minimal redundant puzzles?

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

minimal redundant puzzles?

Here's a challenge. Find the puzzle with the least amount of clues such that every clue is redundant, that is every clue can be removed and still leave a vaild puzzle.
ab

Posts: 451
Joined: 06 September 2005

What an interesting challenge
here's my first attempt
Code: Select all
`+---+---+---+|189|273|645||672|845|931||435|169|827|+---+---+---+|546|728|319||317|956|284||298|431|756|+---+---+---+|824|597|163||953|612|478||761|384|592|+---+---+---+`

hehehe

I'll play properly i promise, just give me a minute on it[/code]
Pi

Posts: 389
Joined: 27 May 2005

It's probably one of the Gordon's list + 1 clue (?)

JPF
JPF
2017 Supporter

Posts: 3754
Joined: 06 December 2005
Location: Paris, France

Re: minimal redundant puzzles?

ab wrote:Here's a challenge. Find the puzzle with the least amount of clues such that every clue is redundant, that is every clue can be removed and still leave a vaild puzzle.

This may serve as a start (32 clues):
Code: Select all
` 2 . . | . 7 . | . . 1  . . 5 | 3 . 1 | 7 . .  . 4 . | . 5 . | . 8 . -------+-------+------  . 7 . | 8 . 3 | . 4 .  4 . 9 | . 6 . | 8 . .  . 8 . | 9 . 5 | . 7 . -------+-------+------  . 3 . | . 2 . | . 6 .  . . 8 | 6 . 4 | 5 . .  5 . . | . 8 . | . . 7 `
Ocean

Posts: 442
Joined: 29 August 2005

wow that's an excellent starter Ocean!
ab

Posts: 451
Joined: 06 September 2005

This would mean that each unavoidable set has two clues in it [rather than one in a minimal]

That means each 4-set unavoidable has 2 clues.

This grid has no 4-set unavoidables [SFB]
Code: Select all
`+---+---+---+|589|732|614||621|854|379||743|916|825|+---+---+---+|835|129|746||417|568|293||296|347|158|+---+---+---+|968|471|532||372|695|481||154|283|967|+---+---+---+`

Code: Select all
`+---+---+---+|...|...|.1.||.2.|.5.|...||.4.|...|...|+---+---+---+|8..|1.9|...||...|...|2..||...|3..|...|+---+---+---+|.6.|.7.|5.2||3..|...|4..||1..|.8.|...|+---+---+---+ one of its 3 17s`

add a few clues perhaps !
C
coloin

Posts: 1738
Joined: 05 May 2005

Code: Select all
`# 31 clue 31 redundant antidiagonal1 2 .  . . .  . . .3 5 .  . . 8  . 1 .. . 6  . 1 .  . . 3. . .  7 . .  . . 5. . 2  . 4 6  1 . .. 8 .  . 3 5  . 4 6. . .  . 8 .  9 5 .. 4 .  . . 1  6 7 .. . 8  5 . 9  . . 2# 33 clue 33 redundant full rotational (90 180 270 degrees). . 2  . . 3  1 8 .1 . 4  7 . .  6 . .8 5 .  . . .  . 2 94 . .  . 6 .  . 5 .. . .  4 9 2  . . .. 7 .  . 1 .  . . 39 3 .  . . .  . 6 2. . 1  . . 6  3 . 7. 2 7  5 . .  4 . .# 31 clue 31 redundant pi rotational (180 degrees). 8 .  . . .  . . 3. 2 1  . 9 .  8 . .5 . 4  . . 6  . . 2. . .  8 . 1  5 4 .. 4 .  . 3 .  . 1 .. 6 7  4 . 9  . . .7 . .  5 . .  9 . 4. . 6  . 1 .  2 5 .9 . .  . . .  . 3 .# 33 clue 33 redundant diagonal and antidiagonal8 . .  9 . .  . . 7. 6 9  7 . .  . 1 .. 4 3  5 . .  9 . .9 2 7  4 . 8  . . .. . .  . 6 .  . . .. . .  1 . 9  2 4 3. . 4  . . 7  1 8 .. 8 .  . . 4  7 6 .5 . .  . . 2  . . 4# 37 clue 37 redundant full dihedral1 . .  2 3 5  . . 7. 9 .  . 1 .  . 8 .. . 4  . 9 .  6 . .4 . .  . 6 .  . . 86 8 2  1 7 4  5 3 93 . .  . 2 .  . . 1. . 7  . 5 .  1 . .. 3 .  . 4 .  . 7 .9 . .  6 8 7  . . 4`
gsf
2014 Supporter

Posts: 7306
Joined: 21 September 2005
Location: NJ USA

The 17 clue minimal
Code: Select all
`+---+---+---+ |...|...|.1.| |.2.|.5.|...| |.4.|...|...| +---+---+---+ |8..|1.9|...| |...|...|2..| |...|3..|...| +---+---+---+ |.6.|.7.|5.2| |3..|...|4..| |1..|.8.|...| +---+---+---+`

a disjoint 19 clue minimal for the same grid
Code: Select all
`+---+---+---+|.8.|7..|6.4||...|...|3..||7..|91.|...|+---+---+---+|.3.|...|.4.||.1.|5..|.9.||..6|...|...|+---+---+---+|9..|4..|...||...|..5|.8.||...|..3|...|+---+---+---+ `

Put them together
Code: Select all
`+---+---+---+|.8.|7..|614||.2.|.5.|3..||74.|91.|...|+---+---+---+|83.|1.9|.4.||.1.|5..|29.||..6|3..|...|+---+---+---+|96.|47.|5.2||3..|..5|48.||1..|.83|...|+---+---+---+`

How many many clues can you remove and still have every clue superfluous ?
Hmmm, slightly trickier than I initially thought. !
C
coloin

Posts: 1738
Joined: 05 May 2005

I played with that grid and managed to find a 29 clue puzzle:

Code: Select all
`+---+---+---+ |...|7..|614| |.2.|...|3..| |74.|91.|...| +---+---+---+ |8.5|..9|.4.| |.1.|5..|29.| |..6|3..|...| +---+---+---+ |.6.|.7.|5.2| |3..|..5|.8.| |1..|.8.|...| +---+---+---+`

There may be one with less lurking in there.
ab

Posts: 451
Joined: 06 September 2005

here are two 29 clue pi symmetric
Code: Select all
`# 29 clue 29 superfluous pi rotational (180 degrees). . 1  9 . .  3 5 .. . .  . 4 .  . 6 .5 . 3  7 . .  8 . .. 9 .  . . 4  . . 3. . 7  . 6 .  4 . .1 . .  5 . .  . 7 .. . 9  . . 3  2 . 8. 4 .  . 1 .  . . .. 5 2  . . 8  6 . .# 29 clue 29 superfluous pi rotational (180 degrees)1 . .  5 . .  . 7 .. 9 .  . 7 .  1 . 38 7 .  . . 4  . . .. 6 3  . . 7  . . .. . 9  . 8 .  4 . .. . .  1 . .  9 2 .. . .  9 . .  . 4 26 . 5  . 3 .  . 1 .. 4 .  . . 6  . . 8`
gsf
2014 Supporter

Posts: 7306
Joined: 21 September 2005
Location: NJ USA