*thirds*of the line segment. And so on. After placing eight points you'd have something that looks like this.

Here are eight points, each in a different eighth of the segment. But in what

**order**were they placed, and in what

**part**of the 8 intervals must they lie in order for each successive group of points to have comprised a legal arrangement? It may seem a trivial task: it's certainly trivial to describe.

Have a go at it, with some graph paper or a calculator, and see how many points you can place.

Let's standardize the problem as follows: Define the line segment as the number interval [0, 1000], and give your answers as integers. For example, for the pretty easy case of four points you might get {200, 800, 450, 700}. And so on. Have fun.