News and Events
Welcome! You can learn more about the MATHCOUNTS Foundation by reading our Annual Report, newsletters and the latest MATHCOUNTS news updates.
For press or media-related inquiries, please contact:
Amanda Naar, Communications Manager
Phone: (703) 299-9006, ext. 105
Email: amanda@mathcounts.org
Sample MATHCOUNTS Problems
MATHCOUNTS has provided this set of sample problems for the media’s use. These are actual problems from the 2005 MATHCOUNTS Competition Series and are representative of the problems Mathletes® will be solving this year. This year’s problems may not be published or used in any manner by the media. We appreciate your efforts to recognize the students participating in MATHCOUNTS and your assistance to ensure that MATHCOUNTS Competition Series problems are not compromised for students taking the competition at a later date.
Sprint Round
- Students cannot use calculators
- Students have 40 minutes to complete 30 problems
- Students must work independently
SAMPLE PROBLEM #1: A rectangular tile measures 3 inches by 4 inches. What is the fewest number of these tiles that are needed to completely cover a rectangular region that is 2 feet by 5 feet? (answer: 120 tiles)
SAMPLE PROBLEM #2: How many combinations of pennies, nickels and/or dimes are there with a total value of 25 cents? (answer: 12 combinations)
Target Round
- Students are permitted to use calculators
- Students have 6 minutes for each of 4 pairs of problems
- Students must work independently
SAMPLE PROBLEM: What is the greatest whole number that must be a factor of the sum of any four consecutive positive odd numbers? (answer: 8)
Team Round
- Students are permitted to use calculators
- Students have 20 minutes to answer 10 problems
- Students work in teams of 4 members
SAMPLE PROBLEM: A four-digit perfect square integer is created by placing two positive two-digit perfect square integers next to each other. What is the four-digit square integer? (answer: 1681)
Countdown Round
- Students cannot use calculators
- Students have no more than 45 seconds to answer each problem
- Each round is a head-to-head challenge between two students
SAMPLE PROBLEM #1: When Bob exercises, he does jumping jacks for 5 minutes and then walks the track at 4 minutes per lap. If he exercised for 73 minutes on Monday, how many laps did he walk? (answer: 17 laps)
SAMPLE PROBLEM #2: What number is 17 less than its negative? Express your answer as a decimal to the nearest tenth. (answer: -8.5)
