so i was thinking...do you think there is an infinetely large matrix of numbers in which every possible 9x9 box you draw would give you a completed sudoku? is it possible? is it plausible? if either one is correct and the matrix wasn't so infinitely huge, that'd make for an interesting solver. all you'd have to do was plug in the clues and the solver could pinpoint the exact location on the matrix and display the rest of the numbers.
probably wishful thinking...just an American's theories, probably not worth much. oh well, can't hurt to guess.
theory....infinitely large sudoku matrix?
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theory....infinitely large sudoku matrix?
by lobby__boy » Thu Jun 09, 2005 5:17 am
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by abailes » Thu Jun 09, 2005 9:26 am
Lobby_boy,
You have to be careful with terminology here. There is a fundamental difference between infinite and very large finite.
There is of course a limit to the number of grids that are possible. Just putting any number (1-9) in 81 cells has a number of combinations 9^81 (a very large finite number, not an infinite one!), but of course the number of valid Sudoku grids is substantially less than that. If you think of the number of combinations of placing 1 through 9 on each row, you end up with (9!)^9, but of course, the vast majority of even these combinations are not valid sudoku grids.
The exact number is being discussed in great detail in this forum: http://forum.enjoysudoku.com/viewtopic.php?t=44
Whatever the eventual answer is, the list of grids is definitely too large for it to be worth a human checking through them in order to get to a solution to a particular puzzle. And it has already been established that it is trivial to code a computer programme to solve it by trial and error in each empty cell (some of them take 0.1 seconds to complete any given puzzle). So there would appear to be little value in a computer programme using the list of complete grids to solve it, if such a list could be generated.
Sudokus can be solved much more easily by computers (through trial and error, or by definied logical steps) than by humans - accept it. The fun of sudoku is for human solvers to solve them in any way they can. There are a bunch of natural logical stages at the moment as listed here: http://www.simes.clara.co.uk/programs/sudokutechniques.htm
Don't stop thinking. I'm sure there are other techniques out there and I would love for somebody to find them. But, sorry, checking through a vast list of possible grids isn't going to be one of them.
You have to be careful with terminology here. There is a fundamental difference between infinite and very large finite.
There is of course a limit to the number of grids that are possible. Just putting any number (1-9) in 81 cells has a number of combinations 9^81 (a very large finite number, not an infinite one!), but of course the number of valid Sudoku grids is substantially less than that. If you think of the number of combinations of placing 1 through 9 on each row, you end up with (9!)^9, but of course, the vast majority of even these combinations are not valid sudoku grids.
The exact number is being discussed in great detail in this forum: http://forum.enjoysudoku.com/viewtopic.php?t=44
Whatever the eventual answer is, the list of grids is definitely too large for it to be worth a human checking through them in order to get to a solution to a particular puzzle. And it has already been established that it is trivial to code a computer programme to solve it by trial and error in each empty cell (some of them take 0.1 seconds to complete any given puzzle). So there would appear to be little value in a computer programme using the list of complete grids to solve it, if such a list could be generated.
Sudokus can be solved much more easily by computers (through trial and error, or by definied logical steps) than by humans - accept it. The fun of sudoku is for human solvers to solve them in any way they can. There are a bunch of natural logical stages at the moment as listed here: http://www.simes.clara.co.uk/programs/sudokutechniques.htm
Don't stop thinking. I'm sure there are other techniques out there and I would love for somebody to find them. But, sorry, checking through a vast list of possible grids isn't going to be one of them.
- abailes
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by lobby__boy » Thu Jun 09, 2005 11:40 am
yeah...i thought about it after i posted and i figured 'ifinite' was probably the wrong word. it was around 12:30 in the morning (i'm obsesively addicted to this game...which isn't good because i'm in high school and i have finals today), so i was rather tired and not thinking in my best capacity. apologies for the mixup
- lobby__boy
- Posts: 29
- Joined: 08 June 2005
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