We consider two very basic problems – one in unsupervisedand one in supervised learning. In the former, we are given a set ofpoints and have to label half of the points red and half the points blueso as to maximize the red–blue separation, i.e., the length of a shortestbichromatic edge. In the latter, the data (points in the plane) are alreadylabeled red and blue, and we seek a linear classifier (a separator of thetwo given point sets) that can be described using the smallest integers.We give algorithms for both problems. Our solutions are simple; themain contribution of the paper is highlighting the problems and theiralgorithmic solutions, which, to our knowledge, have not been presentedpreviously, despite the problems being fundamental to the field. We alsoconsider related problems.