Monthly Archives: December 2019

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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MATHCOUNTS Exercises – 5

Posted on December 26, 2019 by kevin

MATHCOUNTS 2016-2017 – 155 Twelve couples participate in a fitness retreat. One strength-building exercise requires participants to form teams of three so that the two people who make up a couple are not on the same team. How many different … Continue reading →

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MATHCOUNTS Exercises – 4

Posted on December 26, 2019 by kevin

MATHCOUNTS 2016-2017 – 240 Circle $P$ is internally tangent to circle $O$ at $A$, as shown. $\overline{AC}$ and $\overline{BE}$ intersect at $F$, which is also the point of tangency between $\overline{BE}$ and circle $P$. $\overline{AD}$ and $\overline{BE}$ are diameters of … Continue reading →

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