Sudoko theory

(Not sure if this should go here or GQ – if not enough math people hang out here, I guess we can move it.)

If not a single 9 is among the given numbers that you start with, will it be possible to pin down the 9’s later on in the game? Or are you doomed to be stuck where I am, which is a whole slew of “this can be this or this” (or, more discouragingly, “this, this, this, or this”) squares and no way to start the domino train that will sort all of them out?

I did my final undergrad Mathematics project on this, the short answer is ‘no, there is not always a domino effect’. The long answer comes with a beautiful Power Point presentation and numerous mentions of Latin Squares.

Unless there is more than 1 possible solution for the numbers you’re looking at, you can eventually arrive at the solution.

Yes, I would agree that there are certainly solvable positions that wouldn’t start with any 9. Somewhere along the way, you’d be able to fill in all other 8 numbers in a row, column, or square, and thus get a 9 by the process of elimination.

On the other hand, obviously you cannot have a solvable sudoku with no 8’s OR nines, because whenever you got all the other 7 numbers filled in, there’s still no conceivable way of telling that one blank space should be an 8 and the other a 9, or vice versa. If you came up with one legal solution, you’d be able to generate another by swapping all the 8s with 9s.

A solution exists. That sounds pretty solvable to me.

Well, yeah, to you :stuck_out_tongue:

Post the puzzle you’re stuck on.

6 _ 7 / 2 4 _ / _ _ 3
4 _ _ / 1 **5 6 ** / _ 7 _
_ 1 _ / _ 3 7 / 6 4 _
2 4 _ / _ 1 5 / 7 6 8
_ _ _ / 7 6 **4 ** / _ 2 _
**7 6 1 ** / _ _ 2 / _ _ 4
_ **2 4 ** / 6 7 _ / _ **8 **_
_ 7 _ / 5 2 _ / 4 _ 6
5 _ 6 / 4 _ **1 / 2 _ 7 **

Bold are the given numbers; not bold is where I think I am with this, which may or may not be correct.

After preview: dang, my extra spaces disappeared. Hope the slashes help.

I had a go, and got to your current situation, where I hit the proverbial wall. It rarely takes me that long to figure out a sudoku, so I went to sudokusolver.co.uk, and ran the puzzle there.

The answer (not to the puzzle, but from the solver):

Solved it, but had to guess, and there might be more than one solution.

So, IMO, not a great puzzle.

If anyone wants to give it a go, I’ve recreated the original puzzle in Excel and HTML. I’ll pass this one over to my wife, who spends a good hour or two each day on sudoko.

I think I have the answer, although I may have made a mistake* that helped me solve it.

6 5 7 | 2 4 9 | 1 5 3

4 3 8 | 1 5 6 | 8 7 9

9 1 2 | 8 3 7 | 6 4 2

2 4 3 | 9 1 5 | 7 6 8

8 9 5 | 7 6 4 | 3 2 1

7 6 1 | 3 8 2 | 5 9 4

1 2 4 | 6 7 3 | 9 8 5

3 7 9 | 5 2 8 | 4 1 6

5 8 6 | 4 9 1 | 2 3 7

*I think I made an invalid assumption on placing the first nine (positioning was correct, but it was lucky versus logical.

Just for the record, if you type out the puzzle like this:
[noparse]



**6 _ 7  /  2**  4 _  /   _ _ **3**
4 _ _   /  1 **5 6 ** /   _ 7 _
_ **1 _  /   _ 3** 7  /   **6 4** _
**2** 4 _  /   _ 1 5  /   **7 6 8**
_ _ _   /  **7** 6 **4 ** /   _ 2 _
**7 6 1 **  /  _ _ 2  /   _ _ **4**
_ **2 4 **  /  6 **7** _  /   _ **8 **_
_ 7 _  /   **5 2** _  /   4 _ 6
**5** _ 6  /   4 _ **1  /   2 _ 7  **   


[/noparse]

you’ll get this as the output:



**6 _ 7  /  2**  4 _  /   _ _ **3**
4 _ _   /  1 **5 6 ** /   _ 7 _
_ **1 _  /   _ 3** 7  /   **6 4** _
**2** 4 _  /   _ 1 5  /   **7 6 8**
_ _ _   /  **7** 6 **4 ** /   _ 2 _
**7 6 1 **  /  _ _ 2  /   _ _ **4**
_ **2 4 **  /  6 **7** _  /   _ **8 **_
_ 7 _  /   **5 2** _  /   4 _ 6
**5** _ 6  /   4 _ **1  /   2 _ 7  **   


Unfortunately, the spaces in the editor don’t look the same as the spaces in the code box, so you’ll have to preview and muck around a bit, but that’s your best bet for representing something with multiple spaces.

ETA: If you want to spoiler your sudoku, you’ll need to put the spoiler box inside the code box.

Shibb, you’re close but you’ve got two 8s in your second row from the top and two 2s in your third row from the top. I think if you invert the 8 and 2 in the upper left box you’re good.

This was a toughie.

lieu,
You are correct about there being at least one mistake in Shibb’s answer, but since there is already an 8 in the third row from the top, your solution won’t work. Incidentally, the first row from the top has two 5s.

As far as I can tell there is only one solution, but to get it required a guess from the stage twickster was at to begin with in order to complete it.

I can provide the link in the chain, if required :wink:

The solution is unique (confirmable with any computer sudoku solver, like this one.

I’m still wondering where the nest is. Any theories on that?

Thanks all. I’ve moved on from that one. The one I did this afternoon had a similar situation – not a single 8 in the given numbers – but turned out to be solvable*, answering my original question in the non-theoretical fashion that works best with me on these things.

*I had all but three numbers in one column. Two of the blanks were each “either a 2 or a 5,” so the 8 was in the third blank.

It’s solveable. I’m not sure what you mean by a guess - agreed that at the point twickster is at, there’s nothing else easily obvious. However, at that point, I’ve found at least one square that only allows two choices, and one of the choices leads to later impossibilities. Finding that out required going pretty far down the “domino train” with the wrong answer however. Once you fill in that square with the other number, the train is easy.

Thanks, Eureka, I kept working between meetings and finally drew Wilson’s conclusion.

Panamajack, what’s a nest?

twickster: I got as far as you did. I plugged it into Simple Sudoku, which gave me a hint: Exclude based on “colors”. The help file offers this:

I swear I am not stupid, but I don’t understand this at all. :frowning: Can anyone help a brother?