| 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 = ax2. 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 n1/(n-7) an integer? |
|
| 5. The reals a, b satisfy a3 - 3a2 + 5a - 17 = 0, b3 - 3b2 + 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? |
|
To avoid possible copyright problems, I have changed the wording, but not the substance, of the problems.
Sweden home
© John Scholes
jscholes@kalva.demon.co.uk
8 Oct 2003
Last corrected/updated 8 Oct 03