Sample MATHCOUNTS® Competition Problems
MATHCOUNTS is providing this set of sample problems for the media’s use. These are actual problems
from the 2005 MATHCOUNTS competition season 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 This year’s problems may not be published or used in any manner by the media.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 the MATHCOUNTS program
and your assistance to ensure the MATHCOUNTS competition problems are not compromised
for students taking the competition at a later date.
Sprint Round (no calculator; 30 problems in 40 minutes; students work alone)
Problem: 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
Problem: How many combinations of pennies, nickels and/or dimes are there with a total value of
25 cents?
Answer: 12 combinations
Target Round (calculator permitted; 6 minutes for each of 4 pairs of problems; students work alone)
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 (calculator permitted; 10 problems in 20 minutes; students work with three other team
members)
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 (no calculator; head-to-head challenge between two students; first-to-answer; no
more than 45 seconds permitted)
Problem: 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
Problem: What number is 17 less than its negative? Express your answer as a decimal to the nearest tenth.
Answer: −8.5
Additional prior-year competition problems and information on MATHCOUNTS is available at
www.mathcounts.org.