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Sudoku

  • Thread starter jimscott
  • Start date

jimscott

Tropical Fish Enthusiast
I love math and puzzles, but this number puzzle is puzzling me! Is there a system to solving them or is it just a whole mess of trial and error?
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what the heck is that?
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aaaaaaaa!!!! i just went to the website. i want to run away... fast. (my mind is lazy at times and i have the attention span of a 5 year old sometimes...)

BTW... nerd!! (yes, i called you a nerd- now go do my homework. i have a physics test and a lab report.)
 
I LOVE sudokus!!

And yes, there is a system to solving them.  It's hard to explain without an actual puzzle in front of us where I can SHOW you, but I'll do my best.

The basic rules are, each row, column, and 3x3 box contains the numbers 1-9.  So, what you want to do is process of elimination.  If a blank square is in a row that already has a 7, then it can't be a 7.  If its column has the numbers 1 through 6, then the only remaining numbers it could possibly be are 8 and 9.  if there's already an 8 in its 3x3 square, bingo, it must be a 9!

they take a little time to get the hang of them...but I guarantee if you love math and puzzles, you will LOVVVEEE sudoku!!
 
For a while I was writing a sudoku-solving algorithm for my math class, but I didn't have enough time to devote to it. A good primer on basic strategy can be found here. The idea behind my solution was to keep a table of which numbers remain unused in each row, column, and square. Such tabulations help eliminate a large amount of choices from consideration. I never figured out a good way to decide on which of the available choices was best, so you're on your own from there, but keeping tabs on unused numbers by itself seems to help noticably. (At least, for me it does.)
~Joe

PS - Keep multiple copies of your solution as you work on it! Nothing slows sudoku-solving down like rewriting the whole grid.
 
I wonder how sudokus are created.
 
[b said:
Quote[/b] (seedjar @ Mar. 29 2006,1:17)]For a while I was writing a sudoku-solving algorithm for my math class, but I didn't have enough time to devote to it. A good primer on basic strategy can be found here. The idea behind my solution was to keep a table of which numbers remain unused in each row, column, and square. Such tabulations help eliminate a large amount of choices from consideration. I never figured out a good way to decide on which of the available choices was best, so you're on your own from there, but keeping tabs on unused numbers by itself seems to help noticably. (At least, for me it does.)
~Joe

PS - Keep multiple copies of your solution as you work on it! Nothing slows sudoku-solving down like rewriting the whole grid.
I think there's an open source sudoku solver, but I can't remember. Anywho I do remember reading the math theory fundamentals of it though, and I think they can be found in the wikipedia.
 
Joe, thank you for the link. I added it to favorites.

Emily, what I had been doing is pick one of the 3x3's and solved that. Then I would move to adjacent 3x3 and get that one solved, with respect to the first one. And them I'd move on from there. But then my luck would run out and I'd realize that I hadn't found the correct combination from the first grid.

Theresa, (LOL!) thank you for the compliment! But I don't wear glasses and I thought all nerds do. Does that then make me a geek? I don't think I'm a dweeb. But I digress.. Hey, good luck with Physics! Just remember, E=mc2 and mgh and 1/2mv2 and pv=nrt!

Does it matter where one starts - center, as opposed to the sides? Is there more than once correct solution or only one?

I gave my 12 year old genius son (also autistic) a Sudoko puzzle book a couple weeks ago. He seemed mildly interested in it.

Is anybody familiar with the 6 x 6 grid whereby you number the squares from 1-36 by using the Knight's move in chess?
 
yeah, committing to a square like that won't work...you have to keep in in context with the entire puzzle.

A lot of the time there will be an easy place to start. If you have 3 3x3 squares in a row, for example, and the first two already have 7s in the middle and bottom rows respectively, and the third one has no 7 but only one blank space on its top row, then that space is a 7.

and most of the time (99.9%) there is only one solution. though my stepdad and I managed to come up with 2 completely different solutions for the same puzzle once!
 
Samurai Sudoku. It's absolute Sudokumania bliss!
It's also far easier if you remove the whole false relationship with mathematics - it has nothing to do with them just because most puzzles are set up with numbers (they can be anything from letters to shapes to colours).
 
