There are 9 rows of numbers across and 9 columns of numbers down.
Numbers 1 through 9 need to go across and down.
You can only use each number once in each row, column, or 3×3 square.

l _ l _ l 8 ll _ l _ l 7 ll _ l _ l 2 l
l _ l 4 l 1 ll 5 l _ l _ ll _ l _ l _ l
l _ l _ l 6 ll _ l _ l _ ll _ l 8 l 5 l

l _ l _ l _ ll 9 l 3 l _ ll 8 l 7 l 1 l
l _ l 6 l _ ll _ l 1 l _ ll _ l 9 l _ l
l 1 l 9 l 3 ll _ l 8 l 4 ll _ l _ l _ l

l 7 l 2 l _ ll _ l _ l _ ll 9 l _ l _ l
l _ l _ l _ ll _ l _ l 9 ll 2 l 5 l _ l
l 6 l _ l _ ll 3 l _ l _ ll 4 l _ l _ l

There are 9 rows of numbers across and 9 columns of numbers down.
Numbers 1 through 9 need to go across and down.
You can only use each number once in each row, column, or 3×3 square.

l _ l _ l 4 ll 1 l _ l 5 ll _ l _ l 9 l
l 3 l _ l _ ll _ l _ l 8 ll 5 l _ l 7 l
l _ l _ l _ ll _ l 7 l _ ll 6 l _ l 1 l

l _ l 9 l _ ll _ l 1 l 2 ll _ l 5 l _ l
l _ l 3 l _ ll _ l _ l _ ll _ l 1 l _ l
l _ l 6 l _ ll 5 l 4 l _ ll _ l 8 l _ l

l 2 l _ l 3 ll _ l 8 l _ ll _ l _ l _ l
l 7 l _ l 6 ll 2 l _ l _ ll _ l _ l 3 l
l 9 l _ l _ ll 7 l _ l 4 ll 2 l _ l _ l

There are 9 rows of numbers across and 9 columns of numbers down.
Numbers 1 through 9 need to go across and down.
You can only use each number once in each row, column, or 3×3 square.

l _ l _ l 1 ll 3 l _ l _ ll _ l 9 l 2 l
l _ l _ l _ ll 4 l 7 l _ ll _ l 5 l 8 l
l 3 l _ l 8 ll _ l _ l 9 ll _ l _ l _ l

l _ l 9 l _ ll _ l 5 l 2 ll _ l _ l _ l
l 8 l _ l 6 ll _ l _ l _ ll 1 l _ l 5 l
l _ l _ l _ ll 8 l 3 l _ ll _ l 7 l _ l

l _ l _ l _ ll 6 l _ l _ ll 2 l _ l 4 l
l 6 l 4 l _ ll _ l 8 l 5 ll _ l _ l _ l
l 2 l 1 l _ ll _ l _ l 3 ll 5 l _ l _ l

There are 9 rows of numbers across and 9 columns of numbers down.
Numbers 1 through 9 need to go across and down.
You can only use each number once in each row, column, or 3×3 square.

l _ l 9 l _ ll 4 l _ l 3 ll 7 l _ l _ l
l _ l 2 l 3 ll _ l 6 l _ ll _ l _ l 4 l
l _ l _ l 1 ll _ l _ l _ ll _ l 3 l 5 l

l _ l _ l _ ll _ l 9 l _ ll _ l 5 l 1 l
l 8 l _ l _ ll 7 l _ l 6 ll _ l _ l 9 l
l 6 l 4 l _ ll _ l 2 l _ ll _ l _ l _ l

l 2 l 8 l _ ll _ l _ l _ ll 4 l _ l _ l
l 1 l _ l _ ll _ l 8 l _ ll 3 l 2 l _ l
l _ l _ l 7 ll 6 l _ l 2 ll _ l 1 l _ l

There are 9 rows of numbers across and 9 columns of numbers down.
Numbers 1 through 9 need to go across and down.
You can only use each number once in each row, column, or 3×3 square.

