This morning, in Italy, there was the national exam of mathematics for students of high schools. One of the exercises asked to solve Heron's problem: given a straight line and two points lying on the same side of the line, find the best path (= the path of minimal length) that connects them and touches the straight line.
As a mathematician I (probably) know the answer. However, every solution published by newspapers assumes that the optimal path is made of two segments, i.e. the solution must be found among piecewise affine curves. This is true, but can such a solution be accepted as correct? Actually, the problem seems rather hard, if no regularity assumption on the class of admissible paths is made.