The New Sudoku Players' Forum

[udosuk]

This might come as a shock to some, but any sudoku puzzle (non-X, vanilla) covered by the following mask:

Code: Select all

 x x x | x x x | x x x
 x x x | . . . | x x x
 x x x | . . . | x x x
-------+-------+-------
 x x x | . . . | x x x
 x x x | . x . | x x x
 x x x | . . . | x x x
-------+-------+-------
 x x x | . . . | x x x
 x x x | . . . | x x x
 x x x | x x x | x x x

... DOES NOT have a unique solution. If you don't believe it, take any random completed grid, empty part of the cells as the above mask, and feed it to a solver program (such as Simple Sudoku)... You'll find it might report 2 or 3, maybe more solutions, but NEVER will it be a valid (i.e. with 1 unique solution) puzzle...

So, anyone trying to generate valid puzzles with these patterns:

Code: Select all

 . . x | x x x | x . .
 . x . | . . . | . x .
 x . . | . . . | . . x
-------+-------+-------
 x . . | . . . | . . x
 x . . | . x . | . . x
 x . . | . . . | . . x
-------+-------+-------
 x . . | . . . | . . x
 . x . | . . . | . x .
 . . x | x x x | x . .

 . . . | x x x | . . .
 . . x | . . . | x . .
 . x . | . . . | . x .
-------+-------+-------
 x . . | . . . | . . x
 x . . | . x . | . . x
 x . . | . . . | . . x
-------+-------+-------
 . x . | . . . | . x .
 . . x | . . . | x . .
 . . . | x x x | . . .

... FORGET IT! Mission impossible...

And kudos to anybody who could write a complete proof to this...

[keith]

udosuk,

A very provocative post! I presume you also exclude all subsets, such as this one:

Code: Select all

 x x x | x x x | x x x
 x . . | . . . | . . x
 x . . | . . . | . . x
-------+-------+-------
 x . . | . . . | . . x
 x . . | . . . | . . x
 x . . | . . . | . . x
-------+-------+-------
 x . . | . . . | . . x
 x . . | . . . | . . x
 x x x | x x x | x x x


which I saw posted a couple of days ago.

Keith

[daj95376]

udosuk,

Toss my first reply. There was something that I misunderstood!

Obviously, JPF has a more thorough understanding than both of us combined!

[udosuk]

Of course! All of these examples have rows/columns that can be exchanged within a chute without changing the template. So, any attempt at solving them will result in multiple solutions.

Excuse me... It isn't that obvious to me... I'm sure it's my own thickness but could you elaborate more please...

For example, how to exchange rows/columns on this one:

Code: Select all

918|765|432
764|...|519
532|...|876
---+---+---
156|...|784
493|.8.|265
827|...|391
---+---+---
641|...|923
385|...|147
279|341|658

As opposed to the following, which has a unique solution:

Code: Select all

.71|345|68.
4..|...|..7
6..|...|..3
---+---+---
9..|...|..6
.2.|...|.7.
7..|...|..4
---+---+---
1..|...|..5
3..|.6.|..8
.46|7.8|31.

Thanks!

[JPF]

And kudos to anybody who could write a complete proof to this...

Code: Select all

 1 9 8 | 2 7 5 | 3 4 6
 4 2 6 | . . . | 5 9 7
 3 5 7 | . . . | 8 1 2
-------+-------+-------
 6 4 3 | . . . | 7 8 1
 2 8 9 | . 6 . | 4 3 5
 7 1 5 | . . . | 6 2 9
-------+-------+-------
 5 3 1 | . . . | 9 7 8
 8 6 2 | . . . | 1 5 4
 9 7 4 | 8 5 1 | 2 6 3



has one and only one solution

Code: Select all

 1 9 8 | 2 7 5 | 3 4 6
 4 2 6 | 3 1 8 | 5 9 7
 3 5 7 | 9 4 6 | 8 1 2
-------+-------+-------
 6 4 3 | 5 9 2 | 7 8 1
 2 8 9 | 1 6 7 | 4 3 5
 7 1 5 | 4 8 3 | 6 2 9
-------+-------+-------
 5 3 1 | 6 2 4 | 9 7 8
 8 6 2 | 7 3 9 | 1 5 4
 9 7 4 | 8 5 1 | 2 6 3



*edit*, or even better :

Code: Select all


 . . . | 2 8 5 | . . .
 . . 4 | . . . | 2 . .
 . 6 . | . . . | . 3 .
-------+-------+-------
 5 . 1 | . . . | . . 4
 3 . . | . 7 . | . . 8
 2 . . | . . . | . . 9
-------+-------+-------
 . 1 . | . . . | . 7 .
 . . 9 | . . . | 5 . .
 . . . | 3 1 2 | . . .



Where is the joke ?

JPF

[udosuk]

Where is the joke ?

The joke's on me, entirely... For some reason I've mistaken today as the April Fool's day... Must be the effect of the Omen film...

Great... At the moment let's deal with:

Code: Select all

 x x x | x x x | x x x
 x x x | . . . | x x x
 x x x | . . . | x x x
-------+-------+-------
 x . . | . . . | . . x
 x . . | . x . | . . x
 x . . | . . . | . . x
-------+-------+-------
 x x x | . . . | x x x
 x x x | . . . | x x x
 x x x | x x x | x x x

&

Code: Select all

 x x x | x x x | x x x
 x x x | . . . | x x x
 x x x | . . . | x x x
-------+-------+-------
 x x x | . . . | x x x
 x x x | . . . | x x x
 x x x | . . . | x x x
-------+-------+-------
 x x x | . . . | x x x
 x x x | . . . | x x x
 x x x | x x x | x x x

[JPF]

At the moment let's deal with...

There are 2^81=2.4x10^24 possible patterns* !

I don't know for the first one...

For the second pattern, here is one solution :

Code: Select all

 1 5 8 | 2 6 9 | 7 3 4
 6 4 3 | . . . | 1 9 2
 9 2 7 | . . . | 5 6 8
-------+-------+-------
 2 6 5 | . . . | 8 4 1
 7 8 9 | . . . | 3 2 5
 3 1 4 | . . . | 6 7 9
-------+-------+-------
 5 9 1 | . . . | 2 8 6
 8 3 2 | . . . | 4 1 7
 4 7 6 | 8 1 2 | 9 5 3



or its minimal little brother :

Code: Select all

 . . 8 | 2 . 9 | 7 . .
 . . . | . . . | . . .
 . 2 7 | . . . | 5 6 .
-------+-------+-------
 . 6 5 | . . . | 8 4 .
 . . . | . . . | . . .
 3 1 . | . . . | . 7 9
-------+-------+-------
 . . . | . . . | . . .
 . 3 . | . . . | . 1 .
 . . 6 | 8 . 2 | 9 . .



JPF

*(before symmetry, etc..)

[udosuk]

JPF, it seems you're truly a master in this! Great work! And best of luck in cracking through this pattern...

Code: Select all

 x x x | x x x | x x x
 x x x | . . . | x x x
 x x x | . . . | x x x
-------+-------+-------
 x . . | . . . | . . x
 x . . | . x . | . . x
 x . . | . . . | . . x
-------+-------+-------
 x x x | . . . | x x x
 x x x | . . . | x x x
 x x x | x x x | x x x

[fermat]

I am guessing no one has, I cannot. I tried it by hand, a few grids.
I let Micheal Kennett's program run for 10 hours, to no effect.

So, I am thinking that there may be no solution or
that Micheal's test stutters on some patterns.

Has anyone tried a different template solver/builder to test this pattern?