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 Mar 24 awarded Popular Question Sep 24 awarded Autobiographer 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