Monthly Archives: January 2022

MATHCOUNTS Exercise – 01/24/2022

Posted on January 24, 2022 by kevin

In unit square $ABCD$, $E$ and $F$ are midpoints of $CD$ and $AD$ respectively. Line $AE$ and $CF$ intersect at $G$. $M$ and $N$ are incenters of $\triangle{AFG}$ and $\triangle{CEG}$. Find $MN$.

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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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