Analysis of xx-ph-00000492-L36-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 1....67...5..8......9.....4....9....7....3.2...8...3..3..1...7......261.....4...5 initial

Autosolve

position: 1....67...5..8......9.....4....9....7....3.2...8...3..3..1..47......261.....4...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: 0:00:53.797706

The following important HDP chains were detected:

* DIS # C7: 2 # I2: 1,9 => CTR => I2: 2,3,6
* DIS # C7: 2 + I2: 2,3,6 # F7: 8,9 => CTR => F7: 5
* DIS # C7: 2 + I2: 2,3,6 + F7: 5 # I5: 8,9 => CTR => I5: 1,6
* DIS # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 # C2: 3,4 => CTR => C2: 6,7
* DIS # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 + C2: 6,7 # F2: 1,7 => CTR => F2: 4,9
* PRF # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 + C2: 6,7 + F2: 4,9 # C5: 1,5 => SOL
* STA # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 + C2: 6,7 + F2: 4,9 + C5: 1,5
* CNT   6 HDP CHAINS /  59 HYP OPENED

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

Details

Positions

1....67...5..8......9.....4....9....7....3.2...8...3..3..1...7......261.....4...5 initial
1....67...5..8......9.....4....9....7....3.2...8...3..3..1..47......261.....4...5 autosolve
123456789456789132879231564231694857745813926968527341392165478584972613617348295 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
E7: 5,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B9,C9: 1.. / B9 = 1  =>  1 pairs (_) / C9 = 1  =>  1 pairs (_)
I7,G9: 2.. / I7 = 2  =>  5 pairs (_) / G9 = 2  =>  3 pairs (_)
B4,C4: 3.. / B4 = 3  =>  1 pairs (_) / C4 = 3  =>  2 pairs (_)
I8,H9: 3.. / I8 = 3  =>  4 pairs (_) / H9 = 3  =>  3 pairs (_)
D9,H9: 3.. / D9 = 3  =>  4 pairs (_) / H9 = 3  =>  3 pairs (_)
H4,H6: 4.. / H4 = 4  =>  1 pairs (_) / H6 = 4  =>  1 pairs (_)
E7,D9: 6.. / E7 = 6  =>  2 pairs (_) / D9 = 6  =>  7 pairs (_)
C2,B3: 7.. / C2 = 7  =>  2 pairs (_) / B3 = 7  =>  3 pairs (_)
I4,I6: 7.. / I4 = 7  =>  1 pairs (_) / I6 = 7  =>  1 pairs (_)
* DURATION: 0:00:04.991586  START: 02:24:10.426127  END: 02:24:15.417713 2020-10-26
* CP COUNT: (9)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:53.562003  START: 02:24:18.576561  END: 02:25:12.138564 2020-10-26
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00000492-L36-base-pr-002.dot
* REASONING
* DIS # C7: 2 # I2: 1,9 => CTR => I2: 2,3,6
* DIS # C7: 2 + I2: 2,3,6 # F7: 8,9 => CTR => F7: 5
* DIS # C7: 2 + I2: 2,3,6 + F7: 5 # I5: 8,9 => CTR => I5: 1,6
* DIS # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 # C2: 3,4 => CTR => C2: 6,7
* DIS # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 + C2: 6,7 # F2: 1,7 => CTR => F2: 4,9
* PRF # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 + C2: 6,7 + F2: 4,9 # C5: 1,5 => SOL
* STA # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 + C2: 6,7 + F2: 4,9 + C5: 1,5
* CNT   6 HDP CHAINS /  59 HYP OPENED

