Hello both of these were in Interm CP as well. The second problem can also be solved with PIE.

What is "Engel" and what is "PSS"?

@above

PSS is the book Problem Solving Strategies written by Arthur Engel. It is quite useful for olympiad level math.

wth is the second problem's problem statement

I am not understanding part of your solution to the coat patches problem. You write
However, if you are intending to count the total area of the patches as 5/2 (i.e. each patch individually),then each common area of up to 1/5 applies to two patches, so you cover a total area of up to 4, i.e. no point on the coat need lie on only one patch (and indeed having each of the 10 area shared by patches be up to 1/5 would more than cover the total coat-area of 1)

It's also easy to see by considering a single patch: if the area it shares with each of the other four is up to 1/5, those four shares could easily cover its total area of 1/5.