Edit: Problems have been edited to be a bit more generic. The questions remains the same in spirit. 1. You have been given an infinite number of ropes, each of which burns completely in exactly one hour. However, the rates at which different parts of any given rope varies. For example, if you cut a rope in half and burn one of those halves you may find it takes one minute. Or it might take 59 minutes. You can't predict how long it will take for a partial segment of a rope to burn to completion. How can you burn ropes, some perhaps simultaneously, so as to measure exactly one hour and 15 minutes? 2. Devise a set of four test masses with integer masses that total to 40 kg such that the test masses can be used on a balance scale to measure the mass of any object with integral mass between 1 and 40 kg, inclusive. 3. Using this image: Design a path through the lands so that you cross each of the seven bridges once and only once. The path must be uni-directional, i.e. you cannot double-back and move the way you came.