Minimal puzzle?

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Minimal puzzle?

Postby 999_Springs » Thu Mar 22, 2007 8:14 pm

Is this puzzle minimal? If not, then which givens can be removed?
Code: Select all
.5.|76.|..9
...|2.5|.1.
6..|...|...
---+---+---
1..|9..|...
9..|.4.|.36
8..|...|7.1
---+---+---
...|..9|...
.7.|...|.5.
.4.|...|3..
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Postby ronk » Thu Mar 22, 2007 8:40 pm

Your puzzle is minimal. (Checked using gsf's sudoku.exe)
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Postby wapati » Thu Mar 22, 2007 8:53 pm

Ugly and easy. It is minimal!
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Postby m_b_metcalf » Thu Mar 22, 2007 10:33 pm

wapati wrote:Ugly and easy. It is minimal!


But it's possible to shake it a bit and lose a couple of cells:
Code: Select all
 . 2 . 7 6 . . . 8
 . . . 4 . 5 . 1 .
 3 . . . . . . . .
 1 . . 3 . . . . .
 9 . . . 1 . . . 4
 5 . . . . . 2 . .
 . . . . . 2 . . .
 . 3 . . . . . 5 .
 . 7 . . . . 6 . .

Regards,

Mike Metcalf
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Postby JPF » Thu Mar 22, 2007 10:55 pm

999_Springs wrote:Is this puzzle minimal? If not, then which givens can be removed?
Code: Select all
.5.|76.|..9
...|2.5|.1.
6..|...|...
---+---+---
1..|9..|...
9..|.4.|.36
8..|...|7.1
---+---+---
...|..9|...
.7.|...|.5.
.4.|...|3..

wapati wrote:Ugly and easy. It is minimal!

change the 2 cells in box 5 :
Code: Select all
 . 5 . | 7 6 . | . . 9
 . . . | 2 . 5 | . 1 .
 6 . . | . . . | . . .
-------+-------+-------
 1 . . | 3 . . | . . .
 9 . . | . 8 . | . 3 6
 8 . . | . . . | 7 . 1
-------+-------+-------
 . . . | . . 9 | . . .
 . 7 . | . . . | . 5 .
 . 4 . | . . . | 3 . .

SE = 8.3

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Postby 999_Springs » Mon Mar 26, 2007 12:34 pm

JPF wrote:
change the 2 cells in box 5 :
Code:

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


SE = 8.3

Is that puzzle minimal? I know that it is evil enough as it is, but...
Why won't "quote" pick up "code"?
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Postby udosuk » Mon Mar 26, 2007 1:40 pm

999_Springs wrote:Why won't "quote" pick up "code"?

Looks like you haven't learned the proper way to use the BBCode... When you post, look at the left side of your window. That link was right under Options...:idea:

This is what you typed:
999_Springs wrote:JPF wrote:
[quote]
change the 2 cells in box 5 :
Code:

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


SE = 8.3
[/quote]

The correct way to do it is as the following:
BBCode master wrote:[quote="JPF"]
change the 2 cells in box 5 :
[code]

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


SE = 8.3
[/code][/quote]

Which will result in this effect:
JPF wrote:change the 2 cells in box 5 :
Code: Select all

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

 
SE = 8.3
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Postby JPF » Mon Mar 26, 2007 2:58 pm

Thanks udosuk !

Yes, this puzzle is minimal.
It means that removing any cell C gives a puzzle with more than 1 solution.

How minimal this puzzle is ?
We can have an idea by counting the number of solutions ni when removing the cell Ci.
With the Sudoku Explainer notations we get the following results :
Code: Select all
Cell    Sol.                                                                     
  H5     12                                                                     
  G6     15                                                                     
  D2     53                                                                     
  D4     53                                                                     
  F2     54                                                                     
  I6    100                                                                     
  E1    162                                                                     
  E5    201                                                                     
  A6    217                                                                     
  I5    226                                                                     
  I1    236                                                                     
  A3    240                                                                     
  D1    250                                                                     
  H8    264                                                                     
  B1    299                                                                     
  H2   >400                                                                     
  A4   >400                                                                     
  A5   >400                                                                     
  F7   >400                                                                     
  B8   >400                                                                     
  B9   >400                                                                     
  G9   >400   

There are 2 weak cells H5, G6 which can be removed in order to get an almost valid puzzle.

For example, if we remove H5, we get a new valid puzzle with B1=3 and D4=5 ; only 21 cells :
Code: Select all
 . 3 . | 7 6 . | . . 9
 . . . | 2 . 5 | . 1 .
 6 . . | . . . | . . .
-------+-------+-------
 1 . . | 5 . . | . . .
 9 . . | . 8 . | . . 6
 8 . . | . . . | 7 . 1
-------+-------+-------
 . . . | . . 9 | . . .
 . 7 . | . . . | . 5 .
 . 4 . | . . . | 3 . .


SE=7.1 ; minimal

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Postby gsf » Tue Mar 27, 2007 3:00 am

here's the same info listed by grid position
Code: Select all
 12 5306

  0   299   0  | 250  162   0  |  0    0   236
  0    0    0  | 53    0   54  |  0   623   0
 240   0    0  |  0    0    0  |  0    0    0
---------------+---------------+---------------
1603   0    0  | 53    0    0  |  0    0    0
1433   0    0  |  0   201   0  |  0   12   226
 217   0    0  |  0    0    0  | 15    0   100
---------------+---------------+---------------
  0    0    0  |  0    0  1072 |  0    0    0
  0  3625   0  |  0    0    0  |  0   264   0
  0  5306   0  |  0    0    0  | 642   0    0
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