## diagonal boxes

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

### diagonal boxes

Hi, I'm new to the forum. Don't know if this question has come up before. But I've been wondering if it would be possible to have a Sudoku puzzel where the boxes that cross diagonally in the center also do not repeat the numbers.

Would that make for a tougher or easier puzzel?
Laura58

Posts: 1
Joined: 28 December 2005

Yes it is possible. And yes it has been asked before.

Easier/Tougher hard to tell... My best guess is that it's could be a little easier...
Animator

Posts: 469
Joined: 08 April 2005

Here's the old thread on that topic: http://forum.enjoysudoku.com/viewtopic.php?p=3366

Oh, and another: http://forum.enjoysudoku.com/viewtopic.php?p=7037

Commercially, this variant is known as Sudoku X.
Red Ed

Posts: 633
Joined: 06 June 2005

Hi Laura,

Here is an example puzzle:

Code: Select all
` *-----------* |.4.|.6.|.9.| |6.8|1..|3.5| |.9.|5.8|..4| |---+---+---| |2.7|...|9.3| |...|7.3|...| |3.1|...|4.7| |---+---+---| |8..|6.5|.4.| |5.2|..4|1.6| |.7.|.1.|.3.| *-----------*`

Just to be clear: the usual Sudoku rule applies, AND each
number 1-9 must appear once in both of the diagonals.

I made this puzzle using Simple Sudoku, based on
this post by george-no1. The solution appears there.
(The post is in one of the threads that Red Ed mentioned.)
Nick67

Posts: 113
Joined: 24 August 2007

Animator wrote:Easier/Tougher hard to tell... My best guess is that it's could be a little easier...

The easy ones will be easier, because there's more chances to have just singles. The harder puzzles will be much harder, though, because there could very likely be pairs or even triples on the diagonals, and they won't be easy to spot.

One other thing is that you can't use the uniqueness rule if one of the cells is on a diagonal...
Lardarse

Posts: 106
Joined: 01 July 2005

Nick67 wrote:Hi Laura,

Here is an example puzzle:

Code: Select all
` *-----------* |.4.|.6.|.9.| |6.8|1..|3.5| |.9.|5.8|..4| |---+---+---| |2.7|...|9.3| |...|7.3|...| |3.1|...|4.7| |---+---+---| |8..|6.5|.4.| |5.2|..4|1.6| |.7.|.1.|.3.| *-----------*`

Just to be clear: the usual Sudoku rule applies, AND each
number 1-9 must appear once in both of the diagonals.

I made this puzzle using Simple Sudoku, based on
this post by george-no1. The solution appears there.
(The post is in one of the threads that Red Ed mentioned.)

Although both diagonals contain the digits 1-9, this puzzle can be solved without that extra information. Compare a proper diagonal sudoku:

Code: Select all
` . . 5 | . . . | . 9 .  . 6 2 | 1 . 7 | . . .  8 . . | . . . | . . 7 -------+-------+------ 2 8 . | . . . | . . .  . . . | . . . | . . .  . . . | . . . | . 7 1 -------+-------+------ 1 . . | . . . | . . 9  . . . | 4 . 9 | 3 8 .  . 5 . | . . . | 7 . . `

Easy to solve using the diagonals, multiple solutions without.
tso

Posts: 798
Joined: 22 June 2005

I like the distinction. A genuine diagonal sudoku puzzle is one with multiple solutions when treated as an ordinary sudoku puzzle. It just happens that exactly one of these completions has 1-9 on both diagonals. Some ordinary sudoku puzzles have a solution (one solution of course) which happens to have 1-9 on both diagonals, so we could call them diagonal sudokus, but perhaps they should be considered fake and not allowed in this category.

Have you got a genuine diagonal sudoku puzzle with 17 clues?
Moschopulus

Posts: 256
Joined: 16 July 2005

Moschopulus wrote:Have you got a genuine diagonal sudoku puzzle with 17 clues?

How about this..

Code: Select all
`1.. 9.4 ...2.. ... ...... 6.. ..8..5 .3. ...... ... .29.6. ... ...... ... ...... ..6 ....3. ... 5..`

Not mine.. it was sent to me by someone who thought it might be of interest with respect to the 16-clue search...

Gordon
gfroyle

Posts: 214
Joined: 21 June 2005

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