MathMania 2024

  1. You have a total of 45 quarters and dimes worth $9. How many coins of each type do you have?
  2. What is the area of a triangle with sides of length 10, 17 and 21?
  3. Jane can paddle a canoe 4 mph in still water. If she paddles upstream 15 miles, then downstream 15 miles, it takes her 8 hours for the round trip. What is the speed of the current? You may assume the speed is constant.
  4. The measure of an interior angle of a regular polygon is 176 degrees. How many sides does the polygon have?
  5. What are the last two digits of 20242024?
  6. Find all real solutions to the following: ln(ln x · ln x) = 1.
  7. If four standard six-sided dice are thrown, what is the probability that the face values sum to 6? Please give your answer as a reduced fraction.
  8. How many five-digit numbers in base 10 contain at least one 3?

Here are the answers.