minimal redundant puzzles?

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minimal redundant puzzles?

Postby ab » Mon Apr 10, 2006 1:41 pm

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.
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Postby Pi » Mon Apr 10, 2006 1:51 pm

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]
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Postby JPF » Mon Apr 10, 2006 3:03 pm

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

JPF
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Re: minimal redundant puzzles?

Postby Ocean » Mon Apr 10, 2006 5:15 pm

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
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Postby ab » Mon Apr 10, 2006 7:13 pm

wow that's an excellent starter Ocean!
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Postby coloin » Mon Apr 10, 2006 10:25 pm

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
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Postby gsf » Tue Apr 11, 2006 4:38 am

Code: Select all
# 31 clue 31 redundant antidiagonal

1 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 9

4 . .  . 6 .  . 5 .
. . .  4 9 2  . . .
. 7 .  . 1 .  . . 3

9 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 antidiagonal

8 . .  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 dihedral

1 . .  2 3 5  . . 7
. 9 .  . 1 .  . 8 .
. . 4  . 9 .  6 . .

4 . .  . 6 .  . . 8
6 8 2  1 7 4  5 3 9
3 . .  . 2 .  . . 1

. . 7  . 5 .  1 . .
. 3 .  . 4 .  . 7 .
9 . .  6 8 7  . . 4
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Postby coloin » Tue Apr 11, 2006 7:10 pm

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 ?
Answer........not many !
Hmmm, slightly trickier than I initially thought. !
C
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Postby ab » Tue Apr 11, 2006 10:08 pm

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.
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Postby gsf » Tue Apr 11, 2006 10:44 pm

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 . 3
8 7 .  . . 4  . . .

. 6 3  . . 7  . . .
. . 9  . 8 .  4 . .
. . .  1 . .  9 2 .

. . .  9 . .  . 4 2
6 . 5  . 3 .  . 1 .
. 4 .  . . 6  . . 8
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