Found problems: 229
2025 CMIMC Team, 4
A non-self intersecting hexagon $RANDOM$ is formed by assigning the labels $R, A, N, D, O, M$ in some order to the points $$(0,0), (10,0), (10,10), (0,10), (3,4), (6,2).$$ Let $a_{\text{max}}$ be the greatest possible area of $RANDOM$ and $a_{\text{min}}$ the least possible area of $RANDOM.$ Find $a_{\text{max}}-a_{\text{min}}.$
2024 LMT Fall, 1
A positive integer $n$ is called "foursic'' if there exists a placement of $0$ in the digits of $n$ such that the resulting number a multiple of $4.$ For example, $14$ is foursic because $104$ is a multiple of $4.$ Find the number of two-digit foursic numbers.
MOAA Team Rounds, 2019.1
Jeffrey stands on a straight horizontal bridge that measures $20000$ meters across. He wishes to place a pole vertically at the center of the bridge so that the sum of the distances from the top of the pole to the two ends of the bridge is $20001$ meters. To the nearest meter, how long of a pole does Jeffrey need?
2017 CMIMC Team, 9
Circles $\omega_1$ and $\omega_2$ are externally tangent to each other. Circle $\Omega$ is placed such that $\omega_1$ is internally tangent to $\Omega$ at $X$ while $\omega_2$ is internally tangent to $\Omega$ at $Y$. Line $\ell$ is tangent to $\omega_1$ at $P$ and $\omega_2$ at $Q$ and furthermore intersects $\Omega$ at points $A$ and $B$ with $AP<AQ$. Suppose that $AP=2$, $PQ=4$, and $QB=3$. Compute the length of line segment $\overline{XY}$.