

1. 268 numbers are written around a circle. The 17th number is 3, the 83rd is 4 and the 144th is 9, The sum of every 20 consecutive numbers is 72. Find the 210th number.


2. A, B, C can walk at 5km/hr. They have a car that can accomodate any two of them whch travels at 50km/hr. Can they reach a point 62km away in less than 3 hrs?


3. C is the circle center (0,1), radius 1. P is the parabola y = ax^{2}. They meet at (0, 0). For what values of a do they meet at another point or points?


4. For which integers n ≥8 is n^{1/(n7)} an integer?


5. The reals a, b satisfy a^{3}  3a^{2} + 5a  17 = 0, b^{3}  3b^{2} + 5b + 11 = 0. Find a+b.


6. A tetrahedron has five edges length 3 and circumradius 2. What is the length of the sixth edge?

