The New Sudoku Players' Forum

[warrentrammell]

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???????

[Leren]

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

Leren

[Yogi]

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.

[m_b_metcalf]

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 . .   


Mike

[coloin]

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.

[Mathimagics]

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

[faskversi]

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

{spam removed} is a link to a program which reliably morphs a puzzle [81 digit text string] to its minimum numerographic ! form.

It's also possible that the selection process for the puzzles prioritized those with a zero in the upper left hand corner, for example, because they may be considered easier or more standard in terms of Sudoku puzzle construction.

[Yogi]

Perhaps Mike could explain in what sense his two examples are the same puzzle.

[m_b_metcalf]

Perhaps Mike could explain in what sense his two examples are the same puzzle.

This thread looks like a troll, but I'll nevertheless answer your question. The two puzzles in line format are:

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..   


but they have the same minlex form:

Code: Select all

........1.......2......3.......4.5....6...3....781.....1..2...4.3.....7.95.......


Mike

[Yogi]

I think we’ve dealt with warrentrammell's question of why there appears to be many more 17-clue puzzles which start with 0. The false impression is caused by the way we typically list such collections of puzzles. Maybe tracyberge can let us know what more she would like to know.
For mike: thanks for your input. Reducing the puzzles to MinLex form is clearly of value to some, especially if you are attempting to assemble a definitive list of puzzles of a specific type. However, I don’t get involved in such things so the 3 codes in your last post look like different puzzles to a player like me: different starting clues and different end solutions. All were solved easily with singles, but that prompts another question: Would all puzzles that reduce to the same MinLex code have similar difficulty ratings?

[champagne]

Would all puzzles that reduce to the same MinLex code have similar difficulty ratings?

The answer is basically "yes". If we forget oddities appearing in very high ratings and with some UR/UL morph dependent rules, all morphs of a given puzzles have the same SER rating.

[Yogi]

Thanx. I think it's over and out for me.