Analysis of xx-ph-00001330-420-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: ..34....9.5.......6.....4..2...6..7...89..1.......8..3...8....1..4..13...7..2..5. initial

Autosolve

position: ..34....945.......6.....4..2...6..7...89..1.......8..3...8....1..4..13...7..2..5. 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: 0:00:55.850288

The following important HDP chains were detected:

* DIS # F7: 3,6 # D2: 1,2,7 => CTR => D2: 3,6
* DIS # F9: 3,6 # G4: 5,8 => CTR => G4: 9
* DIS # F9: 3,6 + G4: 9 # C6: 1,9 => CTR => C6: 5,6,7
* DIS # F9: 3,6 + G4: 9 + C6: 5,6,7 # F2: 3,6 => CTR => F2: 2,7,9
* DIS # F9: 3,6 + G4: 9 + C6: 5,6,7 + F2: 2,7,9 # B1: 1,8 => CTR => B1: 2
* DIS # F9: 3,6 + G4: 9 + C6: 5,6,7 + F2: 2,7,9 + B1: 2 # A6: 1,9 => CTR => A6: 7
* PRF # F9: 3,6 + G4: 9 + C6: 5,6,7 + F2: 2,7,9 + B1: 2 + A6: 7 => SOL
* STA F9: 3,6
* CNT   7 HDP CHAINS /  59 HYP OPENED

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

Details

Positions

..34....9.5.......6.....4..2...6..7...89..1.......8..3...8....1..4..13...7..2..5. initial
..34....945.......6.....4..2...6..7...89..1.......8..3...8....1..4..13...7..2..5. autosolve
123456789457189236689732415215364978348975162796218543532847691864591327971623854 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
D9: 3,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A9,C9: 1.. / A9 = 1  =>  4 pairs (_) / C9 = 1  =>  2 pairs (_)
F5,D6: 2.. / F5 = 2  =>  2 pairs (_) / D6 = 2  =>  1 pairs (_)
H2,H3: 3.. / H2 = 3  =>  1 pairs (_) / H3 = 3  =>  1 pairs (_)
H7,I9: 4.. / H7 = 4  =>  4 pairs (_) / I9 = 4  =>  2 pairs (_)
F9,I9: 4.. / F9 = 4  =>  4 pairs (_) / I9 = 4  =>  2 pairs (_)
G1,I3: 5.. / G1 = 5  =>  2 pairs (_) / I3 = 5  =>  2 pairs (_)
G7,I8: 7.. / G7 = 7  =>  1 pairs (_) / I8 = 7  =>  3 pairs (_)
G4,I4: 8.. / G4 = 8  =>  4 pairs (_) / I4 = 8  =>  3 pairs (_)
* DURATION: 0:00:05.377640  START: 09:20:54.834537  END: 09:21:00.212177 2020-11-27
* CP COUNT: (8)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:55.471443  START: 09:21:04.309319  END: 09:21:59.780762 2020-11-27
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00001330-420-base-pr-002.dot
* REASONING
* DIS # F7: 3,6 # D2: 1,2,7 => CTR => D2: 3,6
* DIS # F9: 3,6 # G4: 5,8 => CTR => G4: 9
* DIS # F9: 3,6 + G4: 9 # C6: 1,9 => CTR => C6: 5,6,7
* DIS # F9: 3,6 + G4: 9 + C6: 5,6,7 # F2: 3,6 => CTR => F2: 2,7,9
* DIS # F9: 3,6 + G4: 9 + C6: 5,6,7 + F2: 2,7,9 # B1: 1,8 => CTR => B1: 2
* DIS # F9: 3,6 + G4: 9 + C6: 5,6,7 + F2: 2,7,9 + B1: 2 # A6: 1,9 => CTR => A6: 7
* PRF # F9: 3,6 + G4: 9 + C6: 5,6,7 + F2: 2,7,9 + B1: 2 + A6: 7 => SOL
* STA F9: 3,6
* CNT   7 HDP CHAINS /  59 HYP OPENED

