Note that a grid can be OK so far and still have no solution. The following is a simple example:

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

| 1 2 3 | 4 5 6 | 7 8 . |

| . . . | . . . | . . 9 |

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

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

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

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

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

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

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

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

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

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

Question 1. For which values of N (N=0 through N=81) do there exist grids with N cells filled in, which are OK so far and yet have no solutions?

Question 2. For which values of N (N=0 through N=81) do there exist grids with N cells filled in, which are OK so far and have multiple solutions?

I am guessing that, for question 1, the minimum N is 9, and the maximum is 77 or fewer.

For question 2, the minimum N is obviously 0, and the maximum is probably 77.

Bill Smythe