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Define the relation M @ N as M @ N = M2 + 2M/N. What is the value of 9 @ 4? Express your answer as a common fraction. Substituting 9 for M and 4 for N in the given relation, we get 9 @ 4 = 92 + 2 × 9...

Darcy has two part-time jobs during her summer vacation. She works part-time as a counselor at a local day camp, and she has another part-time job as a lifeguard at the community swimming pool. Darcy...

Gretchen is going to make a witch’s hat for Halloween. Her pattern consists of a right circular cone without a base attached to a circle with a hole cut out of the middle, as shown below. The hole is...

In honor of Engineers Week, we’re posting a throwback to a sampling of previous years’ Future Engineers Problems of the Day. Join us next week for all new engineering-themed Problems of the Day for...

Last Thursday, March 17 was St. Patrick’s Day when, typically, more people than usual wear some article of green clothing. Patrick has a leprechaun hat that looks like a tall, green top hat. The main...

Mother's Day is a holiday honoring mothers and is celebrated on the second Sunday in May in the United States. In 1914, President Woodrow Wilson declared the first national Mother's Day. Mother's Day...

Kaleb has a bag containing red, black and white LEGO® bricks. If he has 12 more red bricks than white bricks and 15 fewer white bricks than black bricks, what is the positive difference between the...

The Zappone family has a table that can seat eight people comfortably, which is perfect, since there will be eight people sitting down to Thanksgiving dinner. The rectangular table can seat three...

While there were many problems written and solved for MATHCOUNTS in 2021, below is a selection of some of the best of the year! 2020-2021 School Handbook, #113 A fair coin is flipped 5 times. What is...

In June, MATHCOUNTS joined the Data Science 4 Every­one Commitment Campaign to build capacity for K-12 data science ed­ucation. As part of this commitment, MATHCOUNTS will create and share additional...