sudoku

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

Vers la solution / to the solution.

How to Calculate the number of possible Sudokus

The notepad where I had a few sudokus I had constructed has, alas, been taken away. Three possibilities for who could have taken it, no use accusing one of these.

However, this doesn't quite stop me from thinking of sudokus.

I tried to figure out how many sudokus can be made, only by nine by nine and solutions (each sudoku being at once a solution and the grids with empty spaces leaving you to find the solution, for each solution, what can be left empty is of course various, and I'm not considering that).

I made a mistake, but I'll give my first thought first.

First slot obviously can be filled in nine ways, any numeral from 1 to 9. Next, 8 ways, all except the one taken. Next, 7 ways and so on. First row or column, whichever way you prefer to count, is therefore obviously 9*8*7*6*5*4*3*2*1.

This is obvious.

Now, I considered, next row (as I count) begins with 8. Also obvious. Then you go on with 7 so, second row = 1st row:9. And so on, then only to multiply possibilities for the rows.

No. First slot in second row is 8, but second is not necessarily 7 (except between these two it is, I'll come back to that). If the second of first row and first of second row are two different numerals, yes, then second of second row has only seven possibilities. But if they are same numeral (not possible except where that would be two different 3 by 3 squares, not the case here, but the complication actually comes in later on if not here), the second also would have 8 numerals, any which was not the one which was "both second of first and first of second" (applicable at other places than the one mentioned).

Despite this complication, as there are only nine rows, and as the ban on identic numerals within same 3 by 3 square poses further limitations, the number of sudoku solutions is finite. While they are many, probably many more than a man can solve sudokus in a normal lifetime.

However, computers can deal with "infinite" combination possibilities more than men, but an infinite use of all the possibilities is not necessary.

Constructing sudokus is a passionate pastime, which can then be used (if your notepad isn't taken away) to write others entertaining sudokus.

And, when your projects are being cancelled by people referring to you as meshuggah, perhaps a passionate pastime is needed. Not accusing the man in Jewish outfit sitting in front of me who pronounced the word, not exonerating him either. It could be a coincidence, it could be not such.

Either way, I did some sudokus earlier here, and as I link to them via label sudoku, you click the label and enjoy my former sudokus (solutions on another blog, originally serving as a test blog to disprove AI)./HGL

sudoku

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

Apparent Only Options - illustrated by a sudoku row ...

... or what remained of it when previous boxes were already filled in, five boxes left.

Bold style, small numerals = options, as had.

Normal style, normal size = solutions, alternative or consecutively consequent.

The options given as had depend in part not just on the row previous to it, but also on what square and what column they are in. I here ignore that option 2 for second box was already off, as I already had that one in the square while examinating this row.

479	2478	28	47	278
	2
	2	8
	2	8		7
	2	8	4	7
9	2	8	4	7
479	2478	28	47	278
	4
	4		7
9	4		7
9	4	28	7	28
479	2478	28	47	278
	7
	7		4
9	7		4
9	7	28	4	28
479	2478	28	47	278
	8
	8	2
	8	2		7
	8	2	4	7
9	8	2	4	7
So, first box needs to be a nine ? What about possibilities 4 and 7 ?
479	2478	28	47	278
4
4			7
4		28	7	28
4	?	28	7	28
479	2478	28	47	278
7
7			4
7		28	4	28
7	?	28	4	28
Actually, there is another reason why first needs to be a nine, which I had overlooked. No other box is open to a nine, so it is the only place one can put it.

The lesson of this is that a "why can't" doesn't always work.

My adversaries would apply this to my question "why can't angels be dancing the so called parallax with the stars". I would apply it to their "all parallax observations are dependent on Earth moving around the Sun each year". Except that, when it comes to negative parallax - my reason - and this observed by the Tycho experiment, they would make exceptions. Obviously a parallactic movement of a star has to be opposite rotation to that of Earth, it cannot be "negative", i e cannot be same apparent rotation as Earths real rotation. Their solution : some of the observations are not accurate. My solution : Earth is not moving. It is angels dancing with the stars. Well, their "some observations are not accurate" is defeating their position. If so many observations are inaccurate, how could we know any are accurate?*

Hans Georg Lundahl
Bibliothèque Audoux
St Cléophas of Emmaus
25-IX-2015

* A bit like the 4 or 7 options leading to a question mark too.

Sudoku

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

Solution click here/clicquez ici.