Math Club Activities
This will be updated weekly based on what we did in our meetings.
Problem of the Week
- Steve and Josh played a game. Steve wrote on a blackboard all integers from 1 to 18 and challenged Josh to choose 8 different integers from this list. To win the game Josh had to choose 8 integers so that among them the difference between any two of them is either less than 7 or greater than 11. Can Josh win the game? Justify your answer.
- What is the smallest positive number k such that there are real numbers a and b satisfying a + b = k and ab = k?
- Patty is picking peppermints off a tree. They come in two colors, red and white. She picks fewer than 100 total peppermints but at least one of each color. The white flavor is stronger, so she prefers red to white. Thus, she always picks fewer white peppermints than ten times the number of reds. How many different combinations of peppermints can she go home with?
- A class average mark in an exam is 70. The average of students who scored below 60 is 50. The average of students who scored 60 or more is 75. If the total number of students in this class is 20, how many students scored below 60?
- The sum of 5 real numbers is 8 and the sum of their squares is 16. What is the largest possible value for one of the numbers?
- My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son, and I together are 120 years. Can you tell me my age in years?
- David, Steven, and Harry are going to the mall to buy clothes. 1/4 of David's money plus 1/4 of Steven's money is equal to 3 dollars. 1/5 of David's money plus 1/5 of Harry's money is equal to 2 dollars. If the sum of all their money is a multiple of 7 and they individually have whole number amounts of dollars, what are the possible values for David's money? (there may be more than one)
More problems will be posted at the top.