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Apr
4
awarded  Scholar
Apr
4
awarded  Benefactor
Apr
4
accepted How many squares does a line between two points pass through?
Mar
28
awarded  Nice Question
Mar
28
awarded  Promoter
Mar
23
comment How many squares does a line between two points pass through?
I think your answer is correct if we don't condition on $D$. But I meant for the answer to depend on $D$. So for example, if $N$=2 and $D$ is small enough, then I would think $E(d(a,B))$ would be close to 1. But if $D$ is large $E(\cdot)$ must be at least 2. Does that make sense?
Mar
23
comment How many squares does a line between two points pass through?
Isn't this double-counting some squares? A square that is passed through in the $x$ direction may be the same square that is passed through in the $y$ direction.
Mar
23
awarded  Editor
Mar
23
revised How many squares does a line between two points pass through?
Clarifying the question
Mar
23
comment How many squares does a line between two points pass through?
Yes, you're right. Sorry for the confusion.
Mar
23
comment How many squares does a line between two points pass through?
I mean partition it into some prespecified number of squares. Now that I think about it, $x=1$ doesn't make any sense -- that wouldn't be a partition. But we could partition it into 4 squares, or 9 squares, etc. So I meant, choose an integer greater than one, square it, and that's how many sub-squares there will be. I could have specified the number of partitions, but I want the answer to depend on $x$.
Mar
22
comment How many squares does a line between two points pass through?
All of the sub-squares are the same size. But we only pick one point $A$ and $B$ in the big square, not in each sub-square. Maybe it's clearer if you think about the points first, and then do the partition. Thanks.
Mar
22
awarded  Student
Mar
22
asked How many squares does a line between two points pass through?
Mar
5
awarded  Supporter