Number cluster

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Number cluster

Postby Addlan » Thu Jul 21, 2005 5:14 pm

It seems to me that number cluster in the initial Sudoku is quite against Sudoku rule. However, it will be interested to know how and why. I have a question which I don't know how to solve and I wonder if folks can help me out.

I wonder if the following pattern is designed properly, will it lead to a unique Sudoku. * represents a grid with a digit from '1' to '9' and dot represents empty grid.

... |... |...
... |... |...
..*|***|*..
-----------
..*|***|*..
..*|***|*..
..*|***|*..
-----------
..*|***|*..
... |... |...
... |... |...
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Postby PaulIQ164 » Thu Jul 21, 2005 5:40 pm

I'm afraid there'll always be rather a lot of solutions to a puzzle looking like that. However you fill it in, you'll be able to swap round columns 1 and 2 at the left, columns 7 and 8 at the right, rows 1 and 2 at the top, and/or rows 7 and 8 at the bottom, and get another valid solution. That's at least 8 different solutions.
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Postby udosuk » Thu Jul 21, 2005 6:54 pm

Good reasoning except replace "7 and 8" as "8 and 9"... ^_^
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Postby PaulIQ164 » Thu Jul 21, 2005 7:03 pm

Oops. Yes, I of course meant 8 and 9. In fact, I typed that, but someone has switched round the keys on my keyboard. Honest.
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Re: Number cluster

Postby tso » Thu Jul 21, 2005 7:57 pm

Addlan wrote:It seems to me that number cluster in the initial Sudoku is quite against Sudoku rule.


There's nothing wrong with clustering the clues. For example, the following are all perfectly correct Sudokus. The first two are medium difficulty, the second two are harder:

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



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



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


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


(You might want to used the CODE command to make your diagrams legible.]
Last edited by tso on Fri Jul 22, 2005 6:47 am, edited 1 time in total.
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Postby Addlan » Thu Jul 21, 2005 8:57 pm

Thanks. Then what about something that cann't be swapped?

It seems to me the following pattern cann't be swapped at least in a row or a column level. However, will it be able to construct a unique Sudoku? A * represents an initial digit, ? presents an emply grid.

***|???|???
***|???|???
***|???|???
-------------
???|***|???
???|***|???
???|***|???
-------------
???|???|***
???|???|***
???|???|***
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Postby PaulIQ164 » Thu Jul 21, 2005 9:23 pm

Ignore this post.
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