6. On the number line, points with coordinates $0,1,2,3,5,8,2016$ are marked.

Consider the set of lengths of segments with endpoints at these points. How many elements does it contain?

ANSWER: 14.
Solution: Notice that the points $0,1,2,3,5,8$ form segments of all lengths from 1 to 8. In addition, 2016 forms segments of different lengths with each of these points.