  • #10
Actually shoku, sudoku is very mathematical. Even if you take away the numbers, you still have nine distinct symbols and a definite set of rules, which is enough to have math do the hard work for you. I spent most of last year writing general solutions to constraint-based problems like this for a math/computer programming class. Combinatorics (the math of countable objects) and formal logic (logic based on symbol manipulation, which can be boiled down to arithmetic) have lots to say about games like sudoku. For example, when choosing which number to place next, what number will take the least amount of consideration? Generally speaking (and assuming your partial solution is correct,) it's whatever number has been used most often in the solution; if you're placed eight 5s and less of everything else, then there will be only one available choice for where to put the last 5, whereas the rest of the numbers require consideration of a larger number of choices to determine the correct placement. Further, you can ignore the 'each row, column and square has 1-9' rule and instead focus on the simpler concept of not having doubles in any row, column or square, because in the confines of sudoku these two rules imply exactly the same thing.
~Joe
 
  • #11
Shoku's blatant statement forced me to renew my knowledge of sudoku
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while reading this article strictly about the math involved in solving a puzzle I strayed across a sudoku CUBE
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here and some other obscure variant here.
 
  • #12
I apologise, I should've clarified. I was referring to how to play/solve it, in which case you don't need the math consciously (I've cleared all sudoku puzzles I've come across to this day, and that's well over 300 - I just use my eyes, common sense (maths, subconsciously, perhaps?), and a pen/pencil) - how it works is definitely mathematical but I'm not interested in the mechanics of the puzzle - just to solve it
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  • #13
Hi Amori and welcome to the discussion! I know what you are saying. That made sense.

Would you all say that it doesn't matter if one approaches as a micro-grid of 9, as opposed to solving for a row or column?

My introduction to this was a couple months ago, in the back of an airplane magazine. I found it a bit frustrating that I never solved the puzzle and had numerous crossouts on the way to exasperation. This is especially bothersome because I do well with puzles, particularly those of math orientation. Perhaps I should have done more Rubic's Cube as a kid!

I just can't see past process of elimination, trial & error, and common sense. I can't even do an integral!

Here is a link for sudoku online:

<a href="http://www.google.com/url?sa=l&ai=Bpf7kxikrRJeBNLukiAGMzcn4B7W08AbZzO6XAeOMsHngxQgQARgBIJVOKAVIjDlQ3NfULaoBCm5hcnJvd2JhbmTIA
QGVAiKRIgo&num=1&q=http://www.gametownamerica.com/Destination/CategoryPage.aspx%3Ftag%3DFree.Games.Sudoku%26ref%3D12831" target="_blank">Sudoku online</a>

Emily, I tried cutting and pasting a grid, only the contours didn't show up. Would it be possible for you to illustrate how you would approach this sample puzzle?


8 1 5
4 2 3 1 6
7 6 9 3
1 4 6 5
9 8 6 7
6 3 9 2
8 4 5 7
3 2 7 9 4
5 4 2
 
  • #14
I'm having trouble figuring out which columns the numbers go in..could you maybe put zeros where there are blank spaces, Jim?
 
  • #15
Sorry about that, Emily! Okay, I went back to that site and the grid changed. Must be a daily puzzle. Anyways, here's today's grid:

0 0 0 6 0 0 0 3 2
0 5 6 8 0 0 7 0 0
8 0 7 9 1 0 0 5 0
0 0 2 3 0 0 0 6 7
9 0 0 5 0 4 0 0 3
7 4 0 0 0 6 1 0 0
0 3 0 0 2 8 5 0 1
0 0 8 0 0 5 9 4 0
4 1 0 0 0 9 0 0 0
 
  • #16
A coworker of mine was crazy over Sudoku so I tried it. She said it was about logic...but I didn't see any logic to it. It just placing numbers in squares. It seemed pretty random to me...but I didn't spend a lot time with it as I found it rather boring. I would give it another shot though since people seem to love it.
 
  • #17
Noooo! Please, please, pleeease don't say it's random!
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Jim:

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

I think that's right.
 
  • #18
Amori, do you have a system other than picking a row (or column)with the most numbers in it and working off of that, with having to backtrack when it doesn't work?
 
  • #19
You know what, Jim? I really don't know anymore. At first it was a matter of doing lines and boxes but now it's just automatic and I don't think about it (I go into a trance of some sort - last summer I completely lost track of time and solved about 50 hard and fiendish puzzles from dusk to dawn!).
In the case of this puzzle it was mostly by lines, then completing them and the 3x3 boxes.
Unless I'm really stuck I seek how many of the same number can interact and work from there.

OK, that didn't make any sense!
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  • #20
[b said:
Quote[/b] (shokuchuu @ Mar. 30 2006,11:54)]In the case of this puzzle it was mostly by lines, then completing them and the 3x3 boxes.
Unless I'm really stuck I seek how many of the same number can interact and work from there.

OK, that didn't make any sense!  
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Now that needs some eluscidation!!
 
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