On Monday the Pied Piper caught 1000 rats in a city. On Tuesday he caught 10% fewer rats than on Monday.
On Wednesday he caught 20% more than on Tuesday.
On Thursday he caught 30% fewer than on Wednesday.
On Friday he rested.

How many rats did he catch in total that week?

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.