1. Let k>0 and let A1,A2,...,An be a collection of k-subsets of finite set X such that every element of X appears in exactly k sets in the collection. Prove that |X| = n 2. Teacher provided us with the following hints: -- Use a variation of Hall's Theorem. 3. I have no clue how to approach this problem. I don't even understand how proving |X|=n implies anything?