As a teenager I was given this problem which took me a few years to solve. I'd like to know if this hae ever been published. When I presented my solution I was told that it was similar to one of several he had seen.
n dimensional space, develop a formula that evaluates the maximum number of
n dimensional regions when divided by
n-1 dimensional (hyper)planes.
Example: A line is partitioned by points: 1 point, 2 line segments. 10 points, 11 line segments, and so one.