72 Free Printable Sudoku Puzzles | SaturdayGift - Free Printable

The user has uploaded an image containing 4 Sudoku puzzles labeled as "HARD". They want me to solve them. Let me work through each puzzle carefully.

Let me first transcribe each puzzle from the image, then solve them using a Sudoku solver approach.

Puzzle #1:
```
_ _ 6 | _ 7 9 | _ _ 3
7 8 _ | 2 1 _ | _ _ 6
1 _ 3 | _ _ 6 | _ 8 9
------+-------+------
_ 1 4 | _ _ _ | 8 _ _
_ 6 _ | 9 _ 7 | 2 _ _
_ _ 7 | 1 2 _ | 3 6 _
------+-------+------
9 7 8 | _ _ _ | 6 4 _
5 _ _ | 4 _ 2 | 9 _ _
_ _ _ | _ 9 _ | _ 3 1
```

Puzzle #2:
```
_ 4 _ | 3 _ 1 | _ 7 _
9 _ _ | 4 _ 2 | _ _ 5
5 3 _ | _ _ _ | 2 _ 6
------+-------+------
_ _ _ | _ _ _ | 3 2 1
_ 5 _ | _ 1 _ | 9 _ 7
1 _ _ | 8 7 9 | _ _ _
------+-------+------
_ _ 5 | _ _ 4 | _ 9 8
_ _ 7 | 6 _ 5 | 4 _ 2
2 1 4 | 9 8 _ | 5 _ _
```

Now I'm looking at Puzzle #3 and Puzzle #4, which have similar grid structures with some numbers already filled in. I need to extract all the given values accurately before attempting to solve these harder puzzles. I'm going to write a backtracking solver to handle these Sudoku puzzles systematically rather than trying to solve them manually.