## Ask for some patterns that they don't have puzzles.

Everything about Sudoku that doesn't fit in one of the other sections
coloin wrote:But the minimum that has been found is 7
Well done that man - again he saves us a lot of random generations

Ah.. but did he prove it was 7 ?

I don't think so, but he is Red Ed and I trust him.
Back to the topic :

So, this pattern doesn't have a valid puzzle
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`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 | . . . | x x x x x x | x x x | x x x `

Havard wrote:it is a bit freaky that the last minimum solutions discovered are:
80 - 64 - 48 - 32, since each of these can be derived by a -16 (80-16 = 64, 64-16=48 etc). Does this mean that we can find a grid with 16 solutions but none with 1 (only with 16-16=0)??? `

Havard wrote:The search is recursive, trying all possibilities for all numbers in all cells. I guess 172800000 is the number of nodes visited. I have found a lot of 32 solution ones, but none so far with any less...

Have you found any with less than 32 solutions since then ?
What are the possible numbers of solutions (...,32,48,64,80,...) ? like here

Same question for this one :
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 x | . . . | x x x x x x | x x x | x x x `

Min=2 ; Max ? ; structure of the number of solutions...

Any (logical) explanation that by adding a clue in r5c4 =>Min=1 ?

JPF
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JPF wrote:Have you found any with less than 32 solutions since then ?

That computional power is now used in the search of new 17. So no. However, I think it is quite unlikely that one with any less exists.

Havard
Havard

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Can anyone help with this?

I have a partially filled out sudoku that looks like this:

Code: Select all
`. . .|1 . .|. . .1 . .|. . .|. . .. . .|. . .|1 . .-----+-----+-----. 1 .|. . .|. . .. . .|. 1 .|. . .. . .|. . .|. 1 .-----+-----+-----2 3 1|4 5 7|6 8 94 5 6|8 9 1|2 3 77 8 9|2 3 6|4 5 1`

Now, is it possible to make this a valid sudoku by placing 5 (or less) more clues? Any one care to prove wheter this is impossible or not?

thanks!

Havard
Havard

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Havard wrote:Now, is it possible to make this a valid sudoku by placing 5 (or less) more clues? Any one care to prove wheter this is impossible or not?

If someone is about to throw their computational arsenal on this problem, I can give you a hint: in any possible unique puzzle one of the added clues has to be either 2 or 4 and one of the added clues must be either 3 or 5.

My guess is that it can't be solved with only 5 extra clues, but JPF is known for finding puzzles that are a lot more unlikely than that...

RW
RW
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Good call RW. Another way of looking at it is that without loss of generality, in row 1 of the solution grid, the first '2' occurs before the first '4' and the first '3' occurs before the first '5'.
Red Ed

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Havard wrote:Now, is it possible to make this a valid sudoku by placing 5 (or less) more clues? Any one care to prove wheter this is impossible or not?

Nothing to do with what you are looking for ...
just in case

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

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

JPF

very nice! But if I add the 1's, there is 6 extra clues.
The "rule" that I am trying to prove is right is that: "in the first 11 clues of a sudoku, you can't have more than 5 occurences of the same number". I guess your example proves that this is not right for the first 12 clues, but does it hold for the first 11?

Havard
Havard

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Havard wrote:The "rule" that I am trying to prove is right is that: "in the first 11 clues of a sudoku, you can't have more than 5 occurences of the same number".

Like this
Code: Select all
`...12.....8...6..1.1........5..1....4......1.178492365843251697792364158561987234`

and here's a 6/10:
Code: Select all
`...13..8...4...5.1.1...........1...........1.178492365843251697792364158561987234`

RW
RW
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and a 6/9 :

Code: Select all
`...15..8...4.....1.1...........1...........1.175842369843521697792634158561987423`

JPF
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Slightly related question. If a puzzle has no given clues of one digit, what is the maximum amount of digits that appear only once as givens in an unique puzzle? (In other words, is there a puzzle with the digit distribution 01111XXXX, 011111XXX...) I know this is answered somewhere on this forum, but I can't find it...

RW
RW
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JPF wrote:and a 6/9 :

Code: Select all
`...15..8...4.....1.1...........1...........1.175842369843521697792634158561987423`

JPF

wow! Great work guys. Thanks a lot!
This last one of JPF also proved another question I had about how many of the same digit that can follow eachother. And here we have 5 1's lined up. Fantastic! So what ratio is safe to assume? Is 7 / 11 possible? Is a run of 6 1's possible!

Havard
Havard

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Here are 6 "1"s in a row

Code: Select all
`236571...........1.1...........1...........1.175842369843125697792436158561789423`

Ocean posted these 17s, which isnst quite what RW wanted
Code: Select all
`V:433221110000000130000080005420000000600000020005010000000000400070402000000600200000000001000031600200000007000000100050200040036000000001000000800710000000000020000000300000401200800600010300000500040100700200030000000000000000020080010000000000000030040030000000000052000000670080000300000200000000700000203000100700502000000080000160500000000008700500000000450100060007000300000020000000000051000073000000000000600300000000000081000000000018000050005600000000703000200010000400000600060000300830020000200500100000000000070000082000601000000000000020080030001000600400000000 `

It must be possible to remove one and add a few other clues, but not easy !

C
Last edited by coloin on Thu May 24, 2007 5:58 am, edited 1 time in total.
coloin

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RW wrote:Slightly related question. If a puzzle has no given clues of one digit, what is the maximum amount of digits that appear only once as givens in an unique puzzle? (In other words, is there a puzzle with the digit distribution 01111XXXX, 011111XXX...) I know this is answered somewhere on this forum, but I can't find it...

Here is the distribution of the digits for the 40095 new 17s :
Code: Select all
`    15    011122334                                                                                   226    011123333                                                                                   315    011222234                                                                                  7537    011222333                                                                                    25    012222224                                                                                 10028    012222233                                                                                   850    022222223                                                                                    15    111113333                                                                                   121    111122234                                                                                  2847    111122333                                                                                    21    111222224                                                                                 13394    111222233                                                                                  4696    112222223                                                                                     5    122222222                                                                                 ------                                                                                                  40095 `

Code: Select all
`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`

JPF
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Thanks JPF

Which combinations tended to improve the most, with the adddition of the latest 3500 puzzles ?

when Ocean did this count on 32930 puzzles , for example he only had 7 of the [011122334] pattern. All 5 [12222222] and 10 out of 15 [111113333] were accounted for.

C
coloin

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see here the stats given by Gordon at that time.

JPF
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