678294351152673849934851672315968427487532196296147583523786914749315268861429735 solved
Solution

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 # G4: 1,4 => UNS
* INC # G4: 2,8 => UNS
* INC # A5: 1,4 => UNS
* INC # C5: 1,4 => UNS
* INC # G7: 1,4 => UNS
* INC # G9: 1,4 => UNS
* INC # I6: 6,8 => UNS
* INC # I6: 3,4 => UNS
* INC # H7: 6,8 => UNS
* INC # H8: 6,8 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G4: 1,4 => UNS
* INC # G4: 2,8 => UNS
* INC # A5: 1,4 => UNS
* INC # C5: 1,4 => UNS
* INC # G7: 1,4 => UNS
* INC # G9: 1,4 => UNS
* INC # I6: 6,8 => UNS
* INC # I6: 3,4 => UNS
* INC # H7: 6,8 => UNS
* INC # H8: 6,8 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # G4: 1,4 => UNS
* INC # G4: 2,8 => UNS
* INC # A5: 1,4 => UNS
* INC # C5: 1,4 => UNS
* INC # G7: 1,4 => UNS
* INC # G9: 1,4 => UNS
* INC # I6: 6,8 => UNS
* INC # I6: 3,4 => UNS
* INC # H7: 6,8 => UNS
* INC # H8: 6,8 => UNS
* DIS # G4: 1,4 # D1: 6,8 => CTR => D1: 2,4,9
* INC # G4: 1,4 + D1: 2,4,9 # F1: 6,8 => UNS
* INC # G4: 1,4 + D1: 2,4,9 # F1: 6,8 => UNS
* INC # G4: 1,4 + D1: 2,4,9 # F1: 4,7 => UNS
* DIS # G4: 1,4 + D1: 2,4,9 # D8: 6,8 => CTR => D8: 2,3,5
* INC # G4: 1,4 + D1: 2,4,9 + D8: 2,3,5 # F1: 6,8 => UNS
* INC # G4: 1,4 + D1: 2,4,9 + D8: 2,3,5 # F1: 4,7 => UNS
* DIS # G4: 1,4 + D1: 2,4,9 + D8: 2,3,5 # H1: 7,8 => CTR => H1: 5
* INC # G4: 1,4 + D1: 2,4,9 + D8: 2,3,5 + H1: 5 # G2: 7,8 => UNS
* INC # G4: 1,4 + D1: 2,4,9 + D8: 2,3,5 + H1: 5 # G2: 7,8 => UNS
* INC # G4: 1,4 + D1: 2,4,9 + D8: 2,3,5 + H1: 5 # G2: 9 => UNS
* INC # G4: 1,4 + D1: 2,4,9 + D8: 2,3,5 + H1: 5 # C3: 7,8 => UNS
* INC # G4: 1,4 + D1: 2,4,9 + D8: 2,3,5 + H1: 5 # F3: 7,8 => UNS
* INC # G4: 1,4 + D1: 2,4,9 + D8: 2,3,5 + H1: 5 # H8: 7,8 => UNS
* INC # G4: 1,4 + D1: 2,4,9 + D8: 2,3,5 + H1: 5 # H8: 1,6 => UNS
* INC # G4: 1,4 + D1: 2,4,9 + D8: 2,3,5 + H1: 5 # E5: 4,7 => UNS
* PRF # G4: 1,4 + D1: 2,4,9 + D8: 2,3,5 + H1: 5 # E6: 4,7 => SOL
* STA # G4: 1,4 + D1: 2,4,9 + D8: 2,3,5 + H1: 5 + E6: 4,7
* CNT  27 HDP CHAINS /  28 HYP OPENED