I hate to break it to you, but being able to pinpoint exactly what is and is not specified in a given statement is as much mathematics as the calculation is.
Case in point: the old “farmer’s five sons” problem. Basically, the setup speficies a graph which is not four-colorable. However, due to the precise wording it didn’t specify what would correspond to a planar graph. Imagine the look on my third-grade teacher’s face when I brought in two styrofoam tori the next day, one painted to solve the problem as stated and one to solve it if there had been seven sons: the most I could figure out how to do (and, incidentally, the maximum on a torus). My justification: the problem never said that the farmer’s land was not on the surface of a toroidal asteroid.
