Fully symmetrical puzzles

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

Postby ravel » Fri Sep 28, 2007 9:14 pm

Red Ed wrote:No, no, no! Aren't you paying attention? Pears, not apples. Do try to keep up.
lol:D
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Postby JPF » Fri Sep 28, 2007 9:44 pm

Congratulations TTHsieh, simple but brilliant !

Proofs concerning pattern properties are so rare...

Does it mean that any (sub)puzzle containing this (sub)pattern is not minimal ?
Code: Select all
 . . . | . . . | . . .
 . . . | . x . | . . .
 . . . | . . . | . . .
-------+-------+-------
 . . . | x x x | . . .
 . . . | x . x | . . .
 . . . | x x x | . . .
-------+-------+-------
 . . . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .

JPF
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Postby Mauricio » Fri Sep 28, 2007 9:47 pm

JPF wrote:Does it mean that any (sub)puzzle containing this (sub)pattern is not minimal ?
Code: Select all
 . . . | . . . | . . .
 . . . | . x . | . . .
 . . . | . . . | . . .
-------+-------+-------
 . . . | x x x | . . .
 . . . | x . x | . . .
 . . . | x x x | . . .
-------+-------+-------
 . . . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .


That is true, they cannot have minimal puzzles.
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Postby coloin » Sat Sep 29, 2007 12:47 am

Indeed, two of the symmetrically minimal puzzles which RW refered us to are
Code: Select all
1 2 3|9 5 .|. . .
9 . 4|. . .|. . .
7 6 5|. . .|. . .
-----+-----+-----
3 . .|6 . .|. . .
5 . .|. 9 .|. . 8
. . .|. . 3|. . 7
-----+-----+-----
. . .|. . .|1 5 4
. . .|. . .|7 . 2
. . .|. 2 7|8 6 9

and

5 7 2|. . 4|. . .
4 . 1|. . .|. . .
6 9 3|. . .|. . .
-----+-----+-----
. . .|1 8 9|. . 7
. . .|3 . 7|. . .
3 . .|4 2 5|. . .
-----+-----+-----
. . .|. . .|7 8 2
. . .|. . .|6 . 5
. . .|2 . .|4 3 1

and unsurprisingly they do confirm TThsieh's observation.
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Postby Mauricio » Sat Sep 29, 2007 9:22 am

TTHsieh wrote:
Code: Select all
 x . . | . . . | . . x
 . x . | x a x | . x .
 . . . | . . . | . . .
 - - - + - - - + - - -
 . x . | 1 2 3 | . x .
 . . . | 4 . 6 | . . .
 . x . | 7 8 9 | . x .
 - - - + - - - + - - -
 . . . | . . . | . . .
 . x . | x . x | . x .
 x . . | . . . | . . x

    a <> 2, 5, 8
    a = 1, 4, 7, 3, 6, 9

    if a = 1 then you can remove 1 from box 5
    if a = 4 then you can remove 4 from box 5
    ...

In fact, more can be said about it:
Code: Select all
 . . . | x . x | . . .
 . . . | x . x | . . .
 . . . | x . x | . . .
 - - - + - - - + - - -
 x x x | 1 2 3 | x x x
 . . . | 4 . 6 | . . .
 x x x | 7 8 9 | x x x
 - - - + - - - + - - -
 . . . | x . x | . . .
 . . . | x . x | . . .
 . . . | x . x | . . .


If a 5 is given as a clue in row 4 or column 4, then 1 at r4c4 can be removed; if a 5 is given as a clue in row 6 or column 6, then 9 at r6c6 can be removed. So no 5 can be a given clue in r456, c456 in a minimal puzzle containing box 5 as above.
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Postby TTHsieh » Sat Sep 29, 2007 7:40 pm

Mauricio wrote:
Code: Select all
#32 clues, abs. minimal
+-------+-------+-------+
| . . . | . . . | . . . |
| . . 1 | . 2 . | 3 . . |
| . 2 3 | 1 4 5 | 6 7 . |
+-------+-------+-------+
| . . 2 | . 3 . | 7 . . |
| . 7 5 | 2 . 4 | 1 3 . |
| . . 4 | . 1 . | 5 . . |
+-------+-------+-------+
| . 4 7 | 3 6 2 | 8 5 . |
| . . 6 | . 5 . | 4 . . |
| . . . | . . . | . . . |
+-------+-------+-------+


