## Minimal puzzle?

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

### Minimal puzzle?

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.|.368..|...|7.1---+---+---...|..9|....7.|...|.5..4.|...|3..`
Hidden Text: Show
Once upon a time I was a teenager who was active on here 2007-2011
999_Springs

Posts: 367
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

Your puzzle is minimal. (Checked using gsf's sudoku.exe)
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

Ugly and easy. It is minimal!
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006

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

m_b_metcalf
2017 Supporter

Posts: 8290
Joined: 15 May 2006
Location: Berlin

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.|.368..|...|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

JPF
JPF
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Posts: 3752
Joined: 06 December 2005
Location: Paris, France

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"?
Hidden Text: Show
Once upon a time I was a teenager who was active on here 2007-2011
999_Springs

Posts: 367
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

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...

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`
udosuk

Posts: 2698
Joined: 17 July 2005

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

JPF
JPF
2017 Supporter

Posts: 3752
Joined: 06 December 2005
Location: Paris, France

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    01433   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`
gsf
2014 Supporter

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Location: NJ USA