A point \(P\) and a line \(L\) are drawn on a piece of paper. What is the shortest path from \(P\) to \(L\)? You should give a proof that your path is indeed the shortest.
Show that if any \(12\) two-digit numbers are given, you can always choose two of them such that their difference is of the form \(AA\) where \(A\) is some digit from \(0\) to \(9\).
Let \(a,b,c\) be whole numbers. Show that if \(a^2+b^2=c^2\), then at least one of \(a,b,\) or \(c\) must be even.