## More Homework !

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

### Re: More Homework !

n=3
you wrote:I havn't explored the minimality of the n=3 puzzles

I got more than 1000 minimal puzzles.
I stopped the search.
Here is an example:
Code: Select all
`+---+---+---+|123|...|...||4.5|...|...||678|...|...|+---+---+---+|...|857|..3||...|9.3|...||7..|216|...|+---+---+---+|...|...|156||...|...|4.7||...|5..|392|+---+---+---+  SE=7.2`

Finding minimal puzzles when 4<=n<=8 seems not too difficult.
Of course, Mauricio's lemma helps to place the clues.
Here is one (out of 4000+) for n=8 having main diagonal and anti-diagonal symmetries which btw implies 180° rotational symmetry
Code: Select all
`+---+---+---+|123|4..|..5||4.6|...|...||578|...|4..|+---+---+---+|2..|594|...||...|1.2|...||...|678|..2|+---+---+---+|..4|...|253||...|...|1.7||7..|..5|864|+---+---+---+  SE=9.0`

I will have a look at n=9+; it seems more challenging!

JPF
JPF
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### Re: More Homework !

JPF wrote:
Code: Select all
`+---+---+---+|123|...|...||4.5|...|...||678|...|...|+---+---+---+|...|857|..3||...|9.3|...||7..|216|...|+---+---+---+|...|...|156||...|...|4.7||...|5..|392|+---+---+---+  SE=7.2`

Indeed you only need one ... i hadnt thought that there could be ...
JPF wrote:
Code: Select all
`+---+---+---+|123|4..|..5||4.6|...|...||578|...|4..|+---+---+---+|2..|594|...||...|1.2|...||...|678|..2|+---+---+---+|..4|...|253||...|...|1.7||7..|..5|864|+---+---+---+  SE=9.0`

and the highest rating for good measure ! It seems that some of these puzzles have neat solving properties
coloin

Posts: 2175
Joined: 05 May 2005
Location: Tenerife

### Re: More Homework !

JPF wrote:I will have a look at n=9+; it seems more challenging!

It was:
Code: Select all
` 2 8 3 7 . . . . 6 5 . 7 . . . . . . 9 1 6 3 . . 8 . . 1 . . 5 3 8 . . . . . . 1 . 9 . . . . . . 2 6 7 . . 9 . . 2 . . . 6 9 1 . . . . . . 3 . 5 6 . . . . 3 7 2 8   ED=7.2/1.0/1.0, n = 9`

m_b_metcalf
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Location: Berlin

### Re: More Homework !

well done Mike!

I give up: my approach is not very effective for puzzles with a large number of clues.
I also have another homework to do...

JPF
JPF
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### Re: More Homework !

JPF wrote:well done Mike!

Well, thanks too for your seed pattern!

M

m_b_metcalf
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### Re: More Homework !

Hi, Marek!
marek stefanik wrote:
Code: Select all
`+-----+-----+-----+|x x x|x . x|. . .||. . .|. . .|. . .||x x x|x . x|. . .|+-----+-----+-----+|. . .|x x x|. . .||. . .|x . x|. . .||. . .|x x x|. . .|+-----+-----+-----+|. . .|. . .|. . .||. . .|. . .|. . .||. . .|. . .|. . .|+-----+-----+-----+`
This pattern is not minimal.

Good point! (I spent some time to understand your proof.) What is WLOG and PC?

Serg
Serg
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### Re: More Homework !

Hi Serg,

WLOG means 'without loss of generality' (if a is given in c6 instead, you can just swap the two columns).
PC means 'pointing candidates'.

Marek
marek stefanik

Posts: 250
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### Re: More Homework !

coloin wrote:I think there maybe a limitation of 3 on the rows/columns as well
Sadly that's not the case, I found a minimal subpuzzle (3352 solutions) with that pattern:
1236.87.44.5......678.........837......9.5......216.........165......4.7......923
(I haven't checked if it can produce minimal puzzles, though)

Marek
marek stefanik

Posts: 250
Joined: 05 May 2021

### Re: More Homework !

coloin wrote: .... but I do know that there is some way to go with n

So, how far is there still to go?

m_b_metcalf
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Location: Berlin

### Re: More Homework !

n=12
coloin

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Joined: 05 May 2005
Location: Tenerife

### Re: More Homework !

coloin wrote:n=12

Gasp! I give up. This puzzle has 12 extra clues, all of which are minimal, but those in B1B5B9 are not
Code: Select all
` 8 3 9 . . 2 . . . 4 . 5 . . . 9 . . 2 6 7 . . . . . . 7 8 . 3 6 9 . . . . . 3 2 . 4 . . . . . 2 7 8 5 . 3 . . . . . . . 3 9 8 9 . 8 5 . . 2 . 6 . 2 . 9 . . 1 7 5    ED=4.2/1.0/1.0No. of givens =  36`

m_b_metcalf
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### Re: More Homework !

Am on vacation ( and my files are at home ) and quietly trying to repeat the exercise ….
Generating the n=10 is not a problem … eventually a n=11 is produced …
I am persevering to get a n=12 …. Knowing that it is possible is reassuring…. and a good question might be whether I will find the same puzzle ….
coloin

Posts: 2175
Joined: 05 May 2005
Location: Tenerife

### n=12

Code: Select all
`+-----+-----+-----+|1 2 3|. . 5|4 . 6||4 . 5|. . .|. . .||6 7 8|. . 2|. . 5|+-----+-----+-----+|. . .|5 2 9|6 . 4||. . .|7 . 6|. . .||2 . .|1 3 4|. . .|+-----+-----+-----+|7 . .|. . .|2 6 1||. . .|. . .|5 . 7||5 . .|2 . 7|8 4 3|+-----+-----+-----+      n=12     36 clues minimal `

Finally one was found ..... not sure how all the UA fit in ....
coloin

Posts: 2175
Joined: 05 May 2005
Location: Tenerife

### Re: n=12

coloin wrote:
Code: Select all
`    n=12     36 clues minimal `

Finally one was found ..... not sure how all the UA fit in ....

Brilliant! And here's a list of the UA4s:
Code: Select all
`1=H r1 c1 r2 c2 2=V  1  2  1  3  4  1  1  1  2  7  1  1  3  2  6  1  2  3  3  9  1  1  4  2  9  1  2  6  3  8  1  4  1  6  5  1  5  1  6  9  1  4  3  6  7  1  4  6  6  9  1  8  1  9  7  1  7  2  9  9  2  2  1  5  2  2  3  2  4  3  2  1  7  4  9`

Mike

m_b_metcalf
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### Re: More Homework !

And I think your puzzle has a cousin:
Code: Select all
` 1 2 3 . . 4 5 . 6 5 . 4 . . . . . . 6 7 8 . . 2 . . 4 . . . 3 1 9 6 . 5 . . . 7 . 6 . . . 3 . . 4 2 5 . . . 7 . . . . . 2 6 1 . . . . . . 4 . 7      n=12, all minimal 4 . . 2 . 7 8 5 3      ED=1.5/1.0/1.0`

m_b_metcalf
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Joined: 15 May 2006
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