## Why Sudoku Is so designed?

Advanced methods and approaches for solving Sudoku puzzles

### Why Sudoku Is so designed?

I am observing every Sudoku puzzles appearing in daily newspapers. The thing surprising me is all the sudoku puzzles are wriiten such a way that it looks like a mirror image. If you are not understanding what I have said Please compare first 3x3 region and ninth 3x3 region,2nd 3x3 region and 8th 3x3 region,3rd region and 7 th region, 4th region and 6 th region. Now I think you have got my words, Ok. Any answers why it is so designed? please reply. I am very curious to know.
nagesha

Posts: 1
Joined: 24 July 2005

That would be 'rotational symmetry' you're on about then. Some (Pappocom/Wayne's) have this property, others don't. As I learned yesterday, the symmetrical appearance is apparently a Japanese thing, originally they (sudoku) weren't.

Probably just a preference thing.
Karyobin

Posts: 396
Joined: 18 June 2005

Yes, I've noticed that too -- sometimes when entering a puzzle into Simple Sudoku, and when I go to start it, it says, (paraphrasing), "your puzzle isn't symmetrical, start anyway?"

I suspect Karyobin is correct, in that it is a beauty thing.
Dusty Chalk

Posts: 21
Joined: 15 August 2005

Dell Magazine's Number Place had no symmetry -- but it wasn't
called Sudoku. Nikoli made three changes:

1) Reduced the number of clues allowed to under 30.
2) Arranged the clues in a symmetrical pattern.
3) Created each puzzle by hand.

Nikoli nearly always uses 180 degree rotational symmetry,
as does Pappocom. Most (but not all) others seem to be following
suit. In addition to the aesthic aspect, having some sort of order
to the placement of clues, there's another advantage -- it's
easier to tell if you've transcribed it incorrectly, as the missing
or missplaced clue will stick out.

I've seen puzzles with all of the following types of order in
Japanese puzzle magazines and elsewhere. Have I missed any?

1) Vertical mirror only.
Code: Select all
`. . . . . . . . . . . 9 8 4 5 2 . . . . 2 7 . 6 8 . . . 2 4 . . . 9 6 . . . . . . . . . . . 7 5 1 8 9 4 2 . 5 6 3 . . . 1 8 9 . 8 . . . . . 3 . . . . . . . . . . `

2) Vertical and horizontal mirror.
(Subset of those with 180 degree rotation)
Code: Select all
`. . . . . . . . . . 3 . . 1 . . 4 . . . 5 . 7 . 2 . . 7 . 9 4 . 8 3 . 6 . . . . . . . . . 5 . 1 3 . 7 8 . 4 . . 7 . 9 . 5 . . . 4 . . 8 . . 2 . . . . . . . . . . `

3) 180 degree rotation, no reflections
This is the current standard form.
Code: Select all
`. . . . . . . 5 . . 9 4 3 . . . . 8 6 . . . 2 8 . . . . . . . 5 . . 6 . . 2 . . 6 . . 4 . . 3 . . 4 . . . . . . . 1 7 . . . 6 5 . . . . 9 1 2 . . 8 . . . . . . . `

4) 90 degree rotation, no reflections
Code: Select all
`8 5 . . . . . 1 3 9 . 6 . . 4 . . 5 . . . 3 5 . . 8 . . 8 . . . . 7 . . . . 4 . . . 8 . . . . 2 . . . . 3 . . 1 . . 9 5 . . . 4 . . 8 . . 6 . 9 7 9 . . . . . 2 8 `

5) Diagonal reflection, no rotation
Code: Select all
`7 . . . . . . 2 6 . . 4 . . . . 3 1 . 1 . . 2 . . . . . . . 5 . . . . . . . 1 . . 6 . . . . . . . 3 . 5 9 . . . . . . 8 . . 7 6 9 . . . 2 . . . 3 2 . . . . 4 . . `

6) Double diagonal mirror
(subset of those with 180 degree rotation)
Code: Select all
`. . 4 . . . . 1 2 . . . 3 . . . 4 5 3 . . . 7 . . . . . 3 . 9 . . . . . . . 1 . . . 4 . . . . . . . 2 . 5 . . . . . 2 . . . 3 8 4 . . . 9 . . . 7 9 . . . . 6 . . `

7) All of the above
Code: Select all
`. . 3 . . . 7 . . . 7 . 9 . 8 . 6 . 6 . . . 7 . . . 9 . 3 . 1 . 4 . 7 . . . 9 . . . 6 . . . 8 . 6 . 5 . 4 . 5 . . . 1 . . . 6 . 1 . 5 . 6 . 9 . . . 2 . . . 3 . . `

8) Translational or glide symmetry
Code: Select all
`. . 8 . . . . . . . 2 . . . 8 . . . 9 . . . 4 . . . 5 4 . . 7 . . . 5 . 5 . . 8 . . 3 . . . 8 . 2 . . 7 . . . 6 . . 1 . 2 . . . . . . 5 . . 9 . . . . . . . . 4 . `

9) Non-symmetrical patterns, letters or symbols:
Code: Select all
`. 7 3 . . . . . . 9 . . 3 . . 5 . . 8 . . 6 . . 9 1 3 . 5 6 . . 4 1 7 . . . . . . . . 8 . . . 9 . . 2 . . . . . . 8 4 . . . . . . . 7 5 . . . . . . 1 . . 3 . . . `

10) ... and of course, no symmetry, just a random placement.
The only Sudoku's with 17 clues found so far are of this type.
Code: Select all
`. . . . . . . 1 3 . . . 7 . . . 6 . . . . 5 . 9 . . . . . . 4 . . 9 . . 1 . 6 . . . . . . . . . . . . 2 . . 7 4 . . . . . 5 . . 8 . . . . 4 . . . . . . 1 . . . . `
tso

Posts: 798
Joined: 22 June 2005