The material is designed to be unfamiliar to almost all high school students; this is simply our way of making sure everyone is on an equal footing. Despite initial appearances, many problems have a simple, short, correct answer. See some questions and answers from past exams below.
Answer (no peeking until after you try!)
A woman and her husband attended a party with four other couples. As is normal at parties, handshaking took place. Of course, no one shook their own hand or the hand of the person they came with. And not everyone shook everyone else's hand. But when the woman asked the other (9) people present how many different people's hands they had shaken they all gave a different answer. Question (this is NOT a trick!): How many different people's hands did the woman's husband shake?
Answer (hey! we said no peeking until after you try!)
A man starts walking up a narrow mountain path at 6:00 a.m. He walks at different speeds, stopping to eat, sometimes going back a few steps to look at a flower, but never leaving the path. He eventually arrives at the top at 10:00 p.m. the same day. He camps out over night and starts down the same path at 6:00 a.m. the next day. After stopping to eat and so forth he arrives at the bottom at 10:00 p.m.
True or False? There is some point on the path that the man occupied at exactly the same time on the two different days. Explain your answer.
Answer (did you peek?)
We bet your brain is getting warmed up now....