Problem 1:
There are n points in a circle, all joined with line segments. Assume that no three (or more) segments intersect in the same point. How many regions inside the circle are formed in this way?
Problem 2:
Do there exist 10,000 10-digit numbers divisible by 7, all of which can be obtained from one another by a re-ordering of their digits?
Solutions will be put up in a couple of days.
Nalin Pithwa.