Header Info

1330;420;elev;22;11.30;1.20;1.20

Solution

position: 123456789457189236689732415215364978348975162796218543532847691864591327971623854 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 # F7: 3,6 => UNS
* INC # F9: 3,6 => UNS
* INC # D2: 3,6 => UNS
* INC # D2: 1,2,7 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F7: 3,6 => UNS
* INC # F9: 3,6 => UNS
* INC # D2: 3,6 => UNS
* INC # D2: 1,2,7 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # F7: 3,6 => UNS
* INC # F9: 3,6 => UNS
* INC # D2: 3,6 => UNS
* INC # D2: 1,2,7 => UNS
* INC # F7: 3,6 # B7: 3,6 => UNS
* INC # F7: 3,6 # B7: 2,9 => UNS
* INC # F7: 3,6 # F2: 3,6 => UNS
* INC # F7: 3,6 # F2: 2,7,9 => UNS
* INC # F7: 3,6 # E7: 5,7 => UNS
* INC # F7: 3,6 # E8: 5,7 => UNS
* INC # F7: 3,6 # D3: 5,7 => UNS
* INC # F7: 3,6 # D6: 5,7 => UNS
* INC # F7: 3,6 # D2: 3,6 => UNS
* DIS # F7: 3,6 # D2: 1,2,7 => CTR => D2: 3,6
* INC # F7: 3,6 + D2: 3,6 # E7: 4,9 => UNS
* INC # F7: 3,6 + D2: 3,6 # E7: 5,7 => UNS
* INC # F7: 3,6 + D2: 3,6 # F2: 3,6 => UNS
* INC # F7: 3,6 + D2: 3,6 # F2: 2,7,9 => UNS
* INC # F7: 3,6 + D2: 3,6 # H2: 3,6 => UNS
* INC # F7: 3,6 + D2: 3,6 # H2: 1,2,8 => UNS
* INC # F7: 3,6 + D2: 3,6 # D6: 1,5 => UNS
* INC # F7: 3,6 + D2: 3,6 # E6: 1,5 => UNS
* INC # F7: 3,6 + D2: 3,6 # C4: 1,5 => UNS
* INC # F7: 3,6 + D2: 3,6 # C4: 9 => UNS
* INC # F7: 3,6 + D2: 3,6 # D3: 1,5 => UNS
* INC # F7: 3,6 + D2: 3,6 # D3: 2,7 => UNS
* INC # F7: 3,6 + D2: 3,6 # B7: 3,6 => UNS
* INC # F7: 3,6 + D2: 3,6 # B7: 2,9 => UNS
* INC # F7: 3,6 + D2: 3,6 # F2: 3,6 => UNS
* INC # F7: 3,6 + D2: 3,6 # F2: 2,7,9 => UNS
* INC # F7: 3,6 + D2: 3,6 # E7: 5,7 => UNS
* INC # F7: 3,6 + D2: 3,6 # E8: 5,7 => UNS
* INC # F7: 3,6 + D2: 3,6 # D3: 5,7 => UNS
* INC # F7: 3,6 + D2: 3,6 # D6: 5,7 => UNS
* INC # F7: 3,6 + D2: 3,6 # E7: 4,9 => UNS
* INC # F7: 3,6 + D2: 3,6 # E7: 5,7 => UNS
* INC # F7: 3,6 + D2: 3,6 => UNS
* DIS # F9: 3,6 # G4: 5,8 => CTR => G4: 9
* INC # F9: 3,6 + G4: 9 # C2: 1,9 => UNS
* INC # F9: 3,6 + G4: 9 # C3: 1,9 => UNS
* DIS # F9: 3,6 + G4: 9 # C6: 1,9 => CTR => C6: 5,6,7
* INC # F9: 3,6 + G4: 9 + C6: 5,6,7 # C2: 1,9 => UNS
* INC # F9: 3,6 + G4: 9 + C6: 5,6,7 # C3: 1,9 => UNS
* INC # F9: 3,6 + G4: 9 + C6: 5,6,7 # E7: 5,7 => UNS
* INC # F9: 3,6 + G4: 9 + C6: 5,6,7 # F7: 5,7 => UNS
* INC # F9: 3,6 + G4: 9 + C6: 5,6,7 # E8: 5,7 => UNS
* INC # F9: 3,6 + G4: 9 + C6: 5,6,7 # D3: 5,7 => UNS
* INC # F9: 3,6 + G4: 9 + C6: 5,6,7 # D6: 5,7 => UNS
* INC # F9: 3,6 + G4: 9 + C6: 5,6,7 # D2: 3,6 => UNS
* INC # F9: 3,6 + G4: 9 + C6: 5,6,7 # D2: 1,2,7 => UNS
* DIS # F9: 3,6 + G4: 9 + C6: 5,6,7 # F2: 3,6 => CTR => F2: 2,7,9
* INC # F9: 3,6 + G4: 9 + C6: 5,6,7 + F2: 2,7,9 # H2: 1,8 => UNS
* INC # F9: 3,6 + G4: 9 + C6: 5,6,7 + F2: 2,7,9 # H3: 1,8 => UNS
* INC # F9: 3,6 + G4: 9 + C6: 5,6,7 + F2: 2,7,9 # A1: 1,8 => UNS
* DIS # F9: 3,6 + G4: 9 + C6: 5,6,7 + F2: 2,7,9 # B1: 1,8 => CTR => B1: 2
* INC # F9: 3,6 + G4: 9 + C6: 5,6,7 + F2: 2,7,9 + B1: 2 # H2: 1,8 => UNS
* INC # F9: 3,6 + G4: 9 + C6: 5,6,7 + F2: 2,7,9 + B1: 2 # H3: 1,8 => UNS
* DIS # F9: 3,6 + G4: 9 + C6: 5,6,7 + F2: 2,7,9 + B1: 2 # A6: 1,9 => CTR => A6: 7
* PRF # F9: 3,6 + G4: 9 + C6: 5,6,7 + F2: 2,7,9 + B1: 2 + A6: 7 => SOL
* STA F9: 3,6
* CNT  59 HDP CHAINS /  59 HYP OPENED