    same pattern, other minimal puzzles
List wrote:
...........1.2.3...4536721...4.7.1...732.154...2.4.7...5861243...7.3.6........... # 2.0
...........1.2.3...4536721...4.7.1...732.154...2.4.7...5861247...7.3.6........... # 2.5
...........1.2.3...4536721...4.7.1...732.184...2.4.7...5681243...8.3.6........... # 3.0
...........1.2.3...3456178...8.7.5...531.287...7.8.2...7265813...5.1.6........... # 3.2
...........1.2.3...3456178...8.3.9...531.287...7.8.5...7265813...5.1.6........... # 3.4
...........1.2.3...4536781...6.1.4...347.216...7.4.2...5263174...3.7.5........... # 4.4
...........1.2.3...4536718...6.8.4...347.286...7.4.2...5263874...3.7.6........... # 4.5
...........1.2.3...3456781...7.8.5...537.218...8.1.9...8265173...5.7.6........... # 6.6
...........1.2.3...2431567...7.8.4...584.372...2.5.8...1387254...5.3.2........... # 7.1



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Postby Mauricio » Sat Sep 29, 2007 9:31 pm

A bit off topic.

Has anyone posted a minimal puzzle with 8 clues in a row?
Arguments like TTHsieh's for 8 clues in a box can be given about the nature of those puzzles, but I don't know if they exist.

Edit:
Nevermind, I've created a few. Post to follow.
Code: Select all
+-------+-------+-------+
| . 1 2 | 3 4 5 | 6 7 8 |
| . . . | 8 7 . | 5 1 . |
| . . . | . 6 . | . 2 . |
+-------+-------+-------+
| . 3 5 | 1 . . | 2 6 . |
| . 7 . | . 5 . | 3 . . |
| . . . | 6 . . | 7 . . |
+-------+-------+-------+
| . 5 1 | . . . | . . . |
| . 6 . | . 8 . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+

I will wait for JPF's new thread.
Last edited by Mauricio on Sat Sep 29, 2007 6:28 pm, edited 3 times in total.
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Postby JPF » Sat Sep 29, 2007 9:52 pm

This pattern is not minimal * :
*a pattern is not minimal if there no minimal puzzle containing this pattern

Code: Select all
 . . . | . . . | . . .
 . . . | . x . | . . .
 . . . | . . . | . . .
-------+-------+-------
 . . . | x . x | . . .
 . . . | x . x | . . .
 . . . | x x x | . . .
-------+-------+-------
 . . . | . . . | . . .
 . . . | . x . | . . .
 . . . | . . . | . . .

Proof :[deleted , wrong proof, but true statement see here]

Mauricio wrote:A bit off topic...
I agree, and I will open a thread on minimality.

JPF
Last edited by JPF on Mon Oct 01, 2007 5:57 am, edited 1 time in total.
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Postby wintder » Sun Sep 30, 2007 3:17 am

Mauricio wrote:Has anyone posted a minimal puzzle with 8 clues in a row?
Arguments like TTHsieh's for 8 clues in a box can be given about the nature of those puzzles, but I don't know if they exist.



This is the most minimal PATTERN that is fully symmetric and has 8 clues in a row. (The row like a column, not in-a-row like consecutive.:)

Code: Select all
1 2 3 | 4 . 5 | 6 7 8
7 . . | . . . | . . 5
5 . . | . . . | . . 9
---------------------
3 . . | 7 . 6 | . . 1
. . . | . . . | . . .
8 . . | 5 . 2 | . . 4
---------------------
4 . . | . . . | . . 7
2 . . | . . . | . . 3
9 5 7 | 1 . 3 | 2 4 6


I have checked about 60,000 and found none of them minimal.
Can one of you logically see that it cannot make a minimal puzzle?
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Postby Mauricio » Sun Sep 30, 2007 4:17 am

wintder wrote:Can one of you logically see that it cannot make a minimal puzzle?

See the minimal puzzles thread, there I proved that if a puzzle has 2 rows or 2 columns with 8 clues, then the pattern is not minimal.
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Postby Mauricio » Mon Oct 01, 2007 7:42 pm

I have used the recent developement on minimal puzzles to reduce the number of fully symmetrical patterns with 36 clues that may contain a minimal puzzle with 36 clues. The number is now 202.

