Today I came across the inclusion-exclusion principle for the first time. I believe I have understood it, however when I tried solving some questions on it, I got severely stuck. I couldn't solve any of them. Could you please suggest some questions of escalating difficulty, so that I can get a good grasp on the topic at hand? One of the questions is this one :inclusion-exclusion problem - sitting arrangement , It was in a Greek contest-math book and I also found it on this site.
The other question I couldn't find it on the internet, so I'll translate it:
Find the number of solutions to the equation $x_1+x_2+x_3=100$, if for every $3\ge i\ge1$, xi is a non negative integer with $40\ge x_i$.
I have found the solutions to both of these questions, the reason which I am posting them as well, is to give a better understanding to the reader of the post (as pointed out in the comments), of what level of questions in inclusion-exclusion principle are giving me difficulty