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The ultimate math question...

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Zak

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I'm not even sure if anyone in the world knows the answer to this, but for anyone here who's REALLY good at math (I thought I was):

I'm sure you're probably familiar with sudokus. And how they always start with a different amount of digits, some are easy and start with around 35, others have about 20. The question is: What's the LEAST amount of digits needed to be given to start with, in order for it to be legitly solvable?

By the way, the lowest one I've heard of is 17. But just wondering if anyone can come up with a formula to figure this out... I know we're not all ivy league students here, but who knows what some of you can do...


~Zak
 
I don't understand what you're asking. I mean you don't need to be given ANY numbers for it to be solvable, you could be given a blank one and just fill it in. Or are you asking how many numbers have to be given to make it so that there is only ONE solution? In that case wouldn't it just be the number of rows/columns minus one? Like in a normal sudoku with 9 rows and 9 columns, you'd need 8 numbers given, making sure at least 8 rows and 8 columns had a number placed in them? Or are you asking something else? It's really not clear.
 
Well. It depends on the exact solutions. Some solutions require more initial positions that others.

There is no simple formula to figure this out, that much I'm sure. The best way is probably to adapt some solving algorithms or puzzle-generation algorithms.
 
ChaosRocket said:
I don't understand what you're asking. I mean you don't need to be given ANY numbers for it to be solvable, you could be given a blank one and just fill it in. Or are you asking how many numbers have to be given to make it so that there is only ONE solution? In that case wouldn't it just be the number of rows/columns minus one? Like in a normal sudoku with 9 rows and 9 columns, you'd need 8 numbers given, making sure at least 8 rows and 8 columns had a number placed in them? Or are you asking something else? It's really not clear.
Click to expand...


Obviously that's what I'm saying, since if it has more that one solution, it isn't really solvable... it's open-ended. What else could I have meant? :rolleyes:

Plus, I don't think that would really work...
 
Having more than one solution doesn't mean it's "not solvable." The definition of "not solvable" is having NO solution, not having multiple solutions. You can have a problem that has more than one right answer.

I dunno, it seems to me it would work.
 
ChaosRocket said:
Having more than one solution doesn't mean it's "not solvable." The definition of "not solvable" is having NO solution, not having multiple solutions. You can have a problem that has more than one right answer.

I dunno, it seems to me it would work.
Click to expand...

Yeah, but the point of one is to have just one answer. And seeing as if it had more than one (but wasn't meant to), when you fill out everything you can PROVE leaving blank the ones you don't know which would most likely be different in the multiple solution, you'd be stuck because you wouldn't know which is right, considering even if there accidentally were two solutions and you didn't know it, I'd be afraid I screwed up if I just made a guess. Or even if I did find both solutions (unless it said at the top "THIS HAS MORE THAN ONE SOLUTION") I'd assume they intended for there to be one, and think there was something in the other one or two that didn't add up that I was missing.


Either way, bottom line is, I meant just one solution... but if you can think of a way with only eight digits to start with having just one solution, I'd call you a genius. Personally, I think it's impossible... but I have yet to find a way to prove that. The one with the least digits I'd ever heard of was 17.





~Zak
 
The least anyone has ever found is 17.

If you permit more than one solution to a grid, then of course, the minimum is zero.
 
Yeah, I was just thinking that since there's a solid reason why you could definitely never have less than 8 numbers and get only one solution, that there was probably some configuration out there that worked with only 8 numbers. Off the top of my head I just can't think of a particular reason why 17 would be the magic number.
 
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