## Has anyone noticed this idiosyncrasy?

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

### Has anyone noticed this idiosyncrasy?

Hello,I have played for several years, and I love it. However, I found a slight "glitch". After playing several thousand games it occurred to me that I never solved a game where any one line, vertical or horizontal, was solved with the numbers going in series. (eg. 1-9 or 9-1). Am I alone here??
abrooks051

Posts: 3
Joined: 12 May 2015

### Re: Has anyone noticed this idiosyncrasy?

Try solving this puzzle. The first row in the solution should be 123456789

Code: Select all
`1..............4.64...183258...3.24.........7....2...823...58..7.49.......9.....3`

Leren

<edit>

Just thinking about this a bit further, the number of permutations of digits in a row or column is 9 ! (9 Factorial = 9*8*7*6*5*4*3*2*1) = 362,880

You have 9*2*2 = 36 ways of being satisfied, so the probability that a random puzzle that meets your requirements is 362,880/36 = 10,080

Maybe you just haven't 'solved enough puzzles yet.

Leren
Leren

Posts: 3462
Joined: 03 June 2012

### Re: Has anyone noticed this idiosyncrasy?

Leren,
Thank you for the help. Math was never one of my best subjects. I thought I had done quite a few games but it seems I have quite a few to go.
abrooks051

Posts: 3
Joined: 12 May 2015

### Re: Has anyone noticed this idiosyncrasy?

If you solve 1 puzzle a day you should find a suitable puzzle on average about once every 27.6 years !

However you can always swap the clues around in any puzzle to get what you want. Here's how:

In the example puzzle I gave you the bottom row solves to 689241573. Now suppose you wanted to see a solved puzzle with the bottom row solved to 987654321

689241573 is what you have in the bottom row.
987654321 is what you want in the bottom row.

All you have to do to get from what you have to what you want is to swap each clue from the top line to the bottom line. So if the puzzle has a clue 6 change that clue to 9 leave 8 as 8, change 9 to 7, 2 to 6 etc all the way along the 2 lines.

The puzzle will solve exactly the same way as before but you will find that the bottom row is 987654321 !

Leren
Leren

Posts: 3462
Joined: 03 June 2012

### Re: Has anyone noticed this idiosyncrasy?

Here' a very hard one with six empty rows and columns to keep you guessing:
Code: Select all
` . . 4 8 . 3 1 . . . 8 9 2 . 1 4 3 . . . . . . . . . . . 4 5 . . . 9 2 . . . . . . . . . . . 1 8 . . . 3 6 . . . . . . . . . . . 3 2 1 . 5 6 9 . . . 1 3 . 2 8 . .`

Regards,

Mike Metcalf

m_b_metcalf
2017 Supporter

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Location: Berlin

### Re: Has anyone noticed this idiosyncrasy?

Leren,
I'm 63 so I guess I better do more than one puzzle a day
Alan
abrooks051

Posts: 3
Joined: 12 May 2015

### Re: Has anyone noticed this idiosyncrasy?

And here's another: 1...5.......1...6...4...2...7...3...5...2...8...6...7...6...3...3...7.......4...1
PC.jpg (22.06 KiB) Viewed 612 times
Yogi
2017 Supporter

Posts: 140
Joined: 05 December 2015
Location: New Zealand

### Re: Has anyone noticed this idiosyncrasy?

Hi Yogi, just tried your puzzle and it solved (apart from basic mark-offs and singles), with just one naked triple in Column 5. You really like those naked triples !

Leren
Last edited by Leren on Fri May 20, 2016 6:30 am, edited 1 time in total.
Leren

Posts: 3462
Joined: 03 June 2012

### Re: Has anyone noticed this idiosyncrasy?

I just tried solving Mike's puzzle by normal methods. It wasn't too hard, but I noticed that there were a lot of single digit moves on 7. That suggested template analysis.

Not too surprisingly the puzzle solved with a single non-basic move : single digit template analysis on 7 :

Code: Select all
`*--------------------------------------------------------------*| 2567 *7-256 4      | 8     5679  3      | 1     57    29     || 57    8     9      | 2    *7-5   1      | 4     3     6      || 1     2567  3      | 4679  45679 4679   |*7-5   8     29     ||--------------------+--------------------+--------------------|| 367   4     5      | 67    13    678    | 9     2     18     || 23679 2679 *7-6    | 45679 13    46789  | 57    457   18     || 79    1     8      | 4579  2     479    | 3     6     7      ||--------------------+--------------------+--------------------|| 45678 5679  67     | 4679  46789 4679   | 2     1    *3-45   ||*7-48  3     2      | 1     478   5      | 6     9     47     || 4679  679   1      | 3     4679  2      | 8    *7-45  457    |*--------------------------------------------------------------*`

Single digit template analysis on 7 => r1c2, r2c5, r3c7, r5c3, r7c9, r8c1 and r9c8 = 7; stte

Here's the solution:

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

Row 4 will keep abrooks051 happy and the template solution will keep people who like computer solutions happy.

Leren
Leren

Posts: 3462
Joined: 03 June 2012

### Re: Has anyone noticed this idiosyncrasy?

Actually, the puzzle I posted was one from a list of 851 puzzles of that pattern and it seems that they are all rated as MILD, whatever that means. I'm getting a bit bored with them myself. I just happened to notice that the solution included a numerical 1-9.
Yogi
2017 Supporter

Posts: 140
Joined: 05 December 2015
Location: New Zealand

Yogi wrote:Actually, the puzzle I posted was one from a list of 851 puzzles of that pattern and it seems that they are all rated as MILD, whatever that means. I'm getting a bit bored with them myself. I just happened to notice that the solution included a numerical 1-9.

{ off-topic }

"mild" ? all ??
Code: Select all
` 1 . . | . 5 . | . . .  . . . | 2 . . | . 3 .  . . 4 | . . . | 6 . . -------+-------+------ . 9 . | . . 3 | . . .  6 . . | . 7 . | . . 5  . . . | 1 . . | . 7 . -------+-------+------ . . 1 | . . . | 2 . .  . 3 . | . . 9 | . . .  . . . | . 6 . | . . 1 `
1...5.......2...3...4...6...9...3...6...7...5...1...7...1...2...3...9.......6...1
[ play ]

Pat

Posts: 3710
Joined: 18 July 2005

Yogi
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Posts: 140
Joined: 05 December 2015
Location: New Zealand