1. Three runners run laps in 5, 7, and 9 minutes. After how many minutes will they all start together again?

2. A team has 2 players named Sam and 3 players named Max. In how many ways can you list the 5 players?

3. You are arranging the word TETRIS. How many unique arrangements are possible?

4. Five people are in a room. Everyone shakes hands with everyone else once. How many handshakes occur?

5. Four doors lead to four prizes. Their signs say:

• Door 1: “This door leads to gold.”
  
  

• Door 2: “This door leads to gold.”
  
  

• Door 3: “Not this door.”
  
  

• Door 4: “Door 1 leads to gold.”

Only one sign is false. Which door has gold?

Set a 30-minute timer and solve the problems. This test is designed to resemble a MOEMS contest with the subjects you have learned so far.