Math Olympiad Questions

1) Cindy arrived at the bus terminal 4 minutes before the time that the bus was supposed to arrive.
However, the bus arrived 3 minutes late. The journet home took 17 minutes. It was 11.18 p.m. when Cindy reached home. At what time was Cindy at the bus terminal?

Method:11.18 p.m - 17 min= 11.01 min
11.01 p.m. (3 + 4) = 10.54 p.m.

Answer: Cindy was at the bus terminal at 10.54 p.m.

Math Olympiad Question

1) Each point in the plane is colored either red or green. Let ABC be a fixed triangle. Prove that there is a triangle DEF in the plane such that DEF is similar to ABC and the vertices of DEF all have the same color.


Answer: All the vertices are red because I can make them whatever color I want. I can also write at a 30 degree angle to the bottom of this paper if thats what I feel like doing at the moment. Just like 2+2=5 if thats what my math teacher says. Math is pretty subjective anyway. (NOTE- this was written at a 30 degree angle.)