The New Sudoku Players' Forum

by **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

by **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

by **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.

by **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.

by **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.

by **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

TTHsieh

by **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.

by **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

by **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?

by **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.

by **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.

000000000001101100011101110011111110000101000011111110011101110001101100000000000
000000000001101100011111110011010110001101100011010110011111110001101100000000000
000000000001101100011111110011101110001000100011101110011111110001101100000000000
000000000001111100010111010011010110011101110011010110010111010001111100000000000
000000000001111100010111010011101110011000110011101110010111010001111100000000000
000000000001111100011101110011010110010101010011010110011101110001111100000000000
000000000001111100011101110011101110010000010011101110011101110001111100000000000
000000000001111100011111110011000110011000110011000110011111110001111100000000000
000000000011010110011111110001010100011101110001010100011111110011010110000000000
000000000011010110011111110001101100011000110001101100011111110011010110000000000
000000000011101110011101110011010110000101000011010110011101110011101110000000000
000000000011101110011101110011101110000000000011101110011101110011101110000000000
000000000011101110011111110011000110001000100011000110011111110011101110000000000
000010000001101100010111010011010110101101101011010110010111010001101100000010000
000010000001101100010111010011101110101000101011101110010111010001101100000010000
000010000001101100011101110011010110100101001011010110011101110001101100000010000
000010000001101100011101110011101110100000001011101110011101110001101100000010000
000010000001101100011111110011000110101000101011000110011111110001101100000010000
000010000001111100010111010011000110111000111011000110010111010001111100000010000
000010000001111100011101110011000110110000011011000110011101110001111100000010000
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000101000001000100011101110101111101000101000101111101011101110001000100000101000
000101000001000100011111110101010101001101100101010101011111110001000100000101000
000101000001000100011111110101101101001000100101101101011111110001000100000101000
000101000001010100010111010101010101011101110101010101010111010001010100000101000
000101000001010100010111010101101101011000110101101101010111010001010100000101000
000101000001010100011101110101010101010101010101010101011101110001010100000101000
000101000001010100011101110101101101010000010101101101011101110001010100000101000
000101000001010100011111110101000101011000110101000101011111110001010100000101000
000101000001101100011000110110111011000101000110111011011000110001101100000101000
000101000001101100011010110110010011001101100110010011011010110001101100000101000
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000101000010010010001111100101010101011101110101010101001111100010010010000101000
000101000010010010001111100101101101011000110101101101001111100010010010000101000
000101000011000110011101110101010101000101000101010101011101110011000110000101000
000101000011000110011101110101101101000000000101101101011101110011000110000101000
000101000011000110011111110101000101001000100101000101011111110011000110000101000
000101000011010110011010110100010001011101110100010001011010110011010110000101000
000101000011010110011010110100101001011000110100101001011010110011010110000101000
000101000011010110011101110101000101010000010101000101011101110011010110000101000
000111000001000100011101110101010101100101001101010101011101110001000100000111000
000111000001000100011101110101101101100000001101101101011101110001000100000111000
000111000001010100010101010101010101110101011101010101010101010001010100000111000
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000111000001101100011000110110101011100000001110101011011000110001101100000111000
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011000110101000101111000111000111000000101000000111000111000111101000101011000110
011000110101000101111010111000010000001101100000010000111010111101000101011000110
011000110101000101111010111000101000001000100000101000111010111101000101011000110
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011000110101010101110010011000101000011000110000101000110010011101010101011000110
011000110101010101110101011001000100010000010001000100110101011101010101011000110
011000110110000011101101101001010100000101000001010100101101101110000011011000110
011000110110000011101101101001101100000000000001101100101101101110000011011000110
011000110110000011101111101001000100001000100001000100101111101110000011011000110
011000110110010011101101101001000100010000010001000100101101101110010011011000110
011010110110000011101010101000010000101101101000010000101010101110000011011010110
011010110110000011101010101000101000101000101000101000101010101110000011011010110
011010110110000011101101101001000100100000001001000100101101101110000011011010110
011101110110000011101010101100000001001000100100000001101010101110000011011101110
100000001010101010001111100011010110001101100011010110001111100010101010100000001
100000001010101010001111100011101110001000100011101110001111100010101010100000001
100000001011000110011101110001111100000101000001111100011101110011000110100000001
100000001011000110011111110001010100001101100001010100011111110011000110100000001
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.

by **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)

by **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

by **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 :?:

tarek

by **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---

The New Sudoku Players' Forum

Fully symmetrical puzzles