## How to create hard sudoku puzzles with only 20(or less)clues

Everything about Sudoku that doesn't fit in one of the other sections

### How to create hard sudoku puzzles with only 20(or less)clues

Hi,
I am a math teacher from Taiwan,and I am very much interested in
sudoku puzzles. I have made a program to solve and create sudoku puzzles .Now I have some questions:
1.what kinds of patterns can create a valid puzzle quickly ?
2.How to create hard sudoku puzzles with only 20 (or less)clues ?
Is there any rule exists in doing this ?

Hope someone can do me a favor . Many thanks !!
albert1950

Posts: 5
Joined: 14 June 2008

I think the basic strategy for making hard sudoku puzzles is to create lots of them and test them to see how hard they are. Some compilers have a theory that certain distributions of clues, such as diagonal type patterns, lead to more hard patterns. It may be that they are finding these patterns here because that's where they're searching for them, ie if they decided that patterns with pairs of clues next to each other had hard puzzles in them and started concentrating their searches there, they'd also find many hard puzzles. Also some compilers have techniques for altering a given puzzle to make a new one with similar, but hopefully slightly harder properties. These include removing two clues and then replacing them with another two clues. You'll find a lot of these ideas discussed here:
http://forum.enjoysudoku.com/viewtopic.php?t=4212
ab

Posts: 451
Joined: 06 September 2005

### diagonality

ab wrote:Some compilers have a theory that certain distributions of clues, such as diagonal type patterns, lead to more hard patterns. It may be that they are finding these patterns here because that's where they're searching for them, ie if they decided that patterns with pairs of clues next to each other had hard puzzles in them and started concentrating their searches there, they'd also find many hard puzzles.

looking in the Patterns Game Results ( using Sudoku Explainer 1.2.1 ratings ),
consider these 20-clue patterns
which are very similar
( differing only by shifting the rows by 1
and the columns likewise by 1
)
yet very opposite --
the one being very low in diagonality,
the other being entirely diagonal ( every 2 clues sharing a box never share a row or a column )

gsf wrote:
game 49
highest rating = 9.1
Code: Select all
` . . . . . . 1 2 .  . . . 3 9 . . . .  . . 4 . . . 5 6 .  . 7 . . . . . . 4  . 9 . . 8 . . . 6  . . . . . 2 . . .  5 . 9 . . . 7 . .  2 . 1 . . . . . .  . . . 8 4 . . . . `

JPF wrote:
game 57
highest rating = 10.4
Code: Select all
` . . 1 2 . . . . .  . 3 . . . 4 5 . .  6 . . . . . . 7 .  1 . . 7 . . . 2 .  . . . . 5 . . . .  . 8 . . . 9 . . 3  . 5 . . . . . . 4  . . 7 6 . . . . .  . . . . . 3 9 . . `

Pat

Posts: 3880
Joined: 18 July 2005