Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2
You are only given the three midpoints of the sides of a triangle.
How can you construct the original triangle?
Brian swims at twice the speed that a river is flowing, downstream
from one moored boat to another and back again, taking 12 minutes
altogether. How long would it have taken him in still water?
This problem is taken from the UKMT Mathematical Challenges.