17 digit puzzles

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17 digit puzzles

Postby warrentrammell » Fri Oct 21, 2022 6:04 pm

I recently downloaded this file. I do not understand why there are over 30,000 puzzles with a zero in upper left hand corner and less than 4000 puzzles with the either of other 9 digits. Any explanation???????
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Re: 17 digit puzzles

Postby Leren » Sat Oct 22, 2022 8:39 am

If you provide a link to the file you downloaded it might be possible to understand and answer your question.

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17 digit puzzles

Postby Yogi » Fri Oct 28, 2022 10:42 am

A possible explanation could be that the intention was to produce a list of valid 17-clue sudoku puzzle codes, assembled numerically in canonical form. This would mean that the list would only include codes which solve to a single unique solution, and would probably start with those puzzles with clues something like 00000100200... followed by 00000102... and so-on. Only after exhausting all possibilities starting with five or more zeros then 1, would it move on to 000002.. and later to 000003
After moving on to codes starting with 000009 the list would only then move on to those with 00001..
Remember also that 0 is not a number. It just represents an unfilled cell in the initial code string.
In some systems they use . instead of 0 to avoid the implication that 0 is a number.
This approach makes it appear (falsely) that there are far more codes with empty top left cells. Another factor which could skew the picture is that a definitive list would not include codes which represent the same puzzles which have been included earlier in the list, but have a different number set. After all, the characters we use in sudoku puzzles are not numbers with numerical values, only symbols, which can be freely interchanged.
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Re: 17 digit puzzles

Postby m_b_metcalf » Fri Oct 28, 2022 12:26 pm

An example is perhaps helpful; here is the first puzzle in two forms:
Code: Select all
 . . . . . . . 1 .
 4 . . . . . . . .
 . 2 . . . . . . .
 . . . . 5 . 4 . 7
 . . 8 . . . 3 . .
 . . 1 . 9 . . . .
 3 . . 4 . . 2 . .
 . 5 . 1 . . . . .
 . . . 8 . 6 . . .   

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

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Re: 17 digit puzzles

Postby coloin » Sat Oct 29, 2022 9:44 am

Yes its an isomorph thing

There are upwards of 6^8 *2 * 9! ways to show the same puzzle.

However by default all 17C puzzles can all be changed so that they start with 8 empty cells

Here is a link to a program which reliably morphs a puzzle [81 digit text string] to its minimum numerographic ! form.
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Re: 17 digit puzzles

Postby Mathimagics » Mon Oct 31, 2022 12:32 pm

You are all wasting your breath, I think!

OP has not even visited the form since Oct 23, and the question that Leren asked ("which file was that?") remains a mystery
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Re: 17 digit puzzles

Postby Thomas32 » Mon Jan 30, 2023 10:41 am

warrentrammell wrote:I recently downloaded this file. I do not understand why there are over 30,000 puzzles with a zero in upper left hand corner and less than 4000 puzzles with the either of other 9 digits. Any explanation???????

It is likely that the puzzles with the number 0 in the upper left corner were specifically generated to have that configuration. This could be due to various reasons, such as creating more puzzles with a specific starting number, or to match a specific request or requirement. Without further information, it is difficult to determine the exact reason.
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