Category Archives: MATHCOUNTS

Suppose today is Wednesday. What day of the week will be 120 days from now? __________ I have five $1¢$ stamps, four $3¢$ stamps, and three $5¢$ stamps. Using one or more of these stamps, how many different amount of … Continue reading →

From a point $P$ inside a unit equilateral $\triangle{ABC}$, draw line $PQ$, $PS$, and $PT$ pendicular to $AB$, $BC$, and $CA$ respectively. The total length of $PQ$, $PS$, and $PT$ is $$ $$ $\textbf{(A) } \dfrac{1}{2} \qquad\textbf{(B) } \dfrac{\sqrt{6}}{4} \qquad\textbf{(C) … Continue reading →

The sum of the first three prime number greater than 50 is $$ $$ $\textbf{(A) }169 \qquad\textbf{(B) }171 \qquad\textbf{(C) }173 \qquad\textbf{(D) }175 \qquad \textbf{(E) } 177$ $$ $$ In a regular hexagon, the ratio between the shortest diagonal and the … Continue reading →

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 →