# Original Sudoku

level: deep

position: 1.......2.2.....6...34..5.....8.5.....8.3.9.....9.4.....53..4...6......77......1. initial

# Autosolve

position: 1.......2.2.....6...34..5.....8.5.....8.3.9.....9.4.....53..4...6......77......1. autosolve

# Pair Reduction Variants

## Deep Constraint Pair Analysis

Time used: 0:00:00.000005

List of important HDP chains detected for C1,A3: 6..:

```* DIS # C1: 6 # B3: 8,9 => CTR => B3: 7
* DIS # C1: 6 + B3: 7 # A8: 8,9 => CTR => A8: 2,3,4
* DIS # C1: 6 + B3: 7 + A8: 2,3,4 # E7: 2,6 => CTR => E7: 1,7,8,9
* DIS # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 # E9: 2,6 => CTR => E9: 4,5,8,9
* DIS # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 # F5: 2,6 => CTR => F5: 1,7
* DIS # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 + F5: 1,7 # F7: 2,6 => CTR => F7: 1,7,8,9
* DIS # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 + F5: 1,7 + F7: 1,7,8,9 # F9: 8 => CTR => F9: 2,6
* DIS # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 + F5: 1,7 + F7: 1,7,8,9 + F9: 2,6 # B1: 4,9 => CTR => B1: 5
* DIS # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 + F5: 1,7 + F7: 1,7,8,9 + F9: 2,6 + B1: 5 # A2: 4,9 => CTR => A2: 8
* PRF # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 + F5: 1,7 + F7: 1,7,8,9 + F9: 2,6 + B1: 5 + A2: 8 # E4: 2,7 => SOL
* STA # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 + F5: 1,7 + F7: 1,7,8,9 + F9: 2,6 + B1: 5 + A2: 8 + E4: 2,7
* CNT  10 HDP CHAINS /  31 HYP OPENED
```

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

# Details

This sudoku is deep. Here is some information that may be helpful on how to proceed.

## Positions

 1.......2.2.....6...34..5.....8.5.....8.3.9.....9.4.....53..4...6......77......1. initial 1.......2.2.....6...34..5.....8.5.....8.3.9.....9.4.....53..4...6......77......1. autosolve

level: deep

## Pairing Analysis

```--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B7,C8: 1.. / B7 = 1  =>  0 pairs (_) / C8 = 1  =>  4 pairs (_)
E3,F3: 2.. / E3 = 2  =>  0 pairs (_) / F3 = 2  =>  0 pairs (_)
F1,F2: 3.. / F1 = 3  =>  1 pairs (_) / F2 = 3  =>  0 pairs (_)
A8,B9: 3.. / A8 = 3  =>  1 pairs (_) / B9 = 3  =>  0 pairs (_)
H1,I2: 4.. / H1 = 4  =>  0 pairs (_) / I2 = 4  =>  1 pairs (_)
E8,E9: 4.. / E8 = 4  =>  0 pairs (_) / E9 = 4  =>  1 pairs (_)
B1,A2: 5.. / B1 = 5  =>  1 pairs (_) / A2 = 5  =>  1 pairs (_)
H8,I9: 5.. / H8 = 5  =>  1 pairs (_) / I9 = 5  =>  1 pairs (_)
C1,A3: 6.. / C1 = 6  =>  4 pairs (_) / A3 = 6  =>  0 pairs (_)
E7,F7: 7.. / E7 = 7  =>  0 pairs (_) / F7 = 7  =>  0 pairs (_)
* DURATION: 0:00:07.918641  START: 17:56:25.605432  END: 17:56:33.524073 2017-04-29
* CP COUNT: (10)

--------------------------------------------------
* DEEP CONSTRAINT PAIRS (PAIR REDUCTION)
C1,A3: 6.. / C1 = 6 ==>  0 pairs (*) / A3 = 6  =>  0 pairs (X)
* DURATION: 0:00:36.790682  START: 17:56:33.524535  END: 17:57:10.315217 2017-04-29
* REASONING C1,A3: 6..
* DIS # C1: 6 # B3: 8,9 => CTR => B3: 7
* DIS # C1: 6 + B3: 7 # A8: 8,9 => CTR => A8: 2,3,4
* DIS # C1: 6 + B3: 7 + A8: 2,3,4 # E7: 2,6 => CTR => E7: 1,7,8,9
* DIS # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 # E9: 2,6 => CTR => E9: 4,5,8,9
* DIS # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 # F5: 2,6 => CTR => F5: 1,7
* DIS # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 + F5: 1,7 # F7: 2,6 => CTR => F7: 1,7,8,9
* DIS # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 + F5: 1,7 + F7: 1,7,8,9 # F9: 8 => CTR => F9: 2,6
* DIS # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 + F5: 1,7 + F7: 1,7,8,9 + F9: 2,6 # B1: 4,9 => CTR => B1: 5
* DIS # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 + F5: 1,7 + F7: 1,7,8,9 + F9: 2,6 + B1: 5 # A2: 4,9 => CTR => A2: 8
* PRF # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 + F5: 1,7 + F7: 1,7,8,9 + F9: 2,6 + B1: 5 + A2: 8 # E4: 2,7 => SOL
* STA # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 + F5: 1,7 + F7: 1,7,8,9 + F9: 2,6 + B1: 5 + A2: 8 + E4: 2,7
* CNT  10 HDP CHAINS /  31 HYP OPENED
* DCP COUNT: (1)
* SOLUTION FOUND
```

```dukdiamond2,coloin,95531,97759,,,,3541,2132
```