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100000001011000110011111110001101100001000100001101100011111110011000110100000001
100000001011010110011101110001010100010101010001010100011101110011010110100000001
100000001011010110011101110001101100010000010001101100011101110011010110100000001
100000001011010110011111110001000100011000110001000100011111110011010110100000001
100000001011101110011101110011000110000000000011000110011101110011101110100000001
100010001010101010001111100011000110101000101011000110001111100010101010100010001
100010001011000110011101110001010100100101001001010100011101110011000110100010001
100010001011000110011101110001101100100000001001101100011101110011000110100010001
100010001011000110011111110001000100101000101001000100011111110011000110100010001
100010001011010110011101110001000100110000011001000100011101110011010110100010001
100101001011000110011000110100111001000101000100111001011000110011000110100101001
100101001011000110011010110100010001001101100100010001011010110011000110100101001
100101001011000110011010110100101001001000100100101001011010110011000110100101001
100101001011000110011101110101000101000000000101000101011101110011000110100101001
100101001011010110011010110100000001011000110100000001011010110011010110100101001


There are 380 non isomorphic fully symetrical patterns with 36 clues.

Edit: I am deleting patterns now proved to be non minimal.
Last edited by Mauricio on Wed Oct 03, 2007 5:11 am, edited 2 times in total.
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Postby ravel » Tue Oct 02, 2007 9:03 am

Nice patterns, e.g. i like this four-leaf clover from 142, which contains the clues of one of TTHsieh's pattern game puzzles.
Code: Select all
+-------+-------+-------+
| . x x | x . x | x x . |
| x . . | . x . | . . x |
| x . . | . x . | . . x |
+-------+-------+-------+
| x . . | . x . | . . x |
| . x x | x . x | x x . |
| x . . | . x . | . . x |
+-------+-------+-------+
| x . . | . x . | . . x |
| x . . | . x . | . . x |
| . x x | x . x | x x . |
+-------+-------+-------+
And there are some for cross afficionados like Claudia (e.g. 180)
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Postby JPF » Sat Mar 29, 2008 10:28 pm

Here are some new 21 clues minimal puzzles.
The list of the 20 – 21 clues puzzles is here.

#39 JPF
ex #32* ab
Code: Select all
 . . . | . . . | . . .
 . 1 . | . . . | . 2 .
 . . 3 | 4 . 5 | 6 . .
-------+-------+-------
 . . 5 | . 6 . | 3 . .
 . . . | 7 8 9 | . . .
 . . 9 | . 1 . | 4 . .
-------+-------+-------
 . . 4 | 6 . 2 | 9 . .
 . 2 . | . . . | . 7 .
 . . . | . . . | . . .

0-8-6-1-1   0-10-4-1-1   16-0-6-1-1   16-10-0-1-1   18-0-4-1-1   18-8-0-1-1


#40 JPF
ex #31* ab
Code: Select all
 . . . | . 1 . | . . .
 . . 2 | . . . | 3 . .
 . 3 4 | . . . | 2 5 .
-------+-------+-------
 . . . | 2 . 4 | . . .
 6 . . | . 7 . | . . 8
 . . . | 6 . 1 | . . .
-------+-------+-------
 . 2 5 | . . . | 4 6 .
 . . 6 | . . . | 7 . .
 . . . | . 9 . | . . .

1-4-4-2-1   1-12-0-2-1   4-1-4-2-1   8-8-1-2-1   20-1-0-2-1   24-0-1-2-1


#41 JPF
[M21 1-2-4-1-1 ]
Code: Select all
 . . . | . 1 . | . . .
 . . . | 2 . 3 | . . .
 . . 4 | . . . | 5 . .
-------+-------+-------
 . 6 . | . 3 . | . 7 .
 2 . . | 7 6 8 | . . 1
 . 1 . | . 9 . | . 4 .
-------+-------+-------
 . . 9 | . . . | 2 . .
 . . . | 1 . 6 | . . .
 . . . | . 4 . | . . .

1-2-4-1-1   1-8-2-1-1   2-1-4-1-1   2-8-1-1-1   16-1-2-1-1   16-2-1-1-1

JPF
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Postby tarek » Mon Apr 14, 2008 12:38 pm

I've genenrated some hunderds-thousands of 20 clue FSMs a while back. these are not isomorphic to the ones posted by Ocean....

Not sure if it is worthwhile posting them here or not:?::idea:

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Postby Pat » Mon Apr 14, 2008 12:58 pm

tarek wrote:I've genenrated --- 20-clue FSMs

these are not isomorphic to the ones posted by Ocean


the puzzles are not equivalent ?

or, the clue-patterns are not equivalent ?
    surely you'd post an example of any new clue-pattern---
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