## 17 digit puzzles

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

### 17 digit puzzles

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???????
warrentrammell

Posts: 1
Joined: 21 October 2022

### Re: 17 digit puzzles

Leren
Leren

Posts: 4527
Joined: 03 June 2012

### 17 digit puzzles

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.

Yogi
2017 Supporter

Posts: 279
Joined: 05 December 2015
Location: New Zealand

### Re: 17 digit puzzles

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

m_b_metcalf
2017 Supporter

Posts: 13322
Joined: 15 May 2006
Location: Berlin

### Re: 17 digit puzzles

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.
coloin

Posts: 2283
Joined: 05 May 2005
Location: Devon

### Re: 17 digit puzzles

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

Mathimagics
2017 Supporter

Posts: 1915
Joined: 27 May 2015
Location: Canberra

### Re: 17 digit puzzles

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.
Thomas32

Posts: 1
Joined: 26 September 2022