I have found that neat game of 'Sudoku' too late (well, I'm 15-year-old, so it wasn't possible much earlier anyway:) ), about two weeks ago and so I haven't been able to (and I will never be able to) read all topics on this forum. So I don't know whether my question has already been posted and replied. I will, however, be very glad if anybody here knows the answer(s) and posts them, even though it isn't about solving sudoku and the game itself.

For sure there are two types of sudoku: These, which have just one possible result and these, which can have two or more solvings (for example blank grid:) ). Well, there are these which don't have any solving, but I don't count them, because I think it's sort of 'breaking the rule'.

1) Which is the SMALLEST possible amount of numbers in the grid in Sudoku's which have just one solving?

2) Which is the BIGGEST possible amount of numbers in the grid in Sudoku's which have more than one solving?

3) How many possible combinations are there in blank grid? I don't think it's 3^36 (81^9). It should be less, but I cannot count how many.

4) In those breaking-the-rule Sudoku's, which don't break the rule in the way that they would have more same digits in row, column or box, but they are simply unsolveable because of duality of one digit in one place, like is:

- Code: Select all
`+-------+-------+-------+`

| . . 8 | . . . | . . . |

| . . . | . 8 . | . . . |

| . . . | . . . | 2 . . |

+-------+-------+-------+

| . . . | . . . | . . . |

| . . . | . . . | . 8 . |

| . . . | . . . | . . . |

+-------+-------+-------+

| . . . | . . . | . . . |

| . . . | . . . | . . 8 |

| . . . | . . . | . . . |

+-------+-------+-------+

is there any possibility with less than five digits? I really have doubts, but maybe I am just blind and dumb, who knows...