## More Homework 3

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

### More Homework 3

What is the total minimum number of clues in B2,B6,B7,B8 required to get a minimal valid puzzle?
Code: Select all
`+-------+-------+-------+| . . . | . . . | . . . || . 1 . | . . . | . . . || . . . | . . . | . . 1 |+-------+-------+-------+| 1 . . | . . . | . . . || . . . | . 1 . | . . . || . . . | . . . | . . . |+-------+-------+-------+| . . . | . . . | . . . || . . . | . . . | . 1 . || . . . | . . . | . . . |+-------+-------+-------+`

JPF
JPF
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### Re: More Homework 3

JPF wrote:What is the total minimum number of clues in B2,B6,B7,B8 required to get a minimal valid puzzle?

2?
Code: Select all
` 2 3 4 . . . . . 9 . 1 . . . . . 3 . . . . . . . 5 6 1 1 2 . . . 7 . . . . . 8 . 1 5 . . . 6 . . 3 9 . . . . . . . . . . 4 . . . 7 . . . . . 1 2 . . . 4 . . . 7 .`

m_b_metcalf
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### Re: More Homework 3

Hi Mike,

Sorry if my question was not clear.
Boxes B1,B3,B4,B5,B9 must have only one clue equal to 1.
The other boxes B2,B6,B7,B8 must be filled in order to have a valid and minimal puzzle.

JPF
JPF
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### Re: More Homework 3

Tough one
Was really difficult to get this grid
Code: Select all
`+---+---+---+|...|47.|...||.1.|685|...||...|239|..1|+---+---+---+|1..|...|237||...|.1.|896||...|...|.54|+---+---+---+|95.|728|...||382|546|.1.||746|.93|...|+---+---+---+`

which gave this minimal puzzle
Code: Select all
`+---+---+---+|...|4..|...||.1.|.85|...||...|.39|..1|+---+---+---+|1..|...|237||...|.1.|8..||...|...|.54|+---+---+---+|.5.|7.8|...||382|...|.1.||..6|.9.|...|+---+---+---+   24C  [5C plus 19C]`
coloin

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Location: Devon

### Re: More Homework 3

That's a good start!

JPF
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### Re: More Homework 3

Code: Select all
` . . . . 3 5 . . . . 1 . 7 . . . . . . . . . . 4 . . 1 1 . . . . . 6 7 3 . . . . 1 . . 2 4 . . . . . . . . 8 . 2 . . . 9 . . . 8 7 . 6 . 2 . 1 .     3 . 4 . 8 . . . .   24 clues, minimal`

m_b_metcalf
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Location: Berlin

### Re: More Homework 3

Code: Select all
`+---+---+---+|...|..2|...||.1.|73.|...||...|698|..1|+---+---+---+|1..|...|372||...|.1.|.4.||...|...|.5.|+---+---+---+|..7|54.|...||29.|...|.1.||6..|.8.|...|+---+---+---+   23C  [5C plus 18C]`

JPF
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### Re: More Homework 3

Here's another:
Code: Select all
` . . . 5 . . . . . . 1 . . 6 . . . . . . . 2 7 . . . 1 1 . . . . . 7 . . . . . . 1 . 6 3 5 . . . . . . . 2 9 . 6 2 . . 3 . . . 7 3 4 . . 2 . 1 . . . . . . 9 . . .  23C`

Mike

m_b_metcalf
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### Re: More Homework 3

slight improvement:
Code: Select all
`+---+---+---+|...|...|...||.1.|..2|...||...|345|..1|+---+---+---+|1..|...|3.2||...|.1.|674||...|...|.8.|+---+---+---+|.63|97.|...||..4|.8.|.1.||2..|...|...|+---+---+---+   22C (5C plus 17C)`

JPF
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### Re: More Homework 3

Code: Select all
`+---+---+---+|...|.2.|...||.1.|345|...||...|.6.|..1|+---+---+---+|1..|...|.5.||...|.1.|342||...|...|.6.|+---+---+---+|...|..7|...||835|...|.1.||.64|2..|...|+---+---+---+   yes another 22 [5plus17]`

Wouldnt bet on finding a 21 .... although presumably there are many valid "full B2B6B7B8 grids"
coloin

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Joined: 05 May 2005
Location: Devon

### Re: More Homework 3

Wouldnt bet on finding a 21...

