Problem Statement Problem Link There are four unequal, positive integers $a$, $b$, $c$, and $N$ such that $N = 5a + 3b + 5c$. It is also true that $N = 4a + 5b + 4c$ and $N$ is between 131 and ...

Problem Statement Square $PQRS$ has side length 4 m. Point $U$ is on $PR$ with $PR = 4UR$. A circle centered at $U$ touches two sides of the square. $PW$ is a tangent to the circle, with $W$ on ...

Problem Statement An ugly light fixture is hanging from point $O$ on the ceiling. Wires $OXM$, $OYN$ and $OZP$ pass through the vertices of a very thin wooden equilateral triangle $XYZ$ of side ...

Problem Statement Three circles have centres A, B and C with radii 2, 4 and 6 respectively. The circles are tangent to each other as shown. $\triangle ABC$ has (A) $\angle A$ obtuse (B) $\angle...

Problem Statement The polynomial $f(x) = x^{4} + ax^{3} + bx^{2} + cx + d$ has real coefficients, and $f(2i) = f(2 + i) = 0.$ What is $a + b + c + d?$ Problem Link Solution $$f(x) = (x - r...

Problem Statement The sets $A = {z : z^{18} = 1}$ and $B = {w : w^{48} = 1}$ are both sets of complex roots of unity. The set $C = {zw : z \in A ~ \mbox{and} ~ w \in B}$ is also a set of complex...

Problem Statement Let $w_1, w_2, \dots, w_n$ be complex numbers. A line $L$ in the complex plane is called a mean line for the points $w_1, w_2, \dots, w_n$ if $L$ contains points (complex numbe...

Problem Statement Find $c$ if $a$, $b$, and $c$ are positive integers which satisfy $c=(a + bi)^3 - 107i$, where $i^2 = -1$. Problem Link Solution $$c = (a^2 + 2abi + b^2i^2)(a + bi) - 107...

Problem Statement The equation $z^6+z^3+1=0$ has complex roots with argument $\theta$ between $90^\circ$ and $180^\circ$ in the complex plane. Determine the degree measure of $\theta$. Problem ...

Problem Statement In triangle $ABC$, if $AB = AC = x + 1$ and $BC = 2x - 2$, where $x > 1$, then the area of the triangle is always equal to Problem Link Solution $$\text{Let the Area...