Author Archives: kevin

MATHCOUNTS Exercises – 10

Posted on January 8, 2020 by kevin

Joseph, Pedro, Samuel and David leave their backpacks by the classroom door. When the alarm rings they rush to leave, each randomly grabbing a backpack on the way out. What is the probability that each boy takes a backpack that … Continue reading →

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MATHCOUNTS Exercises – 9

Posted on January 5, 2020 by kevin

A unit cube is painted with 1 face in red, 1 face in green, 1 face in yellow, and 3 faces in blue color. How many unique ways to paint the cube? Click here for the solution. Solution There are … Continue reading →

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MATHCOUNTS Exercises – 8

Posted on December 31, 2019 by kevin

3 cards are randomly selected from a desk of 9 cards uniquely number from 1 to 9. What is the probability that no two of the cards selected have numbers that differ by 1? Click here to show the solutions. … Continue reading →

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MATHCOUNTS Exercises – 7

Posted on December 31, 2019 by kevin

John has two coins in his pocket. One of them is a fair coin, the other is crooked that will land on head 2 out of 3 throws. John randomly selects one of the coins from his pocket, and flips … Continue reading →

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MATHCOUNTS Exercises – 6

Posted on December 27, 2019 by kevin

How many unique ways to make a change of 63 cents by using any combinations of penny, nickel, dime, and/or quarter coins? Click here for the solution. Solution Let’s assume function \(f_1(n)\) is number of ways using pennies to make … Continue reading →

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