A problem sometimes called Moser's circle problem where a circular region has to be partitioned with chords without any three chords intersecting at one point, is discussed. It is shown that Moser's circle problem makes the students to use a variety of mathematical tools to find correct solutions to problems and gives an opportunity to think about…

Explores the following classical problem: given any 30 points on a circle, join them in pairs by segments in all possible ways. What is the greatest number of nonoverlapping regions into which the interior of the circle can be separated? Presents strategies for solving this problem. (PK)

Investigates the arithmetic curiosity that when any integer is raised to the fifth power, the digits unit of the result is always the same as the digits unit of the original number. Explores results in number bases other than 10 via the computer. (PK)