Author Archives: kevin

MATHCOUNTS 2022 Exercises – 4

Posted on January 14, 2022 by kevin

Given $n>1$, what is the smallest positive integer $n$ whose positive divisors have a product of $n^6$? What is the largest integer value of $n$ for which $8^n$ evenly divides $100!$? A positive number is called $n$-primable if it is … Continue reading →

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Math Olympiad for 3th Grade – 7

Posted on January 7, 2022 by kevin

I have $30$ coins consisting of nickels and quarters. The total value of the coins is $\$4.10$. How many of each kind do I have? If we count by $3s$ starting with $1$, the following sequence is obtained. $1, 4, … Continue reading →

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AIME II 2021 – Problem 8

Posted on December 24, 2021 by kevin

An ant makes a sequence of moves on a cube where a move consists of walking from one vertex to an adjacent vertex along an edge of the cube. Initially the ant is at a vertex of the bottom face … Continue reading →

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MATHCOUNTS 2022 Exercises – 3

Posted on December 17, 2021 by kevin

5 persons to be seated on 5 chairs arranged in a row. Two of these persons cannot sit next to each other. How many seating arrangements are possible? How many four-digit integers for which the thousands digit equals the sum of the other … Continue reading →

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MATHCOUNTS 2022 Exercises – 2

Posted on December 3, 2021 by kevin

An ant is traveling along the side of a regular dodecagon with side length as $1$. What is the expected value of minimum distance the ant travels between two different vertices randomly chosen? Express your answer as a common fraction … Continue reading →

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