Category Archives: Combinatorics

MATHCOUNTS Exercises – 15

Posted on January 22, 2020 by kevin

How many distinct unit cubes are there with two faces painted red, two faces painted green and two faces painted blue? Two unit cubes are considered distinct if one unit cube cannot be obtained by rotating the other. SOURCE: 2014 … Continue reading →

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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 – 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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