Well,...
Code: Select all
`+---+---+---+|...|..5|...||.1.|...|...||...|623|..1|+---+---+---+|1..|...|5..||...|.1.|897||...|...|.4.|+---+---+---+|...|54.|...||6.9|...|.1.||2.5|.8.|...|+---+---+---+   21C (5C plus 16C)`

JPF
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### Re: More Homework 3

Very good .... I cant match the search process... removing clues from a full grid is not efficient !
whereas specific clue removal and insertion is ... [in B2678]

For the record here is an 18C with all different clues in the B13459, so the pattern is possible !!
Code: Select all
`+---+---+---+|...|...|...||.1.|..7|...||...|38.|..2|+---+---+---+|3..|...|.9.||...|.4.|...||...|...|713|+---+---+---+|...|63.|...||.71|...|.5.||.5.|.2.|...|+---+---+---+  18C`
coloin

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Location: Devon

### Re: More Homework 3

coloin wrote:Very good .... I cant match the search process... removing clues from a full grid is not efficient !

My method was to generate large numbers of solutions to the five-clue puzzle, remove from each the other clues from B13459, and retain those puzzles that had only one solution (about 1 in 6000). The last step was then to repeatedly remove clues at random from the full boxes in the usual top-down way. Didn't get to 21C, though

Mike

m_b_metcalf
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### Re: More Homework 3

I'm away from home and can only use a poor performance laptop.
I found 12 21C:
Code: Select all
`.....7....1..........6.9..11.....9.6....1.432..........8..4....63.58..1.5.9...........7....1..........6.9..11.....9.6....1.432..........8..4....63.58..1..29...........5....1..........6.9..11.....5......1.432.......8.78..4....6..58..1..29...........5....1..........6.9..11.....5......1.432.......8.78..3....6..58..1..29...........5....1..........672..11.....5......1.843.......9....54....6.9....1.57..8.........5....1..........672..11.....5......1.843.......9....54....6.9....1.52..8.........2....1..........657..11.....2......1.893.......4....24....6.9....1.5.2.8.........2....1..........657..11.....2......1.893.......4....24....6.9....1.7.2.8.......2......1..........674..11.......2....1.689.......3.....35...79..8..1.2.4.........2......1..........674..11.......4....1.689.......3.....35...79..8..1.2.4...........2....1..........657..11.....2......1.839.......4...2.4....7.3....1.6..28.........2....1..........657..11.....2......1.839.......4...2.4....7.3....1.5..28....`

I guess there is no 20C.

Now here is the last part of the assignment:
same question (lowest number of clues for a valid puzzle) with this template:
Code: Select all
`+-------+-------+-------+| . . . | . . . | . . . || . 1 . | . . . | . . . || . . . | 1 . . | . . . |+-------+-------+-------+| 1 . . | . . . | . . . || . . . | . . . | . 1 . || . . . | . . . | . . . |+-------+-------+-------+| . . . | . . . | . . . || . . . | . . . | . . . || . . . | . . . | . . . |+-------+-------+-------+`

and this one:
Code: Select all
`+-------+-------+-------+| . . . | . . . | . . . || . 1 . | . . . | . . . || . . . | 1 . . | . . . |+-------+-------+-------+| 1 . . | . . . | . . . || . . . | . 1 . | . . . || . . . | . . . | . . . |+-------+-------+-------+| . . . | . . . | . . . || . . . | . . . | . . . || . . . | . . . | . . . |+-------+-------+-------+`

JPF
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### Re: More Homework 3

A
Code: Select all
`+---+---+---+|...|...|..3||.1.|...|45.||...|1..|.89|+---+---+---+|1..|27.|...||...|836|.1.||...|..4|...|+---+---+---+|2..|5..|.7.||37.|.2.|...||84.|..9|...|+---+---+---+  24C`

B
Code: Select all
`+---+---+---+|...|...|..9||.1.|...|4..||...|1..|8.3|+---+---+---+|1..|...|6..||...|71.|98.||...|...|24.|+---+---+---+|92.|.6.|...||.45|.92|...||3..|..4|...|+---+---+---+   23 clues .... but cant get rid of the interlopping clue !`
coloin

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Joined: 05 May 2005
Location: Devon

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