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?
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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?