# Appendix: Full HDP Chains

## A1. Deep Constraint Pair Analysis

Full list of HDP chains traversed for C1,A3: 6..:

```* INC # C1: 6 # B1: 8,9 => UNS
* INC # C1: 6 # A2: 8,9 => UNS
* DIS # C1: 6 # B3: 8,9 => CTR => B3: 7
* INC # C1: 6 + B3: 7 # A7: 8,9 => UNS
* DIS # C1: 6 + B3: 7 # A8: 8,9 => CTR => A8: 2,3,4
* INC # C1: 6 + B3: 7 + A8: 2,3,4 # A7: 8,9 => UNS
* INC # C1: 6 + B3: 7 + A8: 2,3,4 # A7: 2 => UNS
* INC # C1: 6 + B3: 7 + A8: 2,3,4 # B1: 8,9 => UNS
* INC # C1: 6 + B3: 7 + A8: 2,3,4 # A2: 8,9 => UNS
* INC # C1: 6 + B3: 7 + A8: 2,3,4 # A7: 8,9 => UNS
* INC # C1: 6 + B3: 7 + A8: 2,3,4 # A7: 2 => UNS
* INC # C1: 6 + B3: 7 + A8: 2,3,4 # E1: 5,7 => UNS
* INC # C1: 6 + B3: 7 + A8: 2,3,4 # D2: 5,7 => UNS
* INC # C1: 6 + B3: 7 + A8: 2,3,4 # E2: 5,7 => UNS
* INC # C1: 6 + B3: 7 + A8: 2,3,4 # E4: 2,6 => UNS
* INC # C1: 6 + B3: 7 + A8: 2,3,4 # E6: 2,6 => UNS
* DIS # C1: 6 + B3: 7 + A8: 2,3,4 # E7: 2,6 => CTR => E7: 1,7,8,9
* DIS # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 # E9: 2,6 => CTR => E9: 4,5,8,9
* INC # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 # E4: 2,6 => UNS
* INC # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 # E6: 2,6 => UNS
* DIS # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 # F5: 2,6 => CTR => F5: 1,7
* DIS # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 + F5: 1,7 # F7: 2,6 => CTR => F7: 1,7,8,9
* INC # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 + F5: 1,7 + F7: 1,7,8,9 # F9: 2,6 => UNS
* INC # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 + F5: 1,7 + F7: 1,7,8,9 # F9: 2,6 => UNS
* DIS # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 + F5: 1,7 + F7: 1,7,8,9 # F9: 8 => CTR => F9: 2,6
* DIS # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 + F5: 1,7 + F7: 1,7,8,9 + F9: 2,6 # B1: 4,9 => CTR => B1: 5
* DIS # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 + F5: 1,7 + F7: 1,7,8,9 + F9: 2,6 + B1: 5 # A2: 4,9 => CTR => A2: 8
* INC # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 + F5: 1,7 + F7: 1,7,8,9 + F9: 2,6 + B1: 5 + A2: 8 # E4: 2,6 => UNS
* INC # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 + F5: 1,7 + F7: 1,7,8,9 + F9: 2,6 + B1: 5 + A2: 8 # E6: 2,6 => UNS
* PRF # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 + F5: 1,7 + F7: 1,7,8,9 + F9: 2,6 + B1: 5 + A2: 8 # E4: 2,7 => SOL
* STA # C1: 6 + B3: 7 + A8: 2,3,4 + E7: 1,7,8,9 + E9: 4,5,8,9 + F5: 1,7 + F7: 1,7,8,9 + F9: 2,6 + B1: 5 + A2: 8 + E4: 2,7
* CNT  30 HDP CHAINS /  31 HYP OPENED
```