l _ l 7 l _ ll _ l _ l _ ll 6 l _ l 3 l
l _ l 9 l 3 ll _ l 5 l 2 ll _ l _ l _ l
l 5 l _ l _ ll _ l 1 l _ ll 9 l _ l _ l

l _ l 3 l _ ll 8 l _ l 1 ll _ l _ l 2 l
l 9 l _ l _ ll 5 l _ l 7 ll _ l _ l 8 l
l 2 l _ l _ ll 9 l _ l 4 ll _ l 7 l _ l

l _ l _ l 7 ll _ l 4 l _ ll _ l _ l 5 l
l _ l _ l _ ll 2 l 8 l _ ll 4 l 6 l _ l
l 8 l _ l 5 ll _ l _ l _ ll _ l 3 l _ l

There are 9 rows of numbers across and 9 columns of numbers down.
Numbers 1 through 9 need to go across and down.
You can only use each number once in each row, column, or 3×3 square.

l 6 l _ l 3 ll _ l _ l 1 ll _ l 4 l _ l
l _ l _ l 8 ll _ l _ l _ ll _ l 5 l 9 l
l 9 l _ l _ ll _ l 7 l 4 ll _ l _ l _ l

l _ l 7 l _ ll _ l 2 l _ ll 9 l _ l 3 l
l _ l _ l 1 ll 6 l _ l 5 ll 7 l _ l _ l
l 8 l _ l 2 ll _ l 3 l _ ll _ l 1 l _ l

l _ l _ l _ ll 2 l 9 l _ ll _ l _ l 1 l
l 1 l 3 l _ ll _ l _ l _ ll 6 l _ l _ l
l _ l 5 l _ ll 4 l _ l _ ll 3 l _ l 8 l

There are 9 rows of numbers across and 9 columns of numbers down.
Numbers 1 through 9 need to go across and down.
You can only use each number once in each row, column, or 3×3 square.

l _ l _ l _ ll 6 l 9 l _ ll 8 l _ l _ l
l _ l 6 l 8 ll _ l _ l _ ll 2 l 3 l _ l
l 9 l _ l 2 ll 3 l _ l _ ll _ l _ l _ l

l 4 l _ l _ ll _ l 3 l 1 ll _ l _ l 7 l
l 8 l 2 l _ ll _ l _ l _ ll _ l 1 l 3 l
l 6 l _ l _ ll 7 l 2 l _ ll _ l _ l 5 l

l _ l _ l _ ll _ l _ l 3 ll 1 l _ l 4 l
l _ l 4 l 3 ll _ l _ l _ ll 7 l 5 l _ l
l _ l _ l 9 ll _ l 5 l 4 ll _ l _ l _ l

There are 9 rows of numbers across and 9 columns of numbers down.
Numbers 1 through 9 need to go across and down.
You can only use each number once in each row, column, or 3×3 square.

l _ l _ l _ ll 2 l 3 l 8 ll _ l 1 l _ l
l _ l _ l 7 ll _ l _ l 1 ll _ l 8 l _ l
l 1 l _ l 2 ll _ l _ l _ ll _ l _ l 4 l

l 3 l _ l 8 ll _ l _ l _ ll 6 l _ l 5 l
l _ l _ l _ ll 6 l 9 l 3 ll _ l _ l _ l
l 4 l _ l 6 ll _ l _ l _ ll 7 l _ l 3 l

l 9 l _ l _ ll _ l _ l _ ll 4 l _ l 8 l
l _ l 6 l _ ll 1 l _ l _ ll 3 l _ l _ l
l _ l 5 l _ ll 8 l 7 l 4 ll _ l _ l _ l

I see two things: First, the number of blank squares vs pre-answered numbered squares. A puzzles that only has a couple blank squares will be easy.

Second, I suspect the number of unique digits used in pre-answers squares at the start would affect difficulty. For example, if a puzzle starts with 25 squares filled in, but only has 5′s, 6′s, 7′s, 8′s, and 9′s in those squares, then the blanks squares will be may be more difficult to find because you do not have any obvious way to rule out the possibility of a square being a 1, 2, 3, or 4. Conversely, if a puzzle started with 25 squares filled in, but made sure to give at least one of each digit (1-9) in the puzzle, then the player could always rule out some of each number for various squares and that would make things a little easier. I hope my description make sense.

Do any other Sudoku players have ideas on what makes a puzzle easy or hard? If you have an answer, please be specific…. it is hard to program specific game rules from vague information.

Thanks.