89A1 How many primes among the positive integers, written as usual in the base 10, are such that their digits are alternating 1's and 0's, beginning and ending with 1?

89B1 A dart, thrown at random, hits a square target. Assuming that any two parts of the target of equal area are equally likely to be hit, find the probability that the point hit is nearer to the center than to any edge.

88B1 A composite is a product ab with a and b positive integers greater than 1. Show that every composite is expressible as

with x, y, and z positive integers.

82B1 Let M be the midpoint of side BC of a general triangle ABC. Using the smallest possible n, describe a method for cutting triangle AMB into n triangles which can be reassembled to form a triangle congruent to triangle AMC.

89B4 Can a countably infinite set have an uncountable collection of non-empty subsets such that the intersection of any two of them is finite?