Header Info

492;L36;elev;21;11.40;1.20;1.20

Solution

position: 123456789456789132879231564231694857745813926968527341392165478584972613617348295 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 # C7: 5,6 => UNS
* INC # C7: 2 => UNS
* INC # E5: 5,6 => UNS
* INC # E6: 5,6 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C7: 5,6 => UNS
* INC # C7: 2 => UNS
* INC # E5: 5,6 => UNS
* INC # E6: 5,6 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # C7: 5,6 => UNS
* INC # C7: 2 => UNS
* INC # E5: 5,6 => UNS
* INC # E6: 5,6 => UNS
* INC # C7: 5,6 # C4: 5,6 => UNS
* INC # C7: 5,6 # C5: 5,6 => UNS
* INC # C7: 5,6 # E5: 5,6 => UNS
* INC # C7: 5,6 # E6: 5,6 => UNS
* INC # C7: 5,6 # D8: 8,9 => UNS
* INC # C7: 5,6 # D9: 8,9 => UNS
* INC # C7: 5,6 # F9: 8,9 => UNS
* INC # C7: 5,6 # B7: 8,9 => UNS
* INC # C7: 5,6 # I7: 8,9 => UNS
* INC # C7: 5,6 => UNS
* INC # C7: 2 # B1: 3,4 => UNS
* INC # C7: 2 # C2: 3,4 => UNS
* INC # C7: 2 # D1: 3,4 => UNS
* INC # C7: 2 # D1: 2,5,9 => UNS
* INC # C7: 2 # C4: 3,4 => UNS
* INC # C7: 2 # C4: 1,5,6 => UNS
* DIS # C7: 2 # I2: 1,9 => CTR => I2: 2,3,6
* INC # C7: 2 + I2: 2,3,6 # F2: 1,9 => UNS
* INC # C7: 2 + I2: 2,3,6 # F2: 4,7 => UNS
* INC # C7: 2 + I2: 2,3,6 # E5: 5,6 => UNS
* INC # C7: 2 + I2: 2,3,6 # E6: 5,6 => UNS
* INC # C7: 2 + I2: 2,3,6 # D8: 3,7 => UNS
* INC # C7: 2 + I2: 2,3,6 # D9: 3,7 => UNS
* INC # C7: 2 + I2: 2,3,6 # E3: 3,7 => UNS
* INC # C7: 2 + I2: 2,3,6 # E3: 1,2,5 => UNS
* INC # C7: 2 + I2: 2,3,6 # I8: 8,9 => UNS
* INC # C7: 2 + I2: 2,3,6 # H9: 8,9 => UNS
* INC # C7: 2 + I2: 2,3,6 # B7: 8,9 => UNS
* DIS # C7: 2 + I2: 2,3,6 # F7: 8,9 => CTR => F7: 5
* INC # C7: 2 + I2: 2,3,6 + F7: 5 # I1: 8,9 => UNS
* DIS # C7: 2 + I2: 2,3,6 + F7: 5 # I5: 8,9 => CTR => I5: 1,6
* INC # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 # I1: 8,9 => UNS
* INC # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 # I1: 2,3 => UNS
* INC # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 # I8: 8,9 => UNS
* INC # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 # H9: 8,9 => UNS
* INC # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 # I1: 8,9 => UNS
* INC # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 # I1: 2,3 => UNS
* INC # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 # B1: 3,4 => UNS
* DIS # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 # C2: 3,4 => CTR => C2: 6,7
* INC # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 + C2: 6,7 # B1: 3,4 => UNS
* INC # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 + C2: 6,7 # B1: 2,8 => UNS
* INC # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 + C2: 6,7 # D1: 3,4 => UNS
* INC # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 + C2: 6,7 # D1: 2,5,9 => UNS
* INC # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 + C2: 6,7 # C4: 3,4 => UNS
* INC # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 + C2: 6,7 # C4: 1,5,6 => UNS
* DIS # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 + C2: 6,7 # F2: 1,7 => CTR => F2: 4,9
* INC # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 + C2: 6,7 + F2: 4,9 # E3: 1,7 => UNS
* INC # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 + C2: 6,7 + F2: 4,9 # E3: 1,7 => UNS
* INC # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 + C2: 6,7 + F2: 4,9 # E3: 2,3,5 => UNS
* INC # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 + C2: 6,7 + F2: 4,9 # F4: 1,7 => UNS
* INC # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 + C2: 6,7 + F2: 4,9 # F6: 1,7 => UNS
* INC # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 + C2: 6,7 + F2: 4,9 # E6: 1,5 => UNS
* INC # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 + C2: 6,7 + F2: 4,9 # E6: 2,7 => UNS
* PRF # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 + C2: 6,7 + F2: 4,9 # C5: 1,5 => SOL
* STA # C7: 2 + I2: 2,3,6 + F7: 5 + I5: 1,6 + C2: 6,7 + F2: 4,9 + C5: 1,5
* CNT  58 HDP CHAINS /  59 HYP OPENED