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MAΘ Problem Set 3 September 18, 2003 1. Given 1 x 1 = 1, + 1 1+1 y Find y − x. 2. On a 5×5 lattice grid, how many different ways can one select three points such that the three points lie on the same line? . . . . . . . . . . . . . . . . . . . . . . . . . 3. The roots of ax2 + bx + c = 0 are 3/2 and 9/4. If a, b, and c are integers (a > 0), find the minimum possible value of a + b + c. 4. Find the greatest possible number of primes there can be between any two multiples of 12 and show that there can not be more. 5. If p and q (p < q) are randomly chosen from the set {1,4,9,16,...361,400}, what is the probability that the fraction pq reduces? 6. Three non-overlapping circles are drawn inside a 3 × 6 rectangle. What is the greatest possible value for the radius of the smallest of these circles?