/sci/ - Science & Math

Anyone?

HEY SCI DO MY HOMEWORK
Quite a clever disguise, but still.

>>2066493
I have a question for you, sir. How is this homework?

This is a question that I have been pondering about for a little bit now out of pure curiosity. I cannot conjure up a definite answer. And that is why I am asking /sci/.

>>2066423
There is one solution.

Hint; top row has the value of 45. Each 3x3 square has a maximum value of 45.

>>2066512
Rather has exactly the value 45.

write a C program to do it for you. Shouldn't take you more than about 15 minutes.

>>2066512
That is not correct.

Here are two solutions:

123 456 789
456 789 123
789 123 456
234 567 891
567 891 234
891 234 567
345 678 912
678 912 345
912 345 678

and

123 456 789
789 123 456
456 789 123
312 645 978
978 312 645
645 978 312
231 564 897
897 231 564
564 897 231

>>2066522
Bit of a problem there... I don't know how to.

http://en.wikipedia.org/wiki/Mathematics_of_Sudoku

total number of solutions to a full empty grid is 6,670,903,752,021,072,936,960
with 1 to 9 filled in on the top line, this will be considerably less, but i don't know how to work it out...

>>2066544
I have already searched around on the internet for solutions and crap. I've read that, and it was much use to me. However, thanks for trying to help somewhat.

While we're on the Sudoku topic, I have a question, too.

There are some puzzle that seem achievable by logic alone, and others that require trial and error to solve. The latter aren't nearly as satisfying.

How would you qualify the difference between the two types of puzzle? I understand that the latter puzzles are still logical in a sense. Are all trial and error situations solvable by other means?

>>2066549
All puzzles are actually achievable by logic alone. The only reason you would think otherwise is cause you are kinda bad at logic.
If you want, post a problem, and I will show you the logic you need to use.

So back to the main topic, does anyone have any theories as to how many solutions there are for this puzzle?

>>2066549
trial and error is not necessary, there is always one definative solution to these puzzles when they are presented... if not... then there are multiple answers, whic his not the point of a proper su doku puzzle.
as an analgy, lets imagine i gave you a puzzle with only 2 numbers filled in, there would be so many different ways to solve it, you could do it in 30 seconds just by following the rules and putting free numbers in wherever you liked

>>2066580
this is true, but only because trial and error is logic. The only difference is whether you calculate it beforehand or you actually write a number down without knowing if it is correct. It is perfectly valid logic to say "if this was a 7, then ... etc etc so this thing in the same row would be a 7, so it can't be a 7"

>>2066580
i prefer kenken...like su doku, bit a smaller grid, which is empty, and there is one definative solution because mathematical formulas control what can exist in certain 'cells'

>>2066584
seems pretty damn hard for a combinatorics problem. I think I could do it if you removed the box rule (only rows and columns have to have 1 through 9)

If you just care about the answer, take wikipedia's answer posted above for the total solutions, and divide by 9! (the number of orderings for the top row)

>>2066553
Just logic that bitch out, yo.

So for the number under the 1, I have 6 possible choices, Then the number under the 2 gives only 5...etc.

Ie, the amount of possible arragnemnts of the first box will be, 6*5*4*3*2*1. Now this already set some resirtcitions on the second box. The number under the 4 can only be 3 possible choices then, under the 5 would be 2, under the 6 would be 1. Same goes for the bottom line.

Hence 6!*3!*3! are the possible combinations just from the first two boxes (upper left and upper middle). Now you have even more restiations on the upper right box now. You should be able to figure it out.

Does any of this make sense to you?

well the first column can be filled out
6*5*6! ways, given that the next column can only be filled out 4*3*6! and the third column 2*1*3!^2

just do that for he next six columns as well and you should have an answer

>>2066606
this is right for the first box, but becomes very difficult beyond that. This is because the number of combinations for each box after that depends on how the first box is arranged. For example, if you have the top left box as
123
456
789
then you already know that 456 are arranged in the bottom of the topright box. However, with a different arrangement for the first box there are more possibilities for the other two.

>>2066606

>>2066619
And that's the dilemma I face. I cannot figure out a clear path for this. Anyone else have ideas?

>>2066580
Thanks for the offer. I reloaded the page from my history, and it generated another random puzzle, and obliterated the original puzzle from my cache.

>>2066590
I understand that there is a single solution.

>>2066593
Yes, I was trying to avoid the "trial and error is logic" response. I suppose I wasn't all that clear. What I was wondering about is what is the distinction between a puzzle in which the reasoning behind each step is clear, and a puzzle in which I determine a square is not 3 by trying that value unsuccessfully.

I'm hoping for a better answer than "depth of logic", but maybe I'd need to provide a specific puzzle.

>>2066619

Nonsense
This problem really isnt that hard. The combinatiosn start dwendling pretty fast.

The total combinatiosn of the first three boxes (upper) are 6!*3!*3!*3!*3!

6! comes from the first box
3! comes from each row (middle and bottom), in the upper middle and upper left 3X3 boxes.

I might be convinved to solve the rest real quick if OP post some tits! TITS?

You really should just Monte Carlo this for your initial conditions.

>>2066636
see>>2066663

>>2066663
Continue on with this logic. I would like to see if you could solve the entire thing.

>>2066663

>>2066682
I will solve some, but not all. UNLESS I GET SOME TITS PICS UP IN HERE!

>>2066700
Here's a nice thread for ya:
>>>/s/10842353

>>2066682
Ok, so it is easy to see that the top rows of 3x3 boxes, give 6!3!3!3!3! combinations, if you dont get this, ASK QUESTIONS!

Now, moving on, we start with the right colum of the entire puzzle. Setting this colums will again give us 6!, we now see the same structure we had when doing the top three boxes, only in the left three boxes. Each 3 colum, will give 3!
Hence, for the top three 3x3 boxes, as well as the left middle, and bottom middle 3x3 box we have

(6!*3!*3!*3!*3!)^2

Iv'e solved more for 5 of the 9 boxes, I will keep going IF YOU POST TITS! (or cool science pics!)

>>2066740
Nice, symmetery in action!

>>2066740
Ment to say left middle and left bottom, sorry

>>2066423
Is anyone still here?

>>2066789

Yes, I am still here. I am the OP. I am thinking about >>2066740. Could you possibly explain this to the fullest? By 6!, what do you mean?

>>2066